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Applications of Regularized Least Squares to Classification Problems [chapter]

Nicolò Cesa-Bianchi
2004 Lecture Notes in Computer Science  
We present a survey of recent results concerning the theoretical and empirical performance of algorithms for learning regularized least-squares classifiers.  ...  The behavior of these family of learning algorithms is analyzed in both the statistical and the worst-case (individual sequence) data-generating models.  ...  Regularized Least-Squares for Classification In the pattern classification problem, some unknown source is supposed to generate a sequence x 1 , x 2 , . . . of instances (data elements) x t ∈ X , where  ... 
doi:10.1007/978-3-540-30215-5_2 fatcat:r4fq2hmcm5gilcj4qgvcvayfaq

Multi-class least squares classification at binary-classification complexity

Zineb Noumir, Paul Honeine, Cedric Richard
2011 2011 IEEE Statistical Signal Processing Workshop (SSP)  
This paper deals with multi-class classification problems. Many methods extend binary classifiers to operate a multiclass task, with strategies such as the one-vs-one and the onevs-all schemes.  ...  We present a method for multi-class classification, with a computational complexity essentially independent of the number of classes.  ...  MULTI-CLASS LEAST SQUARES CLASSIFICATION In a multi-class classification problem, we consider a set of N training data, belonging to any of the m available classes.  ... 
doi:10.1109/ssp.2011.5967680 fatcat:udptydqw2veaxjmbbmwr6yknpa


2009 International Journal of Information Technology and Decision Making  
in classification of important classes, than to errors in classification of unimportant classes, while keeping the regularized terms in their original form.  ...  The C-VLSSVM classifier can be obtained by a simple modification of the regularization parameter, based on the least squares support vector machine (LSSVM) classifier, whereby more weight is given to errors  ...  Acknowledgements The authors would like to thank the anonymous referees for their valuable comments and suggestions. Their comments helped to improve the quality of the paper immensely.  ... 
doi:10.1142/s0219622009003600 fatcat:abcxc6ma5bctpppamlfp4uwp7y

A General Framework for Sparsity Regularized Feature Selection via Iteratively Reweighted Least Square Minimization

Hanyang Peng, Yong Fan
A variety of feature selection methods based on sparsity regularization have been developed with different loss functions and sparse regularization functions.  ...  a ℓ2,p-norm (0 < p ≤ 2) sparse regularization.  ...  Acknowledgments This study was supported in part by National Key Basic Research and Development Program of China (2015CB856404), National Natural Science Foundation of China (81271514, 61473296), and NIH  ... 
doi:10.1609/aaai.v31i1.10833 fatcat:iiqpd3lew5dx3jedc3bnikga4a

Least Squares Auto-Tuning [article]

Shane Barratt, Stephen Boyd
2019 arXiv   pre-print
We apply our method, which we call least squares auto-tuning, to data fitting.  ...  Least squares is by far the simplest and most commonly applied computational method in many fields. In almost all applications, the least squares objective is rarely the true objective.  ...  The final contribution is our unique application of least squares auto-tuning to data fitting.  ... 
arXiv:1904.05460v1 fatcat:5wfw23ljbnczxgitxnz4kil6xi

Page 1630 of Mathematical Reviews Vol. , Issue 83d [page]

1983 Mathematical Reviews  
An application of these methods to the solution of sparse square nonsymmetric linear systems is also presented.”  ...  This problem, while appearing to be quite special, is the core problem arising in the solution of the general linearly constrained linear least squares problem.  ... 

10.5937/sjm9-5520 = On robust information extraction from high-dimensional data

Jan Kalina
2014 Serbian Journal of Management  
In general, (4) can be described as a regularized version of the least squares estimator.  ...  A requirement to reduce the influence of noise on the computed solution leads to a modification of the least squares method, most commonly by the Tikhonov regularization.  ... 
doi:10.5937/sjm9-5520 fatcat:vuzzfbopnnchddwxslzla3xxw4

Pressure vessel state investigation based upon the least squares support vector machine

Jichen Shen, Hongfei Chang, Yang Li
2011 Mathematical and computer modelling  
In view of the remarkable time-frequency property obtained from wavelet packets and the excellent generalization ability derived from the least squares support vector machine (LS SVM), a novel approach  ...  In addition, the LS SVM is introduced to accomplish classification, for judging the states of pressure vessels.  ...  Just due to this consideration, in 1999, J.A.K. Suykens put forward the least squares support vector machine (LS SVM) based upon the standard SVM [2] .  ... 
doi:10.1016/j.mcm.2010.11.011 fatcat:jhqe5ur3ujdzdnwi3jxvccffam

