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Journal articles on the topic 'Minimum residual sum of squares'

Author: Grafiati

Published: 8 September 2023

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1

Zhou, Zhen, L. N. Zhang, Y. Qin, D. Z. Ma, and B. Niu. "Statistical Inference of LZL-Type Mass Flowmeter Life Distribution Model." Key Engineering Materials 458 (December 2010): 173–78. http://dx.doi.org/10.4028/www.scientific.net/kem.458.173.

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Characteristics of field failure data are analyzed in this paper. The failure data and sales record of LZL-type mass flowmeter are used to infer life distribution of this conduct. The lines can be fitted in coordinates of six distribution using least square and the residual sum of squares are compared, the minimum correspond is the best distribution type. The results show that the life distribution style of this conduct is the two parameter exponential distribution, which is the base to analyze and predict failure development, research failure mechanism and draw up maintenance policy.

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2

DEVITA, HANY, I. KOMANG GDE SUKARSA, and I. PUTU EKA N. KENCANA. "KINERJA JACKKNIFE RIDGE REGRESSION DALAM MENGATASI MULTIKOLINEARITAS." E-Jurnal Matematika 3, no. 4 (2014): 146. http://dx.doi.org/10.24843/mtk.2014.v03.i04.p077.

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Ordinary least square is a parameter estimations for minimizing residual sum of squares. If the multicollinearity was found in the data, unbias estimator with minimum variance could not be reached. Multicollinearity is a linear correlation between independent variabels in model. Jackknife Ridge Regression(JRR) as an extension of Generalized Ridge Regression (GRR) for solving multicollinearity. Generalized Ridge Regression is used to overcome the bias of estimators caused of presents multicollinearity by adding different bias parameter for each independent variabel in least square equation afte

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Araveeporn, Autcha. "Comparing Parameter Estimation of Random Coefficient Autoregressive Model by Frequentist Method." Mathematics 8, no. 1 (2020): 62. http://dx.doi.org/10.3390/math8010062.

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This paper compares the frequentist method that consisted of the least-squares method and the maximum likelihood method for estimating an unknown parameter on the Random Coefficient Autoregressive (RCA) model. The frequentist methods depend on the likelihood function that draws a conclusion from observed data by emphasizing the frequency or proportion of the data namely least squares and maximum likelihood methods. The method of least squares is often used to estimate the parameter of the frequentist method. The minimum of the sum of squared residuals is found by setting the gradient to zero.

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4

Liu, Kexin, Weimin Bao, Yufeng Hu, et al. "Improvement in Ridge Coefficient Optimization Criterion for Ridge Estimation-Based Dynamic System Response Curve Method in Flood Forecasting." Water 13, no. 24 (2021): 3483. http://dx.doi.org/10.3390/w13243483.

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The ridge estimation-based dynamic system response curve (DSRC-R) method, which is an improvement of the dynamic system response curve (DSRC) method via the ridge estimation method, has illustrated its good robustness. However, the optimization criterion for the ridge coefficient in the DSRC-R method still needs further study. In view of this, a new optimization criterion called the balance and random degree criterion considering the sum of squares of flow errors (BSR) is proposed in this paper according to the properties of model-simulated residuals. In this criterion, two indexes, namely, th

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Marjetič, Aleš. "Least-squares adjustment taking into account the errors in variables." Geodetski vestnik 65, no. 02 (2021): 205–18. http://dx.doi.org/10.15292/geodetski-vestnik.2021.02.205-218.

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In this article, we discuss the procedure for computing the values of the unknowns under the condition of the minimum sum of squares of the observation residuals (least-squares method), taking into account the errors in the unknowns. Many authors have already presented the problem, especially in the field of regression analysis and computations of transformation parameters. We present an overview of the theoretical foundations of the least-squares method and extensions of this method by considering the errors in unknowns in the model matrix. The method, which can be called ‘the total least-squ

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Pizarro Inostroza, María Gabriela, Francisco Javier Navas González, Vincenzo Landi, et al. "Goat Milk Nutritional Quality Software-Automatized Individual Curve Model Fitting, Shape Parameters Calculation and Bayesian Flexibility Criteria Comparison." Animals 10, no. 9 (2020): 1693. http://dx.doi.org/10.3390/ani10091693.

