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Maćkiewicz, Andrzej, and Waldemar Ratajczak. "Principal components analysis (PCA)." Computers & Geosciences 19, no. 3 (March 1993): 303–42. http://dx.doi.org/10.1016/0098-3004(93)90090-r.
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Abegaz, Fentaw, Kridsadakorn Chaichoompu, Emmanuelle Génin, David W. Fardo, Inke R. König, Jestinah M. Mahachie John, and Kristel Van Steen. "Principals about principal components in statistical genetics." Briefings in Bioinformatics 20, no. 6 (September 14, 2018): 2200–2216. http://dx.doi.org/10.1093/bib/bby081.
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Abstract Principal components (PCs) are widely used in statistics and refer to a relatively small number of uncorrelated variables derived from an initial pool of variables, while explaining as much of the total variance as possible. Also in statistical genetics, principal component analysis (PCA) is a popular technique. To achieve optimal results, a thorough understanding about the different implementations of PCA is required and their impact on study results, compared to alternative approaches. In this review, we focus on the possibilities, limitations and role of PCs in ancestry prediction, genome-wide association studies, rare variants analyses, imputation strategies, meta-analysis and epistasis detection. We also describe several variations of classic PCA that deserve increased attention in statistical genetics applications.
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Jensen, Matt, Trent Stellingwerff, Courtney Pollock, James Wakeling, and Marc Klimstra. "Can Principal Component Analysis Be Used to Explore the Relationship of Rowing Kinematics and Force Production in Elite Rowers during a Step Test? A Pilot Study." Machine Learning and Knowledge Extraction 5, no. 1 (February 17, 2023): 237–51. http://dx.doi.org/10.3390/make5010015.
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Investigating the relationship between the movement patterns of multiple limb segments during the rowing stroke on the resulting force production in elite rowers can provide foundational insight into optimal technique. It can also highlight potential mechanisms of injury and performance improvement. The purpose of this study was to conduct a kinematic analysis of the rowing stroke together with force production during a step test in elite national-team heavyweight men to evaluate the fundamental patterns that contribute to expert performance. Twelve elite heavyweight male rowers performed a step test on a row-perfect sliding ergometer [5 × 1 min with 1 min rest at set stroke rates (20, 24, 28, 32, 36)]. Joint angle displacement and velocity of the hip, knee and elbow were measured with electrogoniometers, and force was measured with a tension/compression force transducer in line with the handle. To explore interactions between kinematic patterns and stroke performance variables, joint angular velocities of the hip, knee and elbow were entered into principal component analysis (PCA) and separate ANCOVAs were run for each performance variable (peak force, impulse, split time) with dependent variables, and the kinematic loading scores (Kpc,ls) as covariates with athlete/stroke rate as fixed factors. The results suggested that rowers’ kinematic patterns respond differently across varying stroke rates. The first seven PCs accounted for 79.5% (PC1 [26.4%], PC2 [14.6%], PC3 [11.3%], PC4 [8.4%], PC5 [7.5%], PC6 [6.5%], PC7 [4.8%]) of the variances in the signal. The PCs contributing significantly (p ≤ 0.05) to performance metrics based on PC loading scores from an ANCOVA were (PC1, PC2, PC6) for split time, (PC3, PC4, PC5, PC6) for impulse, and (PC1, PC6, PC7) for peak force. The significant PCs for each performance measure were used to reconstruct the kinematic patterns for split time, impulse and peak force separately. Overall, PCA was able to differentiate between rowers and stroke rates, and revealed features of the rowing-stroke technique correlated with measures of performance that may highlight meaningful technique-optimization strategies. PCA could be used to provide insight into differences in kinematic strategies that could result in suboptimal performance, potential asymmetries or to determine how well a desired technique change has been accomplished by group and/or individual athletes.
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López-Rubio, Ezequiel, Juan Miguel Ortiz-de-Lazcano-Lobato, José Muñoz-Pérez, and José Antonio Gómez-Ruiz. "Principal Components Analysis Competitive Learning." Neural Computation 16, no. 11 (November 1, 2004): 2459–81. http://dx.doi.org/10.1162/0899766041941880.
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We present a new neural model that extends the classical competitive learning by performing a principal components analysis (PCA) at each neuron. This model represents an improvement with respect to known local PCA methods, because it is not needed to present the entire data set to the network on each computing step. This allows a fast execution while retaining the dimensionality-reduction properties of the PCA. Furthermore, every neuron is able to modify its behavior to adapt to the local dimensionality of the input distribution. Hence, our model has a dimensionality estimation capability. The experimental results we present show the dimensionality-reduction capabilities of the model with multisensor images.
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Bijarania, Subhash, Anil Pandey, Mainak Barman, Monika Shahani, and Gharsi Ram. "Assesment of divergence among soybean [Glycine max (L.) Merrill] genotypes based on phenological and physiological traits." Environment Conservation Journal 23, no. 1&2 (February 11, 2022): 72–82. http://dx.doi.org/10.36953/ecj.021808-2117.
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A study was conducted to understand genetic divergence in Randomized complete block design accommodating 30 soybean [Glycine max (L.) Merrill] genotypes randomly in three replications. These genotypes were evaluated for twenty-seven traits: five phenological, nine agro-morphological, eight physiological traits (from field-trial) and five physiological traits (from laboratory experiment) recorded and subjected to PCA (Principal Component Analysis) and cluster analysis. Among all the studied cultivars, significant diversity, as well as analysis of dispersion, was recorded for different agro-morphological characters. D2-statistic (Tocher method) framed (generalized distance-based) nine clusters: largest with eight and five were oligo-genotypic. Harvest index>seed yield per plant>germination relative index>seedling dry weight contributed maximum towards total divergence. From the most divergent clusters, 21 crosses involving cluster v genotypes (PS-1347, RKS-18, PS-1092, NRC-142, VLS-94, NRC-136, and Shalimar Soybean-1) with monogenotypic cluster VII (AMS-2014), VIII (RSC-11-15) and III (RSC-10-71) suggested for future hybridization. Out of eighteen, only eight principal components revealed more than 1.00 eigen value and exhibited about 85.03% variability among the traits studied. The highest variability (25.41%) by PC1 followed by PC2 (15.60%), PC3 (12.35%), PC4 (10.13%), PC5 (7.20%), PC6 (5.43%), PC7 (4.80%) and PC8 (4.11%) for characters under study.
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Sonaniya, Rahul, Rajani Bisen, and Pallavi Sonaniya. "Assessment of Exotic Sesame (Sesamum indicum) Accessions through Principal Component Analysis." International Journal of Environment and Climate Change 13, no. 11 (October 7, 2023): 282–90. http://dx.doi.org/10.9734/ijecc/2023/v13i113170.
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The present research conducted over 96 exotic sesame accessions with five checks, to identify the minimum number of components, which could explain maximum variability out of the total variability using Principal Component Analysis (PCA); The investigation was performed under Project Co-ordinating Unit (Sesame and Niger) Research Farm, JNKVV, Jabalpur (M.P.) during kharif 2018 using Augmented block design. Among the studied traits, Component 1 had the contribution from the traits viz., number of primary branches per plant, number of capsules per plant, number of seeds per capsule, oil content and seed yield/plant, which accounted 30.71% to the total variability. Days to flower initiation and days to 50% flowering had contributed 17.11% to the total variability in component 2. The remaining variabilities of 11.26%, 9.94%, 7.48% and 6.73% were consolidated in PC3, PC4, PC5 and PC6 respectievely by various traits like number of secondary branches/plant, capsule length, days to maturity, thousand seed weight and plant height . The cumulative variance of 83.23% of total variation among 12 characters was explained by the first six axes. On the basis of PC scores PC1, PC3 and PC5 accounting mainly to yield and quality traits containing accesions viz., EC-334998, ES-38, EC-346426, EC-334958, EC-340538, RT-351 and GT-10 might be further utilized in breeding programme.
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Kondi, Ravi, Sonali Kar, and Soumya Surakanti. "Agro-morphological and biochemical characterization and principal component analysis for yield and quality characters in fine-scented rice genotypes." Genetika 54, no. 3 (2022): 1005–21. http://dx.doi.org/10.2298/gensr2203005k.
