Relevant bibliographies by topics / Principal component analysis

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Principal component analysis'

Author: Grafiati
Published: 4 June 2021
Last updated: 9 June 2025

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Journal articles on the topic "Principal component analysis"

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Barros, António S., and Douglas N. Rutledge. "Segmented principal component transform–principal component analysis." Chemometrics and Intelligent Laboratory Systems 78, no. 1-2 (July 2005): 125–37. http://dx.doi.org/10.1016/j.chemolab.2005.01.003.

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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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Richards, Larry E., and I. T. Jolliffe. "Principal Component Analysis." Journal of Marketing Research 25, no. 4 (November 1988): 410. http://dx.doi.org/10.2307/3172953.

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Lever, Jake, Martin Krzywinski, and Naomi Altman. "Principal component analysis." Nature Methods 14, no. 7 (July 2017): 641–42. http://dx.doi.org/10.1038/nmeth.4346.

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Timmerman, Marieke E. "Principal Component Analysis." Journal of the American Statistical Association 98, no. 464 (December 2003): 1082–83. http://dx.doi.org/10.1198/jasa.2003.s308.

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Goodall, Colin. "Principal Component Analysis." Technometrics 30, no. 3 (August 1988): 351–52. http://dx.doi.org/10.1080/00401706.1988.10488412.

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Wold, Svante, Kim Esbensen, and Paul Geladi. "Principal component analysis." Chemometrics and Intelligent Laboratory Systems 2, no. 1-3 (August 1987): 37–52. http://dx.doi.org/10.1016/0169-7439(87)80084-9.

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Law, John, and I. T. Jolliffe. "Principal Component Analysis." Statistician 36, no. 4 (1987): 432. http://dx.doi.org/10.2307/2348864.

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Hess, Aaron S., and John R. Hess. "Principal component analysis." Transfusion 58, no. 7 (May 6, 2018): 1580–82. http://dx.doi.org/10.1111/trf.14639.

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Bro, Rasmus, and Age K. Smilde. "Principal component analysis." Anal. Methods 6, no. 9 (2014): 2812–31. http://dx.doi.org/10.1039/c3ay41907j.

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Dissertations / Theses on the topic "Principal component analysis"

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Nunes, Madalena Baioa Paraíso. "Portfolio selection : a study using principal component analysis." Master's thesis, Instituto Superior de Economia e Gestão, 2017. http://hdl.handle.net/10400.5/14598.

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Mestrado em Finanças<br>Nesta tese aplicámos a análise de componentes principais ao mercado bolsista português usando os constituintes do índice PSI-20, de Julho de 2008 a Dezembro de 2016. Os sete primeiros componentes principais foram retidos, por se ter verificado que estes representavam as maiores fontes de risco deste mercado em específico. Assim, foram construídos sete portfólios principais e comparámo-los com outras estratégias de alocação. Foram construídos o portfólio 1/N (portfólio com investimento igual para cada um dos 26 ativos), o PPEqual (portfólio com igual investimento em cada um dos 7 principal portfólios) e o portfólio MV (portfólio que tem por base a teoria moderna de gestão de carteiras de Markowitz (1952)). Concluímos que estes dois últimos portfólios apresentavam os melhores resultados em termos de risco e retorno, sendo o portfólio PPEqual mais adequado a um investidor com maior grau de aversão ao risco e o portfólio MV mais adequado a um investidor que estaria disposto a arriscar mais em prol de maior retorno. No que diz respeito ao nível de risco, o PPEqual é o portfólio com melhores resultados e nenhum outro portfólio conseguiu apresentar valores semelhantes. Assim encontrámos um portfólio que é a ponderação de todos os portfólios principais por nós construídos e este era o portfólio mais eficiente em termos de risco.<br>In this thesis we apply principal component analysis to the Portuguese stock market using the constituents of the PSI-20 index from July 2008 to December 2016. The first seven principal components were retained, as we verified that these represented the major risk sources in this specific market. Seven principal portfolios were constructed and we compared them with other allocation strategies. The 1/N portfolio (with an equal investment in each of the 26 stocks), the PPEqual portfolio (with an equal investment in each of the 7 principal portfolios) and the MV portfolio (based on Markowitz's (1952) mean-variance strategy) were constructed. We concluded that these last two portfolios presented the best results in terms of return and risk, with PPEqual portfolio being more suitable for an investor with a greater degree of risk aversion and the MV portfolio more suitable for an investor willing to risk more in favour of higher returns. Regarding the level of risk, PPEqual is the portfolio with the best results and, so far, no other portfolio has presented similar values. Therefore, we found an equally-weighted portfolio among all the principal portfolios we built, which was the most risk efficient.<br>info:eu-repo/semantics/publishedVersion
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Kpamegan, Neil Racheed. "Robust Principal Component Analysis." Thesis, American University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10784806.