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SPSS syntax was described to evaluate the individual performance of 49 linear and non-linear models to fit the milk component evolution curve of 159 Murciano-Granadina does selected for genotyping analyses. Peak and persistence for protein, fat, dry matter, lactose, and somatic cell counts were evaluated using 3107 controls (3.91 ± 2.01 average lactations/goat). Best-fit (adjusted R2) values (0.548, 0.374, 0.429, and 0.624 for protein, fat, dry matter, and lactose content, respectively) were reached by the five-parameter logarithmic model of Ali and Schaeffer (ALISCH), and for the three-parame

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UTAMI, NI KETUT TRI, and I. KOMANG GDE SUKARSA. "PENERAPAN METODE GENERALIZED RIDGE REGRESSION DALAM MENGATASI MASALAH MULTIKOLINEARITAS." E-Jurnal Matematika 2, no. 1 (2013): 54. http://dx.doi.org/10.24843/mtk.2013.v02.i01.p029.

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Ordinary least square is parameter estimation method for linier regression analysis by minimizing residual sum of square. In the presence of multicollinearity, estimators which are unbiased and have a minimum variance can not be generated. Multicollinearity refers to a situation where regressor variables are highly correlated. Generalized Ridge Regression is an alternative method to deal with multicollinearity problem. In Generalized Ridge Regression, different biasing parameters for each regressor variables were added to the least square equation after transform the data to the space of ortho

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Annan, Richard Fiifi, Yao Yevenyo Ziggah, John Ayer, and Christian Amans Odutola. "ACCURACY ASSESSMENT OF HEIGHTS OBTAINED FROM TOTAL STATION AND LEVEL INSTRUMENT USING TOTAL LEAST SQUARES AND ORDINARY LEAST SQUARES METHODS." Geoplanning: Journal of Geomatics and Planning 3, no. 2 (2016): 87. http://dx.doi.org/10.14710/geoplanning.3.2.87-92.

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Spirit levelling has been the traditional means of determining Reduced Levels (RL’s) of points by most surveyors. The assertion that the level instrument is the best instrument for determining elevations of points needs to be reviewed; this is because technological advancement is making the total station a very reliable tool for determining reduced levels of points. In order to achieve the objective of this research, reduced levels of stations were determined by a spirit level and a total station instrument. Ordinary Least Squares (OLS) and Total Least Squares (TLS) techniques were then applie

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9

Zverev, S. V., V. I. Karpov, and M. A. Nikitina. "Optimization of food compositions according to the ideal protein profile." Food systems 4, no. 1 (2021): 4–11. http://dx.doi.org/10.21323/2618-9771-2021-4-1-4-11.

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The paper emphasizes the importance of not only the quantitative but also qualitative composition of protein in nutrition. The authors propose protein classification into three main groups according to the concept of reference (ideal) protein. A mathematical model is examined to solve the task of rational mixture production upon the given profile of reference protein. Two variants of the criterion for formation of optimal composition are described. One of them presents the classical sum of squares of the residual for essential amino acid scores and 1. The second also presents the sum of square

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Chiang Hsieh, Lin-Han. "How Does the Effect Fade over Distance? An Inquiry into the Decay Pattern of Distance Effect on Property Values in the Case of Taipei, Taiwan." Land 10, no. 11 (2021): 1238. http://dx.doi.org/10.3390/land10111238.