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Forty-one fine-scented rice genotypes were evaluated for 18 agro-morphological and quality characters for characterization, and 21 quantitative characters were evaluated for principal component analysis in R-studio software. Characterization of agro-morphological traits viz., plant height, days to 50% flowering, panicle length, number of effective tillers per plant, test weight, grain length, grain breadth, grain L: B ratio, kernel length, kernel breadth, kernel dimensions, awns, colour of awns, distribution of awns, and quality traits viz., alkali spreading value, gel consistency, grain aroma, and amylose content showed huge diversity among the genotypes. PCA revealed that PC1 showed the highest amount of variance (32.0%) followed by PC2 (15.7%), PC3 (9.0%), PC4 (8.1%), PC5 (7.8%), PC6 (5.4%) for quantitative characters. Out of 21 principal components, only 6 showed an eigenvalue greater than 1 and contributes about 78.1% total variance Genotypes in PC1 showed higher values for grain L: B ratio and kernel L: B ratio. Similarly, PC2 showed higher variable values for characters like test weight, kernel length, grain length, grain breadth, alkali spreading value, grain yield per plot and amylose content. PC3 for harvest index, panicle length, gel consistency, no. of effective tillers per plant and head rice recovery. PC4 for characters like plant height, kernel breadth and days to 50% flowering. PC5 for characters like kernel elongation ratio, and filled grains per panicle. PC6 for characters like no. of tillers in a square meter and no. of panicles in a square meter. This pre-breeding characterization study may be useful in finding potential genotypes which are having both yield and quality characters which may be useful in breeding for high-yielding varieties with good-quality characters.
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Tiwari, Priya, and Stuti Sharma. "Principal component analyses in mungbean genotypes under summer season." INTERNATIONAL JOURNAL OF AGRICULTURAL SCIENCES 17, no. 2 (June 15, 2021): 287–92. http://dx.doi.org/10.15740/has/ijas/17.2/287-292.
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Yield is a complex trait subjective to several components and environmental factors. Therefore, it becomes necessary to apply such technique which can identify and prioritize the key traits to lessen the number of traits for valuable selection and genetic gain. Principal component analysis is primarily a renowned data reduction technique which identifies the least number of components and explain maximum variability, it also rank genotypes on the basis of PC scores. PCA was calculated using Ingebriston and Lyon (1985) method. In present study, PCA performed for phenological and yield component traits presented that out of thirteen, only five principal components (PCs) exhibited more than 1.00 eigen value, and showed about 80.28 per cent of total variability among the traits. Scree plot explained the percentage of variance associated with each principal component obtained by illustrating a graph between eigen values and principal component numbers. PC1 showed 26.12 per cent variability with eigen value 3.40. Graph depicted that the maximum variation was observed in PC1 in contrast to other four PCs. The PC1 was further associated with the phenological and yield attributing traits viz., number of nodes per plant, number of pod cluster per plant, number of pod per plant. PC2 exhibited positive effect for harvest index. The PC3 was more related to yield related traits i.e., number of seeds per pod, number of seeds per plant and biological yield per plant, whereas PC4 was more loaded with phenological traits. PC5 was further related to yield and yield contributing traits i.e. number of primary branches per plant, seed yield per plant and 100 seed weight. A high value of PC score of a particular genotype in a particular PC denotes high value for those variables falling under that specific principal component. Pusa Vishal found in PC 2, in PC 3, PC 4 and PC 5, can be considered as an ideal breeding material for selection and for further deployment in defined breeding programme.
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Uikey, Shivani, Stuti Sharma, M. K. Shrivastava, and Pawan K. Amrate. "Study of principal component analyses for pod traits in soybean." INTERNATIONAL JOURNAL OF AGRICULTURAL SCIENCES 17, no. 2 (June 15, 2021): 341–49. http://dx.doi.org/10.15740/has/ijas/17.2/341-349.
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Yield being a complex entity influenced by several components and environments. PCA is a well-known method of dimension reduction that can be used to reduce a large set of variables to a small set that still contains most of the information in the large set (Massay, 1965 and Jolliffie, 1986). In present study, PCA preformed for pod and yield traits revealed that out of fourteen, only five principal components (PCs) exhibited more than 1.0 eigen value and showed about 70.44% total variability among the traits. PC1 showed 23.83% variability with eigen value 3.33 indicating the maximum variation in comparison to other four PCs. The PC1 was more related to traits viz., days to 50% flowering, total number of pods per plant, number of seeds per plant, biological yield per plant and seed yield per plant. Thus, PC1 allowed for simultaneous selection of yield related traits and it can be regarded as yield factor. PC2 exhibited positive effect for days to maturity, number of primary branches per plant and number of nodes per plant, The PC3 was more related to number of two seeded pods per plant, 100 seed weight and harvest index traits, whereas PC4 was more loaded with three seeded pods per plant. PC5 was more related to plant height and number of one seeded pods per plant. A high value of PC score of a particular advanced line in a particular PC denotes high value for those variables. Genotypes namely KS 103, JS 20-15, PS 1423, Cat 1957, Cat 1958, JS 20-06 and JS 20-66 can be considered an ideotype breeding material for selection and for further utilization in precise breeding programme.
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Gewers, Felipe L., Gustavo R. Ferreira, Henrique F. De Arruda, Filipi N. Silva, Cesar H. Comin, Diego R. Amancio, and Luciano Da F. Costa. "Principal Component Analysis." ACM Computing Surveys 54, no. 4 (May 2021): 1–34. http://dx.doi.org/10.1145/3447755.
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Principal component analysis (PCA) is often applied for analyzing data in the most diverse areas. This work reports, in an accessible and integrated manner, several theoretical and practical aspects of PCA. The basic principles underlying PCA, data standardization, possible visualizations of the PCA results, and outlier detection are subsequently addressed. Next, the potential of using PCA for dimensionality reduction is illustrated on several real-world datasets. Finally, we summarize PCA-related approaches and other dimensionality reduction techniques. All in all, the objective of this work is to assist researchers from the most diverse areas in using and interpreting PCA.
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Lee, Myeounggon, Changhong Youm, Byungjoo Noh, and Hwayoung Park. "Gait Characteristics Based on Shoe-Type Inertial Measurement Units in Healthy Young Adults during Treadmill Walking." Sensors 20, no. 7 (April 8, 2020): 2095. http://dx.doi.org/10.3390/s20072095.
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This study investigated the gait characteristics of healthy young adults using shoe-type inertial measurement units (IMU) during treadmill walking. A total of 1478 participants were tested. Principal component analyses (PCA) were conducted to determine which principal components (PCs) best defined the characteristics of healthy young adults. A non-hierarchical cluster analysis was conducted to evaluate the essential gait ability, according to the results of the PC1 score. One-way repeated analysis of variance with the Bonferroni correction was used to compare gait performances in the cluster groups. PCA outcomes indicated 76.9% variance for PC1–PC6, where PC1 (gait variability (GV): 18.5%), PC2 (pace: 17.8%), PC3 (rhythm and phase: 13.9%), and PC4 (bilateral coordination: 11.2%) were the gait-related factors. All of the pace, rhythm, GV, and variables for bilateral coordination classified the gait ability in the cluster groups. We suggest that the treadmill walking task may be reliable to evaluate the gait performances, which may provide insight into understanding the decline of gait ability. The presented results are considered meaningful for understanding the gait patterns of healthy adults and may prove useful as reference outcomes for future gait analyses.
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Williams, Greetty, and Y. Anbuselvam. "Assessment of Genetic Divergence through Principal Component Analysis and Clustering in Tomato Germplasm Accessions." Environment and Ecology 41, no. 4D (December 2023): 3060–65. http://dx.doi.org/10.60151/envec/ylss4838.
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The base material of this study comprises of 104 tomato accessions including local landraces, varieties and germplasm collections. The collected tomato accessions were evaluated using 13 quantitative traits by Principal Component Analysis (PCA) and Hierarchial clustering. PCA was done to quantify diversity among the germplasm accessions and also the contribution of individual traits towards diversity. In our study, only the first four (PC1, PC2, PC3 and PC4) of the thirteen principal components yielded eigen value more than one indicating the greater influence of identified traits under study. The first six PCs accounts for 84% of variability whereas, PC1 exhibited 41% of total variability. Cluster analysis aids to classify the genotypes based on the grouping pattern of the accessions under evaluation. According to the dendrogram obtained, cluster analysis grouped 104 tomato accessions into two significant clusters. The first cluster consists of 16 genotypes whereas, the second cluster consists of 88 genotypes. Among the genotypes used in this study EC617055, EC617061, EC638302, Periakulam local and EC631390 were found to be best performing in terms of yield and quality. These accessions can be used as a base material in future breeding programs.