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<p> In multivariate analysis, principal component analysis is a widely popular method which is used in many different fields. Though it has been extensively shown to work well when data follows multivariate normality, classical PCA suffers when data is heavy-tailed. Using PCA with the assumption that the data follows a stable distribution, we will show through simulations that a new method is better. We show the modified PCA can be used for heavy-tailed data and that we can more accurately estimate the correct number of components compared to classical PCA and more accurately identify the subspace spanned by the important components.</p><p>
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Akinduko, Ayodeji Akinwumi. "Multiscale principal component analysis." Thesis, University of Leicester, 2016. http://hdl.handle.net/2381/36616.

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The problem of approximating multidimensional data with objects of lower dimension is a classical problem in complexity reduction. It is important that data approximation capture the structure(s) and dynamics of the data, however distortion to data by many methods during approximation implies that some geometric structure(s) of the data may not be preserved during data approximation. For methods that model the manifold of the data, the quality of approximation depends crucially on the initialization of the method. The first part of this thesis investigates the effect of initialization on manifold modelling methods. Using Self Organising Maps (SOM) as a case study, we compared the quality of learning of manifold methods for two popular initialization methods; random initialization and principal component initialization. To further understand the dynamics of manifold learning, datasets were further classified into linear, quasilinear and nonlinear. The second part of this thesis focuses on revealing geometric structure(s) in high dimension data using an extension of Principal Component Analysis (PCA). Feature extraction using (PCA) favours direction with large variance which could obfuscate other interesting geometric structure(s) that could be present in the data. To reveal these intrinsic structures, we analysed the local PCA structures of the dataset. An equivalent definition of PCA is that it seeks subspaces that maximize the sum of pairwise distances of data projection; extending this definition we define localization in term of scale as maximizing the sum of weighted squared pairwise distances between data projections for various distributions of weights (scales). Since for complex data various regions of the dataspace could have different PCA structures, we also define localization with regards to dataspace. The resulting local PCA structures were represented by the projection matrix corresponding to the subspaces and analysed to reveal some structures in the data at various localizations.
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Der, Ralf, Ulrich Steinmetz, Gerd Balzuweit, and Gerrit Schüürmann. "Nonlinear principal component analysis." Universität Leipzig, 1998. https://ul.qucosa.de/id/qucosa%3A34520.

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We study the extraction of nonlinear data models in high-dimensional spaces with modified self-organizing maps. We present a general algorithm which maps low-dimensional lattices into high-dimensional data manifolds without violation of topology. The approach is based on a new principle exploiting the specific dynamical properties of the first order phase transition induced by the noise of the data. Moreover we present a second algorithm for the extraction of generalized principal curves comprising disconnected and branching manifolds. The performance of the algorithm is demonstrated for both one- and two-dimensional principal manifolds and also for the case of sparse data sets. As an application we reveal cluster structures in a set of real world data from the domain of ecotoxicology.
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Solat, Karo. "Generalized Principal Component Analysis." Diss., Virginia Tech, 2018. http://hdl.handle.net/10919/83469.