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It is generally accepted that the perception of homeowners towards certain potential risks or amenities fades as distance from the risk or amenity increases. This study aims to illustrate the distance–decay pattern with an appropriate mathematical function. Distance–decay functions and parameters that yield the minimum residual sum of squares (RSS) for a given regression model are considered to be the optimal approximation for the pattern of decay. The effect of flood risk and mass rapid transit (MRT) accessibility on residential housing prices in Taipei, Taiwan, are used as examples to test t

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Liu, Xiang-Yu, Yu-Ling He, and Jian Yao. "A New Hybrid PSS Optimization Method Based on Improved Active Set Algorithm." Mathematical Problems in Engineering 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/4348257.

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This paper proposes a new hybrid optimization method for the phase-frequency characteristics of the double input power system stabilizer (PSS) based on the improved active set algorithm. This method takes the effect of the filtering section optimization on the parameter improvement into account, and the optimized model focuses on the minimum residual sum of squares between the actual and the target phase-frequency characteristics. The result shows that the improved parameters obtained from the proposed method provide much better phase-frequency characteristics than the widely used engineering

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12

Yang, Zhiwei, Jing Ren, Zichi Zhang, et al. "A New Three-Way Incremental Naive Bayes Classifier." Electronics 12, no. 7 (2023): 1730. http://dx.doi.org/10.3390/electronics12071730.

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Aiming at the problems of the dynamic increase in data in real life and that the naive Bayes (NB) classifier only accepts or rejects the sample processing results, resulting in a high error rate when dealing with uncertain data, this paper combines three-way decision and incremental learning, and a new three-way incremental naive Bayes classifier (3WD-INB) is proposed. First, the NB classifier is established, and the distribution fitting is carried out according to the minimum residual sum of squares (RSS) for continuous data, so that 3WD-INB can process both discrete data and continuous data,

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Zhou, Zilong, Riyan Lan, Yichao Rui, Longjun Dong, and Xin Cai. "A New Algebraic Solution for Acoustic Emission Source Localization without Premeasuring Wave Velocity." Sensors 21, no. 2 (2021): 459. http://dx.doi.org/10.3390/s21020459.

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The technique of acoustic emission (AE) source localization is critical for studying material failure mechanism and predicting the position of potential hazards. Most existing positioning methods heavily depend on the premeasured wave velocity and are not suitable for complex engineering practices where the wave velocity changes dynamically. To reduce the influence of measurement error of wave velocity on location accuracy, this paper proposes a new algebraic solution for AE source localization without premeasuring wave velocity. In this method, the nonlinear TDOA equations are established and

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Zhou, Zilong, Riyan Lan, Yichao Rui, Longjun Dong, and Xin Cai. "A New Algebraic Solution for Acoustic Emission Source Localization without Premeasuring Wave Velocity." Sensors 21, no. 2 (2021): 459. http://dx.doi.org/10.3390/s21020459.

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The technique of acoustic emission (AE) source localization is critical for studying material failure mechanism and predicting the position of potential hazards. Most existing positioning methods heavily depend on the premeasured wave velocity and are not suitable for complex engineering practices where the wave velocity changes dynamically. To reduce the influence of measurement error of wave velocity on location accuracy, this paper proposes a new algebraic solution for AE source localization without premeasuring wave velocity. In this method, the nonlinear TDOA equations are established and

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15

Гиззатова, Э. Р., А. Р. Шагиахметов, Г. К. Хисаметдинова, and С. Л. Подвальный. "CALCULATION OF THE RESIDUAL FUNCTION IN THE BASIS SPACE TO SEARCH FOR AREAS OF UNCERTAINTY OF THE RATE CONSTANTS OF THE POLYMERIZATION PROCESS." ВЕСТНИК ВОРОНЕЖСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА, no. 4(-) (August 30, 2022): 37–43. http://dx.doi.org/10.36622/vstu.2022.18.4.005.