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Okoda, Yuki, Yoko Oya, Shotaro Abe, Ayano Komaki, Yoshimasa Watanabe, and Satoshi Yamamoto. "Molecular Distributions of the Disk/Envelope System of L483: Principal Component Analysis for the Image Cube Data." Astrophysical Journal 923, no. 2 (December 1, 2021): 168. http://dx.doi.org/10.3847/1538-4357/ac2c6c.
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Abstract Unbiased understanding of molecular distributions in a disk/envelope system of a low-mass protostellar source is crucial for investigating physical and chemical evolution processes. We have observed 23 molecular lines toward the Class 0 protostellar source L483 with ALMA and have performed principal component analysis (PCA) for their cube data (PCA-3D) to characterize their distributions and velocity structures in the vicinity of the protostar. The sum of the contributions of the first three components is 63.1%. Most oxygen-bearing complex organic molecule lines have a large correlation with the first principal component (PC1), representing the overall structure of the disk/envelope system around the protostar. Contrary, the C18O and SiO emissions show small and negative correlations with PC1. The NH2CHO lines stand out conspicuously at the second principal component (PC2), revealing more compact distribution. The HNCO lines and the high-excitation line of CH3OH have a similar trend for PC2 to NH2CHO. On the other hand, C18O is well correlated with the third principal component (PC3). Thus, PCA-3D enables us to elucidate the similarities and the differences of the distributions and the velocity structures among molecular lines simultaneously, so that the chemical differentiation between the oxygen-bearing complex organic molecules and the nitrogen-bearing ones is revealed in this source. We have also conducted PCA for the moment 0 maps (PCA-2D) and that for the spectral line profiles (PCA-1D). While they can extract part of characteristics of the molecular line data, PCA-3D is essential for comprehensive understandings. Characteristic features of the molecular line distributions are discussed on NH2CHO.
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Aini Abdul Wahab, Nurul, and Shamshuritawati Sharif. "Rice Odours’ Readings Investigation Using Principal Component Analysis." International Journal of Engineering & Technology 7, no. 2.29 (May 22, 2018): 488. http://dx.doi.org/10.14419/ijet.v7i2.29.13803.
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The use of electronic nose (e-nose) devices plus principal component analysis can help the process of categorizing the 16 different rice into its type. Generally, the physical feature of an e-nose own more than one hole to capture the odour of rice. For example, the portable e-nose so-called Insniff does have 10 holes (or variables). In this situations, we will have a dataset that consist high-dimension dataset where lead to the presence of interdependencies between all variables under study. Therefore, this study is presented to investigate the odour of rice for identifying the most important variables contributing to the rice odour readings. The principal component analysis (PCA) is implemented to determine the component that best represent the all 10 variables in order to eliminate the interdependency problem, and (2) to identify which variable is considered as important and influential to the newly-formed principle component (PC). The results from PCA suggested that the first two principle components is chosen. It is based on three assessments which are Kaiser’s criterion larger than 1, cumulative proportion of total variance, and scree plot. These two principle components explained 89% of total variance. Results showed that sensor 1 (0.931) and sensor 2 (0.966) are the two important variables that highly contribute to PC1. On the other hand, for PC2, the highest contribution is from sensor 8 (0.828). This study demonstrate that PCA is effective for investigating rice odour readings.
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Dinanti, Aldila, and Joko Purwadi. "Analisis Performa Algoritma K-Nearest Neighbor dan Reduksi Dimensi Menggunakan Principal Component Analysis." Jambura Journal of Mathematics 5, no. 1 (February 1, 2023): 155–65. http://dx.doi.org/10.34312/jjom.v5i1.17098.
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This paper discusses the performance of the K-Nearest Neighbor Algorithm with dimension reduction using Principal Component Analysis (PCA) in the case of diabetes disease classification. A large number of variables and data on the diabetes dataset requires a relatively long computation time, so dimensional reduction is needed to speed up the computational process. The dimension reduction method used in this study is PCA. After dimension reduction is done, it is continued with classification using the K-Nearest Neighbor Algorithm. The results on diabetes case studies show that dimension reduction using PCA produces 3 main components of the 8 variables in the original data, namely PC1, PC2, and PC3. Then classification result using K-Nearest Neighbor shows that by choosing 3 closest neighbor parameters (K), for K = 3, K = 5, and K = 7. The result for K = 3 has an accuracy of 67,53%, for K = 5 had an accuracy is 72,72%, and for K=7 had an accuracy of 77,92%. Thus, it was concluded that the best accuracy performance for the classification of diabetes was achieved at K=7 with an accuracy of 77.92%.
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Adamu, Nuraddeen, Samaila Abdullahi, and Sani Musa. "Online Stochastic Principal Component Analysis." Caliphate Journal of Science and Technology 4, no. 1 (February 10, 2022): 101–8. http://dx.doi.org/10.4314/cajost.v4i1.13.
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This paper studied Principal Component Analysis (PCA) in an online. The problem is posed as a subspace optimization problem and solved using gradient based algorithms. One such algorithm is the Variance-Reduced PCA (VR-PCA). The VR-PCA was designed as an improvement to the classical online PCA algorithm known as the Oja’s method where it only handled one sample at a time. The paper developed Block VR-PCA as an improved version of VR-PCA. Unlike prominent VR-PCA, the Block VR-PCA was designed to handle more than one dimension in subspace optimization at a time and it showed good performance. The Block VR-PCA and Block Oja method were compared experimentally in MATLAB using synthetic and real data sets, their convergence results showed Block VR-PCA method appeared to achieve a minimum steady state error than Block Oja method.
Keywords: Online Stochastic; Principal Component Analysis; Block Variance-Reduced; Block Oja
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Kambhatla, Nandakishore, and Todd K. Leen. "Dimension Reduction by Local Principal Component Analysis." Neural Computation 9, no. 7 (October 1, 1997): 1493–516. http://dx.doi.org/10.1162/neco.1997.9.7.1493.
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Reducing or eliminating statistical redundancy between the components of high-dimensional vector data enables a lower-dimensional representation without significant loss of information. Recognizing the limitations of principal component analysis (PCA), researchers in the statistics and neural network communities have developed nonlinear extensions of PCA. This article develops a local linear approach to dimension reduction that provides accurate representations and is fast to compute. We exercise the algorithms on speech and image data, and compare performance with PCA and with neural network implementations of nonlinear PCA. We find that both nonlinear techniques can provide more accurate representations than PCA and show that the local linear techniques outperform neural network implementations.
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Nadaf, Saleem K., Safa'a M. Al-Farsi, Saleh A. Al-Hinai, Aliya S. Al-Hinai, Abdul Aziz S. Al-Harthy, Saif A. Al-Khamisi, and Ahmed N. Al-Bakri. "Genetic diversity of 33 forage cactus pear accessions based on principal component analysis." Journal of the Professional Association for Cactus Development 18 (December 28, 2016): 78–86. http://dx.doi.org/10.56890/jpacd.v18i.56.
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The present research was undertaken to assess genetic diversity of 33 forage cactus pearaccessions introduced from different countries for their suitability in the existing fodderproduction system in Arabian Peninsula countries including Oman. These accessions wereevaluated in randomized complete block design with four replications for two consecutive years2014 and 2015 at Agriculture Research Center, Rumais in Oman. The characters cladodegreen and dry matter yields and their related traits plant height (cm), number of cladodes andcladode weight were considered for study. The results of principal component analysis (PCA)indicated that of the total four components, the first two components PC1 and PC2 accountedfor 97.65 and 2.27%, respectively which in combination contributed to 99.92% of the totalvariation among characters studied in fodder cactus pear accessions whereas remaining twocomponents PC3 (0.06%) and PC4 (0.02 %) contributed a meagre 0.08% to the total variation.The first principal component had high positive loading for only green matter yield with thehighest value of 0.993 whereas second principal component had highest loading for plantheight (0.998) in contributing to the diversity. However, PC3 and PC4 were accounted by higherpositive loading in respect of dry matter yield (0.853) and number of cladodes (0.855). Theresults of correlation analysis indicated that of 10 possible correlations from five charactersstudied, seven correlations which were found significant (p<0.05) were also positive in natureof association. The scatter of accessions based on PC1 and PC2 scores resulted in groupingthem into six clusters consisting of accession ranging from 1 to 9. These results could beapplied in either selecting higher green matter yielding accessions from high yielding groups torecommend for either general cultivation or planning and execution of future breeding programfor higher forage productivity in cactus by selecting accessions from different clusters asparents for hybridization.