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The primary objective of this dissertation is to extend the classical Principal Components Analysis (PCA), aiming to reduce the dimensionality of a large number of Normal interrelated variables, in two directions. The first is to go beyond the static (contemporaneous or synchronous) covariance matrix among these interrelated variables to include certain forms of temporal (over time) dependence. The second direction takes the form of extending the PCA model beyond the Normal multivariate distribution to the Elliptically Symmetric family of distributions, which includes the Normal, the Student's t, the Laplace and the Pearson type II distributions as special cases. The result of these extensions is called the Generalized principal component analysis (GPCA). The GPCA is illustrated using both Monte Carlo simulations as well as an empirical study, in an attempt to demonstrate the enhanced reliability of these more general factor models in the context of out-of-sample forecasting. The empirical study examines the predictive capacity of the GPCA method in the context of Exchange Rate Forecasting, showing how the GPCA method dominates forecasts based on existing standard methods, including the random walk models, with or without including macroeconomic fundamentals.<br>Ph. D.
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Fučík, Vojtěch. "Principal component analysis in Finance." Master's thesis, Vysoká škola ekonomická v Praze, 2015. http://www.nusl.cz/ntk/nusl-264205.

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The main objective of this thesis is to summarize and possibly interconnect the existing methodology on principal components analysis, hierarchical clustering and topological organization in the financial and economic networks, linear regression and GARCH modeling. In the thesis the clustering ability of PCA is compared with the more conventional approaches on a set of world stock market indices returns in different time periods where the time division is represented by The World Financial Crisis of 2007-2009. It is also observed whether the clustering of DJIA index components is underlied by the industry sector to which the individual stocks belong. Joining together PCA with classical linear regression creates principal components regression which is further in the thesis applied to the German DAX 30 index logarithmic returns forecasting using various macroeconomic and financial predictors. The correlation between two energy stocks returns - Chevron and ExxonMobil is forecasted using orthogonal (or PCA) GARCH. The constructed forecast is then compared with the predictions constructed by the conventional multivariate volatility models - EWMA and DCC GARCH.
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Wedlake, Ryan Stuart. "Robust principal component analysis biplots." Thesis, Link to the online version, 2008. http://hdl.handle.net/10019/929.

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Brennan, Victor L. "Principal component analysis with multiresolution." [Gainesville, Fla.] : University of Florida, 2001. http://etd.fcla.edu/etd/uf/2001/ank7079/brennan%5Fdissertation.pdf.

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Thesis (Ph. D.)--University of Florida, 2001.<br>Title from first page of PDF file. Document formatted into pages; contains xi, 124 p.; also contains graphics. Vita. Includes bibliographical references (p. 120-123).
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Cadima, Jorge Filipe Campinos Landerset. "Topics in descriptive Principal Component Analysis." Thesis, University of Kent, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.314686.

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Isaac, Benjamin. "Principal component analysis based combustion models." Doctoral thesis, Universite Libre de Bruxelles, 2014. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209278.

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Energy generation through combustion of hydrocarbons continues to dominate, as the most common method for energy generation. In the U.S. nearly 84% of the energy consump- tion comes from the combustion of fossil fuels. Because of this demand there is a continued need for improvement, enhancement and understanding of the combustion process. As computational power increases, and our methods for modelling these complex combustion systems improve, combustion modelling has become an important tool in gaining deeper insight and understanding for these complex systems. The constant state of change in computational ability lead to a continual need for new combustion models that can take full advantage of the latest computational resources. To this end, the research presented here encompasses the development of new models, which can be tailored to the available resources, allowing one to increase or decrease the amount of modelling error based on the available computational resources, and desired accuracy. Principal component analysis (PCA) is used to identify the low-dimensional manifolds which exist in turbulent combustion systems. These manifolds are unique in there ability to represent a larger dimensional space with fewer components resulting in a minimal addition of error. PCA is well suited for the problem at hand because of its ability to allow the user to define the amount of error in approximation, depending on the resources at hand. The research presented here looks into various methods which exploit the benefits of PCA in modelling combustion systems, demonstrating several models, and providing new and interesting perspectives for the PCA based approaches to modelling turbulent combustion.<br>Doctorat en Sciences de l'ingénieur<br>info:eu-repo/semantics/nonPublished
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Books on the topic "Principal component analysis"

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Jolliffe, I. T. Principal component analysis. 2nd ed. New York: Springer, 2010.

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Jolliffe, I. T. Principal Component Analysis. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4757-1904-8.

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Hyvarinen, Aapo. Independent component analysis. New York: J. Wiley, 2001.

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Juha, Karhunen, and Oja Erkki, eds. Independent component analysis. New York: J. Wiley, 2001.

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Vidal, René, Yi Ma, and S. S. Sastry. Generalized Principal Component Analysis. New York, NY: Springer New York, 2016. http://dx.doi.org/10.1007/978-0-387-87811-9.