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Предлагаeтся к рассмотрению математическая модель процесса полимеризации на катализаторах Циглера-Натта, в предположении существования только трех элементарных стадий: роста полимерной цепи, передачи цепи на мономер и передачи цепи на алюминийорганическое соединение при условии отсутствия стадии инициирования активных центров. Приведены постановки прямой и обратной кинетической задач, последняя из которых заключается в поиске областей неопределенных для констант скоростей стадий роста и передач цепи. Показано, что для рассматриваемого процесса значения констант могут быть определены в базисном

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16

Dhakal, Madhav, Gurbir Singh, Rachel L. Cook, and Taylor Sievers. "Modeling Hairy Vetch and Cereal Rye Cover Crop Decomposition and Nitrogen Release." Agronomy 10, no. 5 (2020): 701. http://dx.doi.org/10.3390/agronomy10050701.

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Empirical models could help us to understand the process of plant residue decomposition and nutrient release into the soil. The objective of this study was to determine an appropriate model to describe the decomposition of hairy vetch (Vicia villosa Roth) and cereal rye (Secale cereale L.) cover crop (CC) residue and nitrogen (N) release. Data pertaining to above and belowground CC residue mass loss and N release for up to 2633 cumulative decomposition degree days (112 d) after litterbag installation were obtained from two cropping system experiments, a 1-yr study conducted in 2015 and a 2-yr

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17

Khalaf, Akram Abbas. "Estimating Soil Hydraulic Parameters of Different Textured Soils in Semiarid Duhok Conditions - Iraqi-Kurdistan Region by using RETC Program." Kufa Journal for Agricultural Sciences 13, no. 2 (2021): 6–17. http://dx.doi.org/10.36077/kjas/2021/v13i2.3651.

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RETC is a computer program that can be used to estimate soil hydraulic functions by easily determining soil properties. Using van Genuchten model in the RETC program gave high accuracy for estimating the hydraulic functions e.g., θ (h), k (θ) and D (h), also the mentioned program is considered a good tool for potential optimization of water management especially though calculating irrigation water after consuming 60% of the available water in root zone restoring technique. In the current study surface, soil samples (0 – 30 cm) from eight locations with a wide range in texture were collec

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18

Wang, Jianmei, Ke Ning, Junliang Xu, and Zhixiong Li. "Reliability-based robust design of wind turbine’s shrink disk." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 15 (2017): 2685–96. http://dx.doi.org/10.1177/0954406217723364.

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Wind turbine’s shrink disk (WTSD), as a component of transmission system, plays a crucial role in the wind turbine work. In this study, the matrix expression of combined pressure and interference magnitude has been derived by analyzing the geometry relationship of interference fit of multi-layer cylinder. The mechanic model is built by simplifying WTSD as interference fit of multi-layer cylinder. The reliability model is established on the basis of pressure-strength model, and the formula regarding reliability sensitivity is derived. In terms of the minimum principle on the square sum of relia

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19

Downey, Peter J. "(Probably) the minimum sum of squares." Communications in Statistics. Stochastic Models 3, no. 3 (1987): 457–65. http://dx.doi.org/10.1080/15326348708807066.

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Bochev, Pavel, Leszek Demkowicz, Jay Gopalakrishnan, and Max Gunzburger. "Minimum Residual and Least Squares Finite Element Methods." Computers & Mathematics with Applications 68, no. 11 (2014): 1479. http://dx.doi.org/10.1016/j.camwa.2014.11.005.

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21

Pyatkin, Artem, Daniel Aloise, and Nenad Mladenović. "NP-Hardness of balanced minimum sum-of-squares clustering." Pattern Recognition Letters 97 (October 2017): 44–45. http://dx.doi.org/10.1016/j.patrec.2017.05.033.

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22

Scott, J. A. "102.52 A sum of squares for the Lester minimum." Mathematical Gazette 102, no. 555 (2018): 529–31. http://dx.doi.org/10.1017/mag.2018.133.

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23

Pal, Jayanta Kumar. "Spiking problem in monotone regression: Penalized residual sum of squares." Statistics & Probability Letters 78, no. 12 (2008): 1548–56. http://dx.doi.org/10.1016/j.spl.2008.01.015.