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Kumar, Preeti, Nilanjaya, and Pankaj Shah. "Study of genetic diversity in rice (Oryza sativa L.) genotypes under direct seeded condition by using principal component analysis." Ecology, Environment and Conservation 29 (2023): 211–19. http://dx.doi.org/10.53550/eec.2023.v29i03s.040.
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The present investigation was carried out to assess the genetic diversity by using principal component analysis for yield and yield contributing traits in thirty-two genotypes of rice under direct seeded condition (DSR). The experiment was conducted at Dr. Rajendra Prasad Central Agricultural University, Pusa, Bihar in randomized block design with three replications. The results revealed that first four component axes had eigen values 1.0, representing a cumulative variability of 76.86 %. Principal component analysis (PCA) indicate that four components (PC1 to PC4) accounted for about 76.86% of the total variation present among all the traits. Out of total principal components PC1, PC2, PC3 and PC4 with values 33.781%, 19.02%, 13.859% and 10.206% respectively, contributed more to the total variation. The first principal component had high positive loading for 15 traits out of 17. Similarly, second and third principal component had 7 traits each, fourth component with 6 traits had high positive loadings which contributed more to the diversity. Genotypes in cluster V showed higher mean performance for most of the yield attributing traits. Therefore, selection of parents for different traits would be effective from this cluster. Thus, result of the present study could be exploited in planning and execution of future breeding programme in rice under direct seeded condition.
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Toleva, Borislava. "ANOVA bootstrapped principal components analysis for logistic regression." Croatian Review of Economic, Business and Social Statistics 8, no. 1 (June 1, 2022): 18–31. http://dx.doi.org/10.2478/crebss-2022-0002.
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Abstract Principal components analysis (PCA) is often used as a dimensionality reduction technique. A small number of principal components is selected to be used in a classification or a regression model to boost accuracy. A central issue in the PCA is how to select the number of principal components. Existing algorithms often result in contradictions and the researcher needs to manually select the final number of principal components to be used. In this research the author proposes a novel algorithm that automatically selects the number of principal components. This is achieved based on a combination of ANOVA ranking of principal components, the bootstrap and classification models. Unlike the classical approach, the algorithm we propose improves the accuracy of the logistic regression and selects the best combination of principal components that may not necessarily be ordered. The ANOVA bootstrapped PCA classification we propose is novel as it automatically selects the number of principal components that would maximise the accuracy of the classification model.
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Sekandari, Milad, and Amin Beiranvand Pour. "Fuzzy Logic Modeling for Integrating the Thematic Layers Derived from Remote Sensing Imagery: A Mineral Exploration Technique." Environmental Sciences Proceedings 6, no. 1 (February 25, 2021): 8. http://dx.doi.org/10.3390/iecms2021-09349.
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In this study, fuzzy logic modeling was implemented to fuse the thematic layers derived from principal components analysis (PCA) in order to generate mineral prospectivity maps. Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) and WorldView-3 (WV-3) satellite remote sensing data were used. A spatial subset zone of the Central Iranian Terrane (CIT), Iran was selected in this study. The PCA technique was implemented for the processing of the datasets and for the production of alteration thematic layers. PCA4, PCA5, and PCA8 were selected as the most rational alteration thematic layers of ASTER for the generation of a prospectivity map. The fuzzy gamma operator was used to fuse the selected alteration thematic layers. The PCA3, PCA4, and PCA6 thematic layers (most rational alteration thematic layers) of WV-3 were fused using the fuzzy AND operator. Field reconnaissance, X-ray diffraction (XRD) analysis, and Analytical Spectral Devices (ASD) spectroscopy were carried out to verify the image processing results. Subsequently, mineral prospectivity maps were produced showing high-potential zones of Pb-Zn mineralization in the study area.
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Sando, Keishi, and Hideitsu Hino. "Modal Principal Component Analysis." Neural Computation 32, no. 10 (October 2020): 1901–35. http://dx.doi.org/10.1162/neco_a_01308.
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Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and various robust PCA methods have been proposed. It has been shown that the robustness of many statistical methods can be improved using mode estimation instead of mean estimation, because mode estimation is not significantly affected by the presence of outliers. Thus, this study proposes a modal principal component analysis (MPCA), which is a robust PCA method based on mode estimation. The proposed method finds the minor component by estimating the mode of the projected data points. As a theoretical contribution, probabilistic convergence property, influence function, finite-sample breakdown point, and its lower bound for the proposed MPCA are derived. The experimental results show that the proposed method has advantages over conventional methods.
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Li, Zhaokai, Zihua Chai, Yuhang Guo, Wentao Ji, Mengqi Wang, Fazhan Shi, Ya Wang, Seth Lloyd, and Jiangfeng Du. "Resonant quantum principal component analysis." Science Advances 7, no. 34 (August 2021): eabg2589. http://dx.doi.org/10.1126/sciadv.abg2589.
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Principal component analysis (PCA) has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the principal components of it, i.e., the eigenvectors of the density matrix with the largest eigenvalues. However, because of the substantial resource requirement, its experimental implementation remains challenging. Here, we develop a resonant analysis algorithm with minimal resource for ancillary qubits, in which only one frequency-scanning probe qubit is required to extract the principal components. In the experiment, we demonstrate the distillation of the first principal component of a 4 × 4 density matrix, with an efficiency of 86.0% and a fidelity of 0.90. This work shows the speedup ability of quantum algorithm in dimension reduction of data and thus could be used as part of quantum artificial intelligence algorithms in the future.
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Praus, Petr. "SVD-based principal component analysis of geochemical data." Open Chemistry 3, no. 4 (December 1, 2005): 731–41. http://dx.doi.org/10.2478/bf02475200.
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AbstractPrincipal Component Analysis (PCA) was used for the mapping of geochemical data. A testing data matrix was prepared from the chemical and physical analyses of the coals altered by thermal and oxidation effects. PCA based on Singular Value Decomposition (SVD) of the standardized (centered and scaled by the standard deviation) data matrix revealed three principal components explaining 85.2% of the variance. Combining the scatter and components weights plots with knowledge of the composition of tested samples, the coal samples were divided into seven groups depending on the degree of their oxidation and thermal alteration.The PCA findings were verified by other multivariate methods. The relationships among geochemical variables were successfully confirmed by Factor Analysis (FA). The data structure was also described by the Average Group dendrogram using Euclidean distance. The found sample clusters were not defined so clearly as in the case of PCA. It can be explained by the PCA filtration of the data noise.
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Machidon, Alina L., Fabio Del Frate, Matteo Picchiani, Octavian M. Machidon, and Petre L. Ogrutan. "Geometrical Approximated Principal Component Analysis for Hyperspectral Image Analysis." Remote Sensing 12, no. 11 (May 26, 2020): 1698. http://dx.doi.org/10.3390/rs12111698.
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Principal Component Analysis (PCA) is a method based on statistics and linear algebra techniques, used in hyperspectral satellite imagery for data dimensionality reduction required in order to speed up and increase the performance of subsequent hyperspectral image processing algorithms. This paper introduces the PCA approximation method based on a geometric construction approach (gaPCA) method, an alternative algorithm for computing the principal components based on a geometrical constructed approximation of the standard PCA and presents its application to remote sensing hyperspectral images. gaPCA has the potential of yielding better land classification results by preserving a higher degree of information related to the smaller objects of the scene (or to the rare spectral objects) than the standard PCA, being focused not on maximizing the variance of the data, but the range. The paper validates gaPCA on four distinct datasets and performs comparative evaluations and metrics with the standard PCA method. A comparative land classification benchmark of gaPCA and the standard PCA using statistical-based tools is also described. The results show gaPCA is an effective dimensionality-reduction tool, with performance similar to, and in several cases, even higher than standard PCA on specific image classification tasks. gaPCA was shown to be more suitable for hyperspectral images with small structures or objects that need to be detected or where preponderantly spectral classes or spectrally similar classes are present.