Hypergraph spectral learning for multi-label classification

Liang Sun, Shuiwang Ji, Jieping Ye
2008 Proceeding of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD 08  
To reduce the computational cost, we propose an approximate formulation, which is shown to be equivalent to a least squares problem under a mild condition.  ...  Based on the approximate formulation, efficient algorithms for solving least squares problems can be applied to scale the formulation to very large data sets.  ...  Such type of problems occurs in many important applications, such as protein function classification [9] , text categorization [25] , and semantic scene classification [4] .  ... 
doi:10.1145/1401890.1401971 dblp:conf/kdd/SunJY08 fatcat:7a6fwviyc5fxzpjamyl2cvzroi

Polynomial Runtime Bounds for Fixed-Rank Unsupervised Least-Squares Classification

Fabian Gieseke, Tapio Pahikkala, Christian Igel
2013 Asian Conference on Machine Learning  
In this work, we consider one of these variants, called unsupervised regularized least-squares classification, which is based on the square loss, and develop polynomial upper runtime bounds for the induced  ...  The goal is to partition unlabeled data into two classes such that a subsequent application of a support vector machine would yield the overall best result (with respect to the optimization problem associated  ...  Acknowledgements We would like to thank the anonymous reviewers for their detailed comments.  ... 
dblp:conf/acml/GiesekePI13 fatcat:s3dgarvluvfezehomdvggsf54u

A scalable two-stage approach for a class of dimensionality reduction techniques

Liang Sun, Betul Ceran, Jieping Ye
2010 Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '10  
In this paper, an efficient two-stage approach is proposed to solve a class of dimensionality reduction techniques, including Canonical Correlation Analysis, Orthonormal Partial Least Squares, Linear Discriminant  ...  Prior work transforms the generalized eigenvalue problem into an equivalent least squares formulation, which can then be solved efficiently.  ...  Acknowledgements This work was supported by NSF IIS-0612069, IIS-0812551, IIS-0953662, NGA HM1582-08-1-0016, the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects  ... 
doi:10.1145/1835804.1835846 dblp:conf/kdd/SunCY10 fatcat:dmlhwdw5hnbttamxy6m2ekgtqy

Sparse LS-SVMs using additive regularization with a penalized validation criterion

Kristiaan Pelckmans, Johan A. K. Suykens, Bart De Moor
2004 The European Symposium on Artificial Neural Networks  
Least Squares Support Vector Machines (LS-SVMs) [9, 10] are reformulations to standard SVMs which lead to solving linear KKT systems for classification tasks as well as regression and primaldual LS-SVM  ...  This paper is based on a new way for determining the regularization trade-off in least squares support vector machines (LS-SVMs) via a mechanism of additive regularization which has been recently introduced  ...  The criterion (11) leads to the unique solution with the following constrained least squares problem 1 N Ω 1 N Ω v b α − y y v 2 2 s.t. 1 T N α = 0. ( 12 ) Straightforward application of the criterion  ... 
dblp:conf/esann/PelckmansSM04 fatcat:qcxwyux4y5eonkv5htgw3xdg3y

Comprehensive Review On Twin Support Vector Machines [article]

M. Tanveer and T. Rajani and R. Rastogi and Y.H. Shao and M. A. Ganaie
2021 arXiv   pre-print
to solve two SVM kind problems.  ...  To begin with we first introduce the basic theory of support vector machine, TWSVM and then focus on the various improvements and applications of TWSVM, and then we introduce TSVR and its various enhancements  ...  [261] formulated a sparse version of least square TSVR by introducing a regularization term to make it strongly convex and also converted the primal problems to linear programming problems.  ... 
arXiv:2105.00336v2 fatcat:prxup4sbavfyxpembij6amrnka

Numerical analysis of least squares and perceptron learning for classification problems [article]

L. Beilina
2020 arXiv   pre-print
This work presents study on regularized and non-regularized versions of perceptron learning and least squares algorithms for classification problems.  ...  Fr'echet derivatives for regularized least squares and perceptron learning algorithms are derived.  ...  Non-regularized least squares problem In non-regularized linear regression or least squares problem the goal is to minimize the sum of squares E(ω) = 1 2 N ∑ n=1 (t n − f (x, ω)) 2 = 1 2 N ∑ n=1 (t n −  ... 
arXiv:2004.01138v4 fatcat:wgxvhr2qgngplimly2byp5qk3q

Regularized logistic regression method for change detection in multispectral data via Pathwise Coordinate optimization

Jiming Li, Yuntao Qian, Sen Jia
2010 2010 IEEE International Conference on Image Processing  
Change detection methods base on classification schemes under this kind of condition should put more emphasis on the model's simplicity and efficiency in addition to the detection accuracy.  ...  When applied on the L1-regularized regression problem, the algorithm can handle large problems in a comparatively very low timing cost.  ...  Then we use coordinate descent to solve the penalized weighted least-squares problem min ( 0, )∈ℝ +1 {−ℓ ( 0 , ) + ( )} (12) All of the above can be formulated to a sequence of nested loops: • OUTER LOOP  ... 
doi:10.1109/icip.2010.5654271 dblp:conf/icip/LiQJ10 fatcat:rmrymngdrvc7tnjqkl2foogbxu
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