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24

Wu, Bang Ye, and Li-Hsuan Chen. "Parameterized Algorithms for the 2-Clustering Problem with Minimum Sum and Minimum Sum of Squares Objective Functions." Algorithmica 72, no. 3 (2014): 818–35. http://dx.doi.org/10.1007/s00453-014-9874-8.

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Gerritsma, Marc, Carsten Carstensen, Leszek Demkowicz, and Jay Gopalakrishnan. "Minimum Residual and Least Squares Finite Element Methods II." Computers & Mathematics with Applications 74, no. 8 (2017): 1922. http://dx.doi.org/10.1016/j.camwa.2017.07.021.

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26

Cuong, Tran Hung, Jen-Chih Yao, and Nguyen Dong Yen. "Qualitative properties of the minimum sum-of-squares clustering problem." Optimization 69, no. 9 (2020): 2131–54. http://dx.doi.org/10.1080/02331934.2020.1778685.

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27

Hansen, Pierre. "Minimum Sum of Squares Clustering in a Low Dimensional Space." Journal of Classification 15, no. 1 (1998): 37–55. http://dx.doi.org/10.1007/s003579900019.

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28

du Merle, O., P. Hansen, B. Jaumard, and N. Mladenovic. "An Interior Point Algorithm for Minimum Sum-of-Squares Clustering." SIAM Journal on Scientific Computing 21, no. 4 (1999): 1485–505. http://dx.doi.org/10.1137/s1064827597328327.

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29

Et.al, Abdul Hadi Bhatti. "Least Square Methods Based on Control Points of Said Ball Curves for Solving Ordinary Differential Equations." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 3 (2021): 2597–607. http://dx.doi.org/10.17762/turcomat.v12i3.1261.

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This paper presents the use of Said Ball curve’s control points to approximate the solutions of linear ordinary differential equations (ODEs). Least squares methods (LSM) is proposed to find the control points of Said Ball curves by minimizing the error of residual function.The residual error is measured by taking the sum of squares of the Said Ball curve’s control points of the residual function. Then the approximate solution of ODEs is obtained by minimizing residual error.Two numerical examples are given in term of error and compared with the exact solution to demonstrate the efficiency of

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30

Caimmi, R., C. Marmo, and T. Valentinuzzi. "A numerical fit of analytical to simulated density profiles in dark matter haloes." Serbian Astronomical Journal, no. 170 (2005): 13–32. http://dx.doi.org/10.2298/saj0570013c.

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Analytical and geometrical properties of generalized power-law (GPL) density profiles are investigated in detail. In particular, a one-to-one correspondence is found between mathematical parameters (a scaling radius, r0, a scaling density, ?0, and three exponents, ?, ?, ?), and geometrical parameters (the coordinates of the intersection of the asymptotes, xC, yC, and three vertical intercepts, b, b?, b?, related to the curve and the asymptotes, respectively): (r0,?0,?,?,?) ? (xC,yC,b,b?,b?). Then GPL density profiles are compared with simulated dark haloes (SDH) density profiles, and nonlinear

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31

Nogueira, Maria Cristina Stolf. "Specific residue: application of orthogonal contrasts when heteroscedasticity is present." Scientia Agricola 67, no. 1 (2010): 117–25. http://dx.doi.org/10.1590/s0103-90162010000100016.

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When experimental data are submitted to analysis of variance, the assumption of data homoscedasticity (variance homogeneity among treatments), associated to the adopted mathematical model must be satisfied. This verification is necessary to ensure the correct test for the analysis. In some cases, when data homoscedascity is not observed, errors may invalidate the analysis. An alternative to overcome this difficulty is the application of the specific residue analysis, which consists of the decomposition of the residual sum of squares in its components, in order to adequately test the correspond

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Martín-Santamaría, R., J. Sánchez-Oro, S. Pérez-Peló, and A. Duarte. "Strategic oscillation for the balanced minimum sum-of-squares clustering problem." Information Sciences 585 (March 2022): 529–42. http://dx.doi.org/10.1016/j.ins.2021.11.048.