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Naik, Ganesh R., ed. Advances in Principal Component Analysis. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-6704-4.

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Sanguansat, Parinya. Principal component analysis - multidisciplinary applications. Rijeka: InTech, 2012.

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Kong, Xiangyu, Changhua Hu, and Zhansheng Duan. Principal Component Analysis Networks and Algorithms. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-2915-8.

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Mori, Yuichi, Masahiro Kuroda, and Naomichi Makino. Nonlinear Principal Component Analysis and Its Applications. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-0159-8.

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D, Mobley Curtis, ed. Principal component analysis in meteorology and oceanography. Amsterdam: Elsevier, 1988.

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Book chapters on the topic "Principal component analysis"

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Jolliffe, I. T. "Principal Component Analysis and Factor Analysis." In Principal Component Analysis, 115–28. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4757-1904-8_7.

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Jolliffe, I. T. "Introduction." In Principal Component Analysis, 1–7. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4757-1904-8_1.

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Jolliffe, I. T. "Outlier Detection, Influential Observations and Robust Estimation of Principal Components." In Principal Component Analysis, 173–98. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4757-1904-8_10.

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Jolliffe, I. T. "Principal Component Analysis for Special Types of Data." In Principal Component Analysis, 199–222. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4757-1904-8_11.

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Jolliffe, I. T. "Generalizations and Adaptations of Principal Component Analysis." In Principal Component Analysis, 223–34. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4757-1904-8_12.

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Jolliffe, I. T. "Mathematical and Statistical Properties of Population Principal Components." In Principal Component Analysis, 8–22. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4757-1904-8_2.

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Jolliffe, I. T. "Mathematical and Statistical Properties of Sample Principal Components." In Principal Component Analysis, 23–49. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4757-1904-8_3.

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Jolliffe, I. T. "Principal Components as a Small Number of Interpretable Variables: Some Examples." In Principal Component Analysis, 50–63. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4757-1904-8_4.

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Jolliffe, I. T. "Graphical Representation of Data Using Principal Components." In Principal Component Analysis, 64–91. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4757-1904-8_5.

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Jolliffe, I. T. "Choosing a Subset of Principal Components or Variables." In Principal Component Analysis, 92–114. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4757-1904-8_6.

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Conference papers on the topic "Principal component analysis"

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Tang, F., and H. Tao. "Binary Principal Component Analysis." In British Machine Vision Conference 2006. British Machine Vision Association, 2006. http://dx.doi.org/10.5244/c.20.39.

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Siirtola, Harri, Tanja Saily, and Terttu Nevalainen. "Interactive Principal Component Analysis." In 2017 21st International Conference on Information Visualisation (IV). IEEE, 2017. http://dx.doi.org/10.1109/iv.2017.39.

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Hsu, Charles, and Harold Szu. "Sequential principal component analysis." In SPIE Defense, Security, and Sensing, edited by Harold Szu. SPIE, 2011. http://dx.doi.org/10.1117/12.887509.

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Wang, Qianqian, Quanxue Gao, Xinbo Gao, and Feiping Nie. "Angle Principal Component Analysis." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/409.

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Recently, many ℓ1-norm based PCA methods have been developed for dimensionality reduction, but they do not explicitly consider the reconstruction error. Moreover, they do not take into account the relationship between reconstruction error and variance of projected data. This reduces the robustness of algorithms. To handle this problem, a novel formulation for PCA, namely angle PCA, is proposed. Angle PCA employs ℓ2-norm to measure reconstruction error and variance of projected da-ta and maximizes the summation of ratio between variance and reconstruction error of each data. Angle PCA not only is robust to outliers but also retains PCA’s desirable property such as rotational invariance. To solve Angle PCA, we propose an iterative algorithm, which has closed-form solution in each iteration. Extensive experiments on several face image databases illustrate that our method is overall superior to the other robust PCA algorithms, such as PCA, PCA-L1 greedy, PCA-L1 nongreedy and HQ-PCA.
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Pimentel-Alarcon, Daniel L., Aritra Biswas, and Claudia R. Solis-Lemus. "Adversarial principal component analysis." In 2017 IEEE International Symposium on Information Theory (ISIT). IEEE, 2017. http://dx.doi.org/10.1109/isit.2017.8006952.