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LÓPEZ-RUBIO, EZEQUIEL, and JUAN MIGUEL ORTIZ-DE-LAZCANO-LOBATO. "DYNAMIC COMPETITIVE PROBABILISTIC PRINCIPAL COMPONENTS ANALYSIS." International Journal of Neural Systems 19, no. 02 (April 2009): 91–103. http://dx.doi.org/10.1142/s0129065709001860.
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We present a new neural model which extends the classical competitive learning (CL) by performing a Probabilistic Principal Components Analysis (PPCA) at each neuron. The model also has the ability to learn the number of basis vectors required to represent the principal directions of each cluster, so it overcomes a drawback of most local PCA models, where the dimensionality of a cluster must be fixed a priori. Experimental results are presented to show the performance of the network with multispectral image data.
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Sorzano, Carlos Oscar S., and Jose Maria Carazo. "Principal component analysis is limited to low-resolution analysis in cryoEM." Acta Crystallographica Section D Structural Biology 77, no. 6 (May 19, 2021): 835–39. http://dx.doi.org/10.1107/s2059798321002291.
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Principal component analysis (PCA) has been widely proposed to analyze flexibility and heterogeneity in cryo-electron microscopy (cryoEM). In this paper, it is argued that (i) PCA is an excellent technique to describe continuous flexibility at low resolution (but not so much at high resolution) and (ii) PCA components should be analyzed in a concerted manner (and not independently).
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Arozi, Moh, Wahyu Caesarendra, Mochammad Ariyanto, M. Munadi, Joga D. Setiawan, and Adam Glowacz. "Pattern Recognition of Single-Channel sEMG Signal Using PCA and ANN Method to Classify Nine Hand Movements." Symmetry 12, no. 4 (April 3, 2020): 541. http://dx.doi.org/10.3390/sym12040541.
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A number of researchers prefer using multi-channel surface electromyography (sEMG) pattern recognition in hand gesture recognition to increase classification accuracy. Using this method can lead to computational complexity. Hand gesture classification by employing single channel sEMG signal acquisition is quite challenging, especially for low-rate sampling frequency. In this paper, a study on the pattern recognition method for sEMG signals of nine finger movements is presented. Common surface single channel electromyography (sEMG) was used to measure five different subjects with no neurological or muscular disorder by having nine hand movements. This research had several sequential processes (i.e., feature extraction, feature reduction, and feature classification). Sixteen time-domain features were employed for feature extraction. The features were then reduced using principal component analysis (PCA) into two and three-dimensional feature space. The artificial neural network (ANN) classifier was tested on two different feature sets: (1) using all principal components obtained from PCA (PC1–PC3) and (2) using selected principal components (PC2 and PC3). The third best principal components were then used for classification using ANN. The average accuracy using all subject signals was 86.7% to discriminate the nine finger movements.
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GUPTA, DEEPAK. "Principal component analysis for yield and its attributing characters of pearl millet (Pennisetum glaucum [L.] R.Br.)." Annals of Plant and Soil Research 24, no. 3 (August 1, 2022): 408–14. http://dx.doi.org/10.47815/apsr.2021.10184.
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An experiment was conducted at Agricultural Research Station, Navgaon (Alwar) during kharif season of 2019 to study the genetic divergence among 31 genotypes of pearl millet based on quantitative data of grain yield and its nine component traits using hierarchical cluster and principal component analysis (PCA). Principal Component Analysis (PCA) indicated that three components with eigen values more than one accounted for about 73.35% of the total variation among nine quantitative characters responsible for seed yield in pearl millet genotypes. The principal components PC1, PC2 and PC3 contributed about 37.44%, 22.63% and 13.28%, respectively to the total variation. The first principal component exhibited high positive loading for grain yield, stover yield, plant height, spike length, spike thickness and 1000-grain weight which contributed more to the diversity. The second principal component showed high loading for days to 50% flowering, days to maturity and 1000-grain weight. Cluster analysis grouped the genotypes into five clusters indicated that grain yield, stover yield, 1000-grain weight and days to maturity contributed maximum towards genetic divergence. The grouping patterns of genotypes in principal component analysis and cluster analysis were almost in agreement with each other with minor deviations. The maximum inter cluster distance between genotypes of cluster V and III with cluster II, indicate that genotypes included in these clusters have high heterotic response and produce better seggregants of used in Pearl millet hybridization programme.
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GUPTA, DEEPAK. "Principal component analysis for yield and its attributing characters of pearl millet (Pennisetum glaucum [L.] R.Br.)." Annals of Plant and Soil Research 24, no. 3 (August 1, 2022): 408–14. http://dx.doi.org/10.47815/apsr.2022.10184.
Full textAbstract:
An experiment was conducted at Agricultural Research Station, Navgaon (Alwar) during kharif season of 2019 to study the genetic divergence among 31 genotypes of pearl millet based on quantitative data of grain yield and its nine component traits using hierarchical cluster and principal component analysis (PCA). Principal Component Analysis (PCA) indicated that three components with eigen values more than one accounted for about 73.35% of the total variation among nine quantitative characters responsible for seed yield in pearl millet genotypes. The principal components PC1, PC2 and PC3 contributed about 37.44%, 22.63% and 13.28%, respectively to the total variation. The first principal component exhibited high positive loading for grain yield, stover yield, plant height, spike length, spike thickness and 1000-grain weight which contributed more to the diversity. The second principal component showed high loading for days to 50% flowering, days to maturity and 1000-grain weight. Cluster analysis grouped the genotypes into five clusters indicated that grain yield, stover yield, 1000-grain weight and days to maturity contributed maximum towards genetic divergence. The grouping patterns of genotypes in principal component analysis and cluster analysis were almost in agreement with each other with minor deviations. The maximum inter cluster distance between genotypes of cluster V and III with cluster II, indicate that genotypes included in these clusters have high heterotic response and produce better seggregants of used in Pearl millet hybridization programme.
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Hareram Sahoo and Aditya Kumar. "Study of genetic divergence among Eucalyptus tereticornis clones through principal component analysis (PCA)." International Journal of Science and Research Archive 6, no. 1 (May 30, 2022): 063–67. http://dx.doi.org/10.30574/ijsra.2022.6.1.0103.
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Eucalyptus tereticornis is one of the fastest growing multipurpose tree species. It is planted extensively under agroforestry and farm forestry. It was needed to estimate the genetic variability and contribution of yield contributing traits towards the total divergence. The PCA summarizes variability present in studied traits into utilizable form and to practical importance. Therefore, in the present study, eight clones of E. tereticornis were studied under field trial for their growth performance and contribution of individual traits towards total divergence were estimated. The eigene value of all three vectors (PCs) were found greater than one, which revealed that all the principal components explained a significant amount of variability present in traits. The proportion of variability explained by PC1 was 48.15 percent, by PC2 was 38.09 percent and by PC3 was 5.75 percent, all together these three vectors explained 92 percent of total variability. In PC1 and PC2, Plant height, biomass, leaf area, number of leaves, number of branches, leaf width and collar diameter were contributed positively towards the divergence hence the selection based on these traits will be rewarding. The times ranked contribution study also confirmed the contribution of L/W ratio (35.71%) and biomass (14.29%) towards the divergence. These traits are very important for the selection of parents in hybridization programs and effective selection of productive clones.
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Ahn, Jong-Hoon, and Jong-Hoon Oh. "A Constrained EM Algorithm for Principal Component Analysis." Neural Computation 15, no. 1 (January 1, 2003): 57–65. http://dx.doi.org/10.1162/089976603321043694.
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We propose a constrained EM algorithm for principal component analysis (PCA) using a coupled probability model derived from single-standard factor analysis models with isotropic noise structure. The single probabilistic PCA, especially for the case where there is no noise, can find only a vector set that is a linear superposition of principal components and requires postprocessing, such as diagonalization of symmetric matrices. By contrast, the proposed algorithm finds the actual principal components, which are sorted in descending order of eigenvalue size and require no additional calculation or postprocessing. The method is easily applied to kernel PCA. It is also shown that the new EM algorithm is derived from a generalized least-squares formulation.
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Chandraker, Pratibha, Bhawana Sharma, Mangla Parikh, and Ritu R. Saxena. "Assessment of Genetic Diversity in Aromatic Short Grain Rice (Oryza sativa L.) Genotypes using PCA and Cluster Analysis." International Journal of Plant & Soil Science 36, no. 5 (March 18, 2024): 82–94. http://dx.doi.org/10.9734/ijpss/2024/v36i54504.
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A population panel of 90 aromatic short grain rice accessions were evaluated for 26 agro-morphological and quality traits using principal component analysis (PCA) and cluster analysis for the determination of genetic variation pattern, and identification of the major traits contributing to the diversity. First six principal components (PCs) exhibited Eigenvalue more than one with 74.4 per cent of total variability among the 26 characters. The PC1 showed 24.55% while, PC2, PC3, PC4, PC5 and PC6 exhibited 15.48 %, 11.48 %, 9.96 %, 7.89 % and 5.12 % variability, respectively among the accessions for the traits under study. The results of PCA suggested that characters such as effective tillers per plant, number of spikelets per panicle, number of filled spikelets per panicle, spikelet fertility %, milling %, head rice recovery %, kernel length and kernel length after cooking were the principal discriminatory characteristics of aromatic short grain accessions of rice. Seven divergent clusters were formed by UPGMA clustering method. The pattern of group constellation proved the existence of significant amount of variability. The intra cluster distance ranged from 0.00 (cluster VI) to 6.33 (cluster V). The inter cluster distance was maximum between cluster VI and VII (18.854) and minimum between cluster II and cluster IV (7.673). To realize much variability and high heterotic effect, parents should be selected from two clusters having wider inter-cluster distance. Considering the importance of genetic distance and relative contribution of characters towards total divergence, the present study indicated that parental lines selected from cluster VI (IGSR -3-1-5) for number of spikelets per panicle, number of filled spikelets per panicle, grain length, kernel length and length breadth ratio, and from cluster VII (Khasakani, Kolijoha) for effective tillers per plant, 1000 grain weight, grain yield per plant, harvest index, grain breadth, length breadth ratio after cooking and elongation index could be used in crossing programmes to achieve desired segregants.
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Kenfack, S. C., K. F. Mkankam, G. Alory, Y. du Penhoat, N. M. Hounkonnou, D. A. Vondou, and G. N. Bawe. "Sea surface temperature patterns in Tropical Atlantic: principal component analysis and nonlinear principal component analysis." Nonlinear Processes in Geophysics Discussions 1, no. 1 (March 21, 2014): 235–67. http://dx.doi.org/10.5194/npgd-1-235-2014.
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Abstract. Principal Component Analysis (PCA) is one of the popular statistical methods for feature extraction. The neural network model has been performed on the PCA to obtain nonlinear principal component analysis (NLPCA), which allows the extraction of nonlinear features in the dataset missed by the PCA. NLPCA is applied to the monthly Sea Surface Temperature (SST) data from the eastern tropical Atlantic Ocean (29° W–21° E, 25° S–7° N) for the period 1982–2005. The focus is on the differences between SST inter-annual variability patterns; either extracted through traditional PCA or the NLPCA methods.The first mode of NLPCA explains 45.5% of the total variance of SST anomaly compared to 42% explained by the first PCA. Results from previous studies that detected the Atlantic cold tongue (ACT) as the main mode are confirmed. It is observed that the maximum signal in the Gulf of Guinea (GOG) is located along coastal Angola. In agreement with composite analysis, NLPCA exhibits two types of ACT, referred to as weak and strong Atlantic cold tongues. These two events are not totally symmetrical. NLPCA thus explains the results given by both PCA and composite analysis. A particular area observed along the northern boundary between 13 and 5° W vanishes in the strong ACT case and reaches maximum extension to the west in the weak ACT case. It is also observed that the original SST data correlates well with NLPCA and PCA, but with a stronger correlation on ACT area for NLPCA and southwest in the case of PCA.
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Akpan, I. I. "Assessment of water chemistry in a segment of Qua Iboe River Estuary by Principal component analysis." Journal of Aquatic Sciences 36, no. 1 (August 3, 2021): 1–11. http://dx.doi.org/10.4314/jas.v36i1.1.
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Assessment of water chemistry in a segment of Qua Iboe River Estuary, Niger Delta Region of Nigeria was carried out from January to December 2018 at three sampling stations. Seventeen physico-chemical parameters were analyzed using standards procedure. A total of 12 samples were collected from each station. Principal Component Analysis (PCA) was employed in the assessment of the study area. Three principal components, accounting for 99.59%, 100.01% and 100% of the total variance of information contained in the original data set for dry season were obtained. In the wet season, the components accounted for 66.0%, 69.97% and 67.50% of the total variance respectively. Results revealed that the most loading factor in the PCA when considering all the sampling stations in different seasons together in PC1, PC2 and PC3 axes were mainly sulphate, phosphate-phosphorus, calcium, potassium, temperature, total dissolved solids, total alkalinity, total hardness, dissolved oxygen, sodium, electrical conductivity, biological oxygen demand, pH, total suspended solids, A and magnesium. These loadings could be grouped into mineral/nutrient, physico-chemical, organic and domestic factors. General assessment of the study area did not indicate much deviation from prescribed standards, but sufficient to maintain a varied aquatic biodiversity.
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Rotaru, Ancuta Simona, Ioana Pop, Anamaria Vatca, and Luisa Andronie. "Principal Components Analysis Utility in the Livestock Field." Bulletin of University of Agricultural Sciences and Veterinary Medicine Cluj-Napoca. Animal Science and Biotechnologies 73, no. 2 (November 28, 2016): 251. http://dx.doi.org/10.15835/buasvmcn-asb:12231.
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Principal Component Analysis is a method factor - factor analysis - and is used to reduce data complexity by replacingmassive data sets by smaller sets. It is also used to highlight the way in which the variables are correlated with eachother and to determining the (less)latent variableswhich are behind the (more)measured variables. These latent variables are called factors, hence the name of the methodi.e. factor analysis. Our paper shows the applicability of Principal Components Analysis (PCA) in livestock area of study by carrying out a researchon some physiological characteristics in the case of tencow breeds.By using PCA only two factors have been preserved, concentrating over 80% of their information from the four variables in question, one factor concentrating weight and height and the other factor concentrating trunk circumference and weight at calving, respectively.
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Migenda, Nico, Ralf Möller, and Wolfram Schenck. "Adaptive dimensionality reduction for neural network-based online principal component analysis." PLOS ONE 16, no. 3 (March 30, 2021): e0248896. http://dx.doi.org/10.1371/journal.pone.0248896.
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“Principal Component Analysis” (PCA) is an established linear technique for dimensionality reduction. It performs an orthonormal transformation to replace possibly correlated variables with a smaller set of linearly independent variables, the so-called principal components, which capture a large portion of the data variance. The problem of finding the optimal number of principal components has been widely studied for offline PCA. However, when working with streaming data, the optimal number changes continuously. This requires to update both the principal components and the dimensionality in every timestep. While the continuous update of the principal components is widely studied, the available algorithms for dimensionality adjustment are limited to an increment of one in neural network-based and incremental PCA. Therefore, existing approaches cannot account for abrupt changes in the presented data. The contribution of this work is to enable in neural network-based PCA the continuous dimensionality adjustment by an arbitrary number without the necessity to learn all principal components. A novel algorithm is presented that utilizes several PCA characteristics to adaptivly update the optimal number of principal components for neural network-based PCA. A precise estimation of the required dimensionality reduces the computational effort while ensuring that the desired amount of variance is kept. The computational complexity of the proposed algorithm is investigated and it is benchmarked in an experimental study against other neural network-based and incremental PCA approaches where it produces highly competitive results.
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Álvarez, Óscar, Juan Luis Fernández-Martínez, Celia Fernández-Brillet, Ana Cernea, Zulima Fernández-Muñiz, and Andrzej Kloczkowski. "Principal component analysis in protein tertiary structure prediction." Journal of Bioinformatics and Computational Biology 16, no. 02 (April 2018): 1850005. http://dx.doi.org/10.1142/s0219720018500051.
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We discuss applicability of principal component analysis (PCA) for protein tertiary structure prediction from amino acid sequence. The algorithm presented in this paper belongs to the category of protein refinement models and involves establishing a low-dimensional space where the sampling (and optimization) is carried out via particle swarm optimizer (PSO). The reduced space is found via PCA performed for a set of low-energy protein models previously found using different optimization techniques. A high frequency term is added into this expansion by projecting the best decoy into the PCA basis set and calculating the residual model. This term is aimed at providing high frequency details in the energy optimization. The goal of this research is to analyze how the dimensionality reduction affects the prediction capability of the PSO procedure. For that purpose, different proteins from the Critical Assessment of Techniques for Protein Structure Prediction experiments were modeled. In all the cases, both the energy of the best decoy and the distance to the native structure have decreased. Our analysis also shows how the predicted backbone structure of native conformation and of alternative low energy states varies with respect to the PCA dimensionality. Generally speaking, the reconstruction can be successfully achieved with 10 principal components and the high frequency term. We also provide a computational analysis of protein energy landscape for the inverse problem of reconstructing structure from the reduced number of principal components, showing that the dimensionality reduction alleviates the ill-posed character of this high-dimensional energy optimization problem. The procedure explained in this paper is very fast and allows testing different PCA expansions. Our results show that PSO improves the energy of the best decoy used in the PCA when the adequate number of PCA terms is considered.
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Das, Gopal, Manojit Chattopadhyay, and Sumeet Gupta. "A Comparison of Self-organising Maps and Principal Components Analysis." International Journal of Market Research 58, no. 6 (November 2016): 815–34. http://dx.doi.org/10.2501/ijmr-2016-039.
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This paper attempts to compare self-organising maps (SOM) and principal components analysis (CPA) by applying them to the marketing construct ‘retail store personality’. Data were collected for the retail store personality construct via a validated scale from previous studies that had used the mall intercept technique. A total of 367 people responded, of whom 353 were found to be valid for data analysis. Data were analysed using CPA and SOM; both methods gave comparable clustering results, although the results for SOM were quite conclusive. In addition, we found that SOM complemented PCA by providing visual clustering results far superior to those of PCA. SOM can be used to further analyse PCA data using visual clustering features; both could be used in tandem. Although SOM have been used in a number of studies in marketing, this is the first paper to compare PCA and SOM on terms of application to the marketing construct ‘retail store personality’.
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Jolliffe, Ian T., and Jorge Cadima. "Principal component analysis: a review and recent developments." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374, no. 2065 (April 13, 2016): 20150202. http://dx.doi.org/10.1098/rsta.2015.0202.
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Large datasets are increasingly common and are often difficult to interpret. Principal component analysis (PCA) is a technique for reducing the dimensionality of such datasets, increasing interpretability but at the same time minimizing information loss. It does so by creating new uncorrelated variables that successively maximize variance. Finding such new variables, the principal components, reduces to solving an eigenvalue/eigenvector problem, and the new variables are defined by the dataset at hand, not a priori , hence making PCA an adaptive data analysis technique. It is adaptive in another sense too, since variants of the technique have been developed that are tailored to various different data types and structures. This article will begin by introducing the basic ideas of PCA, discussing what it can and cannot do. It will then describe some variants of PCA and their application.
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Li, Fei, and Jianhui Zeng. "Characterization of Origin and Evolution of Formation Water in Buried Hill of Jizhong Depression, China, Using Multivariate Statistical Analysis of Geochemical Data." Geofluids 2017 (2017): 1–15. http://dx.doi.org/10.1155/2017/5290686.
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Groundwater samples from buried hill of Jizhong Depression were evaluated using two statistical analyses: hierarchical cluster analysis (HCA) and principal component analysis (PCA). The samples were classified into four clusters, C1–C4, in HCA and the hydrochemical types of C1–C4 are HCO3-Na, Cl·HCO3-Na, Cl-Na, and Cl-Na·Ca. From C1 to C2, C3, and C4, the water-rock interaction becomes increasingly intensive, and rNa/rCl gets lower while total dissolved solids and r(Cl-Na)/rMg get higher. Three components of PCA explain 86.87% of the variance. Component1 (PC1), characterized by highly positive loadings in Na+ and Cl−, is related to evaporation concentration. Component2 (PC2) is defined by highly positive loading in HCO3- and is related to influence of atmospheric water. With high positive loadings in Ca2+ and high negative loadings in Na+ and SO42-, component3 (PC3) suggests plagioclase albitization. The combination of HCA and PCA within the hydrogeological contexts allowed the division of study area into five dynamic areas. From recharge area to discharge area, the influence of atmospheric water gets weaker and water-rock interactions such as evaporation concentration and plagioclase albitization become intensive. Therefore groundwater in buried hill showed paths of hydrochemical evolution, from C1, to C2, C3, and C4. Buried hill reservoir in Jizhong Depression is mainly distributed in hydrodynamic blocking and discharge area; therefore the two regions can be the favorable areas for petroleum migration.
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Barth, Jackson, Duwani Katumullage, Chenyu Yang, and Jing Cao. "Classification of Wines Using Principal Component Analysis." Journal of Wine Economics 16, no. 1 (February 2021): 56–67. http://dx.doi.org/10.1017/jwe.2020.35.
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AbstractClassification of wines with a large number of correlated covariates may lead to classification results that are difficult to interpret. In this study, we use a publicly available dataset on wines from three known cultivars, where there are 13 highly correlated variables measuring chemical compounds of wines. The goal is to produce an efficient classifier with straightforward interpretation to shed light on the important features of wines in the classification. To achieve the goal, we incorporate principal component analysis (PCA) in the k-nearest neighbor (kNN) classification to deal with the serious multicollinearity among the explanatory variables. PCA can identify the underlying dominant features and provide a more succinct and straightforward summary over the correlated covariates. The study shows that kNN combined with PCA yields a much simpler and interpretable classifier that has comparable performance with kNN based on all the 13 variables. The appropriate number of principal components is chosen to strike a balance between predictive accuracy and simplicity of interpretation. Our final classifier is based on only two principal components, which can be interpreted as the strength of taste and level of alcohol and fermentation in wines, respectively. (JEL Classifications: C10, Cl4, D83)
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Kanbur, S. M., D. Iono, N. A. Tanvir, and M. A. Hendry. "The Use of Principal Components Analysis in Analysing Variable Star Data." International Astronomical Union Colloquium 176 (2000): 56–59. http://dx.doi.org/10.1017/s0252921100057067.
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AbstractWe describe the technique of Principal Components Analysis (PCA) as applied to the analysis of variable star data. It is shown that PCA is an efficient way of describing light curve structure.
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Kramarenko, Alexander S., Halyna I. Kalynycnenko, Ruslan L. Susol, Nataliia S. Papakina, and Sergei S. Kramarenko. "Principal Component Analysis of Body Weight Traits and Subsequent Milk Production in Red Steppe Breed Heifers." Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences. 76, no. 2 (April 1, 2022): 307–13. http://dx.doi.org/10.2478/prolas-2022-0044.
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Abstract The main goal of this study was to determine the effects of body weight traits during the rearing period on subsequent milk production of primiparous dairy cows using Principal Component Analysis. Data on lactation performance records of 109 Red Steppe dairy cow progeny of six bulls maintained at the State Enterprise “Pedigree Reproducers” Stepove”” (Mykolayiv region, Ukraine), during 2001–2014, were utilised for the present study. Heifer body weight at birth, 3, 6, 9, 12, 15, and 18 months of age was measured. Records of 305-day milk yield (kg), milk fat percentage (%), milk fat yield (kg), monthly milk yield (kg) and milk fat percentage (%) in the 1st-lactation dairy cows were also available. Principal Components Analysis (PCA) was conducted on the live weights for each heifer between birth and 18 months of age. The first three principal components (PC1-PC3) explained 79.7% of the total variance. Principal component 1 (PC1) showed significant relationship to body weight of heifers at 9, 12, and 15 months of age (post-pubertal period). Body weight at 3 and 6 months of age (pre-pubertal period) had higher scores on the second principal component (PC2). Principal component 3 (PC3) showed significant relationship to body weight of calves at birth. Only groups of heifers with high scores on PC1 and PC2 had significant effect on subsequent milk performance (with the exception of milk fat percentage). Thus, the use of a multivariate technique (Principal Component Analysis) allowed to determine two age intervals of heifers during the rearing period (pre- and postpubertal periods), which were significantly related to subsequent milk production.
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Lennox, J., and C. Rosen. "Adaptive multiscale principal components analysis for online monitoring of wastewater treatment." Water Science and Technology 45, no. 4-5 (February 1, 2002): 227–35. http://dx.doi.org/10.2166/wst.2002.0593.
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Fault detection and isolation (FDI) are important steps in the monitoring and supervision of industrial processes. Biological wastewater treatment (WWT) plants are difficult to model, and hence to monitor, because of the complexity of the biological reactions and because plant influent and disturbances are highly variable and/or unmeasured. Multivariate statistical models have been developed for a wide variety of situations over the past few decades, proving successful in many applications. In this paper we develop a new monitoring algorithm based on Principal Components Analysis (PCA). It can be seen equivalently as making Multiscale PCA (MSPCA) adaptive, or as a multiscale decomposition of adaptive PCA. Adaptive Multiscale PCA (AdMSPCA) exploits the changing multivariate relationships between variables at different time-scales. Adaptation of scale PCA models over time permits them to follow the evolution of the process, inputs or disturbances. Performance of AdMSPCA and adaptive PCA on a real WWT data set is compared and contrasted. The most significant difference observed was the ability of AdMSPCA to adapt to a much wider range of changes. This was mainly due to the flexibility afforded by allowing each scale model to adapt whenever it did not signal an abnormal event at that scale. Relative detection speeds were examined only summarily, but seemed to depend on the characteristics of the faults/disturbances. The results of the algorithms were similar for sudden changes, but AdMSPCA appeared more sensitive to slower changes.
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Thivierge, Jean-Philippe. "Frequency-separated principal component analysis of cortical population activity." Journal of Neurophysiology 124, no. 3 (September 1, 2020): 668–81. http://dx.doi.org/10.1152/jn.00167.2020.
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A method termed frequency-separated principal component analysis (FS-PCA) is introduced for analyzing populations of simultaneously recorded neurons. This framework extends standard principal component analysis by extracting components of activity delimited to specific frequency bands. FS-PCA revealed that circuits of the primary visual cortex generate a broad range of components dominated by low-frequency activity. Furthermore, low-dimensional fluctuations in population activity modulated the response of individual neurons to sensory input.
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Chen, Cheng. "Principal Component Analysis variants for Parkinson datasets." Applied and Computational Engineering 44, no. 1 (March 5, 2024): 48–55. http://dx.doi.org/10.54254/2755-2721/44/20230097.
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Principal Component Analysis (PCA) is one of the most fundamental dimension reduction methods that need further research. With the widespread popularity of machine learning and the arrival of the era of big data, dimension reduction has become a hot topic and principal component analysis is a hot topic. However, although there are a lot of researchers who focus on the methods of the PCA, few researches on Parkinson Datasets have been made. As a result, the aim of our work is to discuss the PCA variants for Parkinson Datasets. This paper first introduces the three most commonly used PCA methods: PCA, Sparse PCA and Kernel PCA, and then introduces the Support Vector Machine (SVM) used to measure the dimension reduction effect. After that, we introduced the Parkinson's dataset and the meanings of root mean square error (RMSE), overall accuracy, Cohens kappa (Kappa) and computational time, the indicators that are used to measure the dimensionality reduction effect. Finally, we identified the variants among different PCA methods on the Parkinson dataset by comparing the indicators of the data obtained after dimensionality reduction using different methods.
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Sidhu, Ameek, Josh Bazely, Els Peeters, and Jan Cami. "A principal component analysis of polycyclic aromatic hydrocarbon emission in NGC 7023." Monthly Notices of the Royal Astronomical Society 511, no. 2 (January 27, 2022): 2186–200. http://dx.doi.org/10.1093/mnras/stac157.
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ABSTRACT We carried out a principal component analysis (PCA) of the fluxes of five polycyclic aromatic hydrocarbon (PAH) bands at 6.2, 7.7, 8.6, 11.0, and 11.2 µm in the reflection nebula NGC 7023 comprising of the photodissociation region (PDR) and a cavity. We find that only two principal components (PCs) are required to explain the majority of the observed variance in PAH fluxes ( 98 per cent). The first PC ( PC1), which is the primary driver of the variance, represents the total PAH emission. The second PC (PC2) is related to the ionization state of PAHs across the nebula. This is consistent with the results of a similar analysis of the PAH emission in NGC 2023. The biplots and the correlations of PCs with the various PAH ratios show that there are two subsets of ionic bands with the 6.2 and 7.7 µm bands forming one subset and the 8.6 and 11.0 µm bands the other. However, the distinction between these subsets is only present in the PDR. We have also carried out a separate PCA analysis of the PAH fluxes, this time only considering variations in the cavity. This shows that in the cavity, PC2 is not related to the charge state of PAHs but possibly to structural molecular changes.
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An, Qiang, Lu Lin, Yuan Yuan Liu, Ning Qiu Huang, and Bin Zhao. "Principal Component Analysis of Eutrophication in the Yangtze River Estuary." Applied Mechanics and Materials 209-211 (October 2012): 1910–14. http://dx.doi.org/10.4028/www.scientific.net/amm.209-211.1910.
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The Yangtze River Estuary has become increasingly challenged by various destructive threats to its ecosystem such as the frequent occurrence of harmful algal blooms. Four cruises were carried out in the Yangtze River Estuary and its adjacent area in 2006. Ten variables including CODMn, PO43--P, SiO3-Si, NO3--N, NO2--N, NH4+-N, TN, TP, TOC and chl-a were analyzed by exploratory data analysis. Nitrate was the dominant form of TN throughout the year. Principal component analysis (PCA) was applied to estimate the sources of nutrients contamination in 2006. Two principal components (PCs) were extracted, namely, CODMn, PO43--P, NO3--N and TN for PC1, NO2--N and chl-a for PC2. Influenced by anthropogenic sewage, PC1 near Shidongkou, Bailonggang, Xinhe and Zhuyuan outlets was higher than other stations. The primary influencing factor of PC1 were the contaminants carried by runoff from the Yangtze River. And the dominating factors of eutrophication in 2006 were CODMn, PO43--P, NO3--N, TN and chl-a in the Yangtze River Estuary and its adjacent area.
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BUSS, RICARDO NIEHUES, RAIMUNDA ALVES SILVA, OSVALDO GUEDES FILHO, and GLÉCIO MACHADO SIQUEIRA. "MANAGEMENT ZONES DESIGN FOR SOYBEAN CROP USING PRINCIPAL COMPONENTS AND GEOSTATISTICS." Revista Caatinga 35, no. 4 (October 2022): 925–35. http://dx.doi.org/10.1590/1983-21252022v35n420rc.
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ABSTRACT In precision agriculture, determining management zones for soil and plant attributes is a complex process that requires knowledge of several variables, which complicates management and decisionmaking processes. This study evaluated the spatial variability of soybean yield and soil chemical properties using geostatistical and multivariate analyses to define management zones in an Oxisol. The soybean yield and soil chemical properties between 0 to 0.2 and 0.2 to 0.4 m soil depths were sampled at 70 points. Geostatistical and multivariate analyses were then performed on these data. The soil chemical properties showed higher variability at 0.2 to 0.4 m soil depth. The semivariogram parameters of the principal component analysis (PCA) data (PCA 1, PCA 2, and PCA 3) for both depths were more homogeneous than the original data. The maps of soil chemical properties showed high similarity to the soybean yield map. The PCA explained 65.34% (0 to 0.2 m) and 70.50% (0.2 to 0.4 m) of data variability, grouping the soybean yield, organic matter, pH, phosphorous, potassium, calcium, magnesium, and sodium. PCA spatialization allowed for the definition of management zones indicated by PCA 1, PCA 2, and PCA 3 for both depths. The result indicates that the area must be managed using different strategies of soil fertility management to increase soybean yield.