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Pacheco, Joaquı́n, and Olga Valencia. "Design of hybrids for the minimum sum-of-squares clustering problem." Computational Statistics & Data Analysis 43, no. 2 (2003): 235–48. http://dx.doi.org/10.1016/s0167-9473(02)00224-4.

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Bagirov, Adil M. "Modified global -means algorithm for minimum sum-of-squares clustering problems." Pattern Recognition 41, no. 10 (2008): 3192–99. http://dx.doi.org/10.1016/j.patcog.2008.04.004.

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35

Aloise, Daniel, Pierre Hansen, and Leo Liberti. "An improved column generation algorithm for minimum sum-of-squares clustering." Mathematical Programming 131, no. 1-2 (2010): 195–220. http://dx.doi.org/10.1007/s10107-010-0349-7.

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Carrizosa, Emilio, Nenad Mladenović, and Raca Todosijević. "Variable neighborhood search for minimum sum-of-squares clustering on networks." European Journal of Operational Research 230, no. 2 (2013): 356–63. http://dx.doi.org/10.1016/j.ejor.2013.04.027.

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Demidenko, Eugene. "Criteria for global minimum of sum of squares in nonlinear regression." Computational Statistics & Data Analysis 51, no. 3 (2006): 1739–53. http://dx.doi.org/10.1016/j.csda.2006.06.015.

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Batra, Luckshay, and Harish Chander Taneja. "Comparison between Information Theoretic Measures to Assess Financial Markets." FinTech 1, no. 2 (2022): 137–54. http://dx.doi.org/10.3390/fintech1020011.

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Information theoretic measures were applied to the study of the randomness associations of different financial time series. We studied the level of similarities between information theoretic measures and the various tools of regression analysis, i.e., between Shannon entropy and the total sum of squares of the dependent variable, relative mutual information and coefficients of correlation, conditional entropy and residual sum of squares, etc. We observed that mutual information and its dynamical extensions provide an alternative approach with some advantages to study the association between se

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Aloise, Daniel, and Pierre Hansen. "A branch-and-cut SDP-based algorithm for minimum sum-of-squares clustering." Pesquisa Operacional 29, no. 3 (2009): 503–16. http://dx.doi.org/10.1590/s0101-74382009000300002.

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Minimum sum-of-squares clustering (MSSC) consists in partitioning a given set of n points into k clusters in order to minimize the sum of squared distances from the points to the centroid of their cluster. Recently, Peng & Xia (2005) established the equivalence between 0-1 semidefinite programming (SDP) and MSSC. In this paper, we propose a branch-and-cut algorithm for the underlying 0-1 SDP model. The algorithm obtains exact solutions for fairly large data sets with computing times comparable with those of the best exact method found in the literature.

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Cho, Seong-Yun. "Simultaneous LTE Signal Propagation Modelling and Base Station Positioning Based on Multiple Virtual Locations." Sensors 22, no. 15 (2022): 5917. http://dx.doi.org/10.3390/s22155917.

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In the Long Term Evolution (LTE) system, the Signal Propagation Model (SPM) and the location information of the base stations are required for positioning a smartphone. To this end, this paper proposes a technique for estimating the SPM and the location of the base station at the same time using location-based Reference Signal Received Power (RSRP) information acquired in a limited area. In the proposed technique, multiple Virtual Locations (VLs) for a base station are set within the service area. Signal propagation modelling is performed based on the assumptions that a base station is in each

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Toral, Fábio Luiz Buranelo, Roberto Augusto de Almeida Torres Júnior, Paulo Sávio Lopes, Luiz Otávio Campos da Silva, and João Cruz Reis Filho. "Modeling the effect of the age of dam at calving on the weaning weight of Charolais-Zebu crossbred calves." Revista Brasileira de Zootecnia 38, no. 7 (2009): 1229–37. http://dx.doi.org/10.1590/s1516-35982009000700011.