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Sehgal, Shruti, Harpreet Singh, Mohit Agarwal, V. Bhasker, and Shantanu. "Data analysis using principal component analysis." In 2014 International Conference on Medical Imaging, m-Health and Emerging Communication Systems (MedCom). IEEE, 2014. http://dx.doi.org/10.1109/medcom.2014.7005973.

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Wojnowicz, Michael, Dinh Nguyen, Li Li, and Xuan Zhao. "Lazy Stochastic Principal Component Analysis." In 2017 IEEE International Conference on Data Mining Workshops (ICDMW). IEEE, 2017. http://dx.doi.org/10.1109/icdmw.2017.79.

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Pei, Yan. "Linear Principal Component Discriminant Analysis." In 2015 IEEE International Conference on Systems, Man, and Cybernetics (SMC). IEEE, 2015. http://dx.doi.org/10.1109/smc.2015.368.

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Chowdhury, Ranak Roy, Muhammad Abdullah Adnan, and Rajesh K. Gupta. "Real Time Principal Component Analysis." In 2019 IEEE 35th International Conference on Data Engineering (ICDE). IEEE, 2019. http://dx.doi.org/10.1109/icde.2019.00171.

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"CONSTRAINED GENERALISED PRINCIPAL COMPONENT ANALYSIS." In International Conference on Computer Vision Theory and Applications. SciTePress - Science and and Technology Publications, 2006. http://dx.doi.org/10.5220/0001362102060212.

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Reports on the topic "Principal component analysis"

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MARTIN, SHAWN B. Kernel Near Principal Component Analysis. Office of Scientific and Technical Information (OSTI), July 2002. http://dx.doi.org/10.2172/810934.

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Hamilton, James, and Jin Xi. Principal Component Analysis for Nonstationary Series. Cambridge, MA: National Bureau of Economic Research, January 2024. http://dx.doi.org/10.3386/w32068.

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Aït-Sahalia, Yacine, and Dacheng Xiu. Principal Component Analysis of High Frequency Data. Cambridge, MA: National Bureau of Economic Research, September 2015. http://dx.doi.org/10.3386/w21584.

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Eick, Brian, Zachary Treece, Billie Spencer, Matthew Smith, Steven Sweeney, Quincy Alexander, and Stuart Foltz. Miter gate gap detection using principal component analysis. Engineer Research and Development Center (U.S.), June 2018. http://dx.doi.org/10.21079/11681/27365.

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Federer, W. T., C. E. McCulloch, and J. J. Miles-McDermott. Illustrative Examples of Principal Component Analysis Using SYSTAT/FACTOR. Fort Belvoir, VA: Defense Technical Information Center, May 1987. http://dx.doi.org/10.21236/ada184920.

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Federer, W. T., C. E. McCulloch, and N. J. Miles-McDermott. Illustrative Examples of Principal Component Analysis using BMDP/4M. Fort Belvoir, VA: Defense Technical Information Center, May 1987. http://dx.doi.org/10.21236/ada185179.

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Krishnaiah, P. R., and S. Sarkar. Principal Component Analysis Under Correlated Multivariate Regression Equations Model. Fort Belvoir, VA: Defense Technical Information Center, April 1985. http://dx.doi.org/10.21236/ada160266.

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Thompson, David C., Janine C. Bennett, Diana C. Roe, and Philippe Pierre Pebay. Scalable multi-correlative statistics and principal component analysis with Titan. Office of Scientific and Technical Information (OSTI), February 2009. http://dx.doi.org/10.2172/984172.

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Fujikoshi, Y., P. R. Krishnaiah, and J. Schmidhammer. Effect of Additional Variables in Principal Component Analysis, Discriminant Analysis and Canonical Correlation Analysis. Fort Belvoir, VA: Defense Technical Information Center, August 1985. http://dx.doi.org/10.21236/ada162069.

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Thompson, David, Ray W. Grout, Nathan D. Fabian, and Janine Camille Bennett. Detecting Combustion and Flow Features In Situ Using Principal Component Analysis. Office of Scientific and Technical Information (OSTI), March 2009. http://dx.doi.org/10.2172/1324759.

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