Linear Centroid Encoder for Supervised Principal Component Analysis

被引:2
作者
Ghosh, Tomojit [1 ]
Kirby, Michael [2 ]
机构
[1] Univ Tennessee Chattanooga, Dept Comp Sci & Engn, 615 McCallie Ave, Chattanooga, TN 37405 USA
[2] Colorado State Univ, Dept Math, 711 Oval Dr, Ft Collins, CO 80521 USA
关键词
Supervised Linear Centroid-Encoder; Centroid-Encoder; Principal component analysis (PCA); Supervised PCA; Linear dimensionality reduction; Supervised dimensionality reduction;
D O I
10.1016/j.patcog.2024.110634
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
We propose a new supervised dimensionality reduction technique called Supervised Linear Centroid-Encoder (SLCE), a linear counterpart of the nonlinear Centroid-Encoder (CE) (Ghosh and Kirby, 2022). SLCE works by mapping the samples of a class to its class centroid using a linear transformation. The transformation is a projection that reconstructs a point such that its distance from the corresponding class centroid, i.e., centroid-reconstruction loss, is minimized in the ambient space. We derive a closed-form solution using an eigendecomposition of a symmetric matrix. We did a detailed analysis and presented some crucial mathematical properties of the proposed approach. We establish a connection between the eigenvalues and the centroidreconstruction loss. In contrast to Principal Component Analysis (PCA) which reconstructs a sample in the ambient space, the transformation of SLCE uses the instances of a class to rebuild the corresponding class centroid. Therefore the proposed method can be considered a form of supervised PCA. Experimental results show the performance advantage of SLCE over other supervised methods.
引用
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页数:13
相关论文
共 38 条
[1]   Early prognosis of respiratory virus shedding in humans [J].
Aminian, M. ;
Ghosh, T. ;
Peterson, A. ;
Rasmussen, A. L. ;
Stiverson, S. ;
Sharma, K. ;
Kirby, M. .
SCIENTIFIC REPORTS, 2021, 11 (01)
[2]  
[Anonymous], 2001, Geometric Data Analysis: An Empirical Approach to Dimensionality Reduction and the Study of Patterns
[3]   Prediction by supervised principal components [J].
Bair, E ;
Hastie, T ;
Paul, D ;
Tibshirani, R .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2006, 101 (473) :119-137
[4]   Supervised principal component analysis: Visualization, classification and regression on subspaces and submanifolds [J].
Barshan, Elnaz ;
Ghodsi, Ali ;
Azimifar, Zohreh ;
Jahromi, Mansoor Zolghadri .
PATTERN RECOGNITION, 2011, 44 (07) :1357-1371
[5]  
Chepushtanova Sofya., 2020, Data Science for Mathematicians, VFirst, P291
[6]  
DUDA R, 2001, PATTERN CLASSIFICATI
[7]   The use of multiple measurements in taxonomic problems [J].
Fisher, RA .
ANNALS OF EUGENICS, 1936, 7 :179-188
[8]  
Ghosh T