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The objective of this study was to evaluate alternatives for modeling the age of dam at calving (AOD) effect on the weaning weight of Charolais-Zebu crossbred calves. Data from 56,965 calves were analyzed, using statistical models considering the fixed effects of the contemporary groups, sire and dam genetic groups, and AOD. The AOD effect was fitted to models using annual age classes, and ordinary quadratic to quintic-ordered polynomials (OP) or segmented polynomials (SP) with two, three, four, six and twelve evenly spaced intervals. In the case of segmented polynomials, general linear and qu

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DEMETRIOU, I. C., and M. J. D. POWELL. "The Minimum Sum of Squares Change to Univariate Data that gives Convexity." IMA Journal of Numerical Analysis 11, no. 3 (1991): 433–48. http://dx.doi.org/10.1093/imanum/11.3.433.

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Hoai An, Le Thi, Le Hoai Minh, and Pham Dinh Tao. "New and efficient DCA based algorithms for minimum sum-of-squares clustering." Pattern Recognition 47, no. 1 (2014): 388–401. http://dx.doi.org/10.1016/j.patcog.2013.07.012.

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Bagirov, Adil M., Sona Taheri, and Julien Ugon. "Nonsmooth DC programming approach to the minimum sum-of-squares clustering problems." Pattern Recognition 53 (May 2016): 12–24. http://dx.doi.org/10.1016/j.patcog.2015.11.011.

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Bagirov, Adil M., and John Yearwood. "A new nonsmooth optimization algorithm for minimum sum-of-squares clustering problems." European Journal of Operational Research 170, no. 2 (2006): 578–96. http://dx.doi.org/10.1016/j.ejor.2004.06.014.

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Liu, Yongguo, Zhang Yi, Hong Wu, Mao Ye, and Kefei Chen. "A tabu search approach for the minimum sum-of-squares clustering problem." Information Sciences 178, no. 12 (2008): 2680–704. http://dx.doi.org/10.1016/j.ins.2008.01.022.

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47

Nie, Jiawang, and James W. Demmel. "Minimum Ellipsoid Bounds for Solutions of Polynomial Systems via Sum of Squares." Journal of Global Optimization 33, no. 4 (2005): 511–25. http://dx.doi.org/10.1007/s10898-005-2099-2.

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48

Ordin, Burak, and Adil M. Bagirov. "A heuristic algorithm for solving the minimum sum-of-squares clustering problems." Journal of Global Optimization 61, no. 2 (2014): 341–61. http://dx.doi.org/10.1007/s10898-014-0171-5.

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49

Pacheco, Joaquı́n A. "A scatter search approach for the minimum sum-of-squares clustering problem." Computers & Operations Research 32, no. 5 (2005): 1325–35. http://dx.doi.org/10.1016/j.cor.2003.11.006.

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Slabospitsky, Alexander. "RECURRENT REPRESENTATION FOR NON-STATIONARY PARAMETER ESTIMATE OF LEAST SQUARES METHOD WITH LEAST DEVIATIONS FROM "ATTRACTION" POINTS FOR BILINEAR DYNAMIC SYSTEMS." Journal of Numerical and Applied Mathematics, no. 2 (131) (2019): 32–38. http://dx.doi.org/10.17721/2706-9699.2019.2.04.

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Abstract:

The estimation problem of non-stationary parameter matrices is considered for bilinear discrete dynamic system in the case when for these unknown parameter matrices their ‘attraction’ points are known at any moment. Explicit and recurrent forms of representation are obtained for these parameter estimates of the least squares method with variable forgetting factor and least deviation norm from ‘attraction’ points under non-classical assumptions. The recurrent algorithm is also proposed for corresponding weighted residual sum of squares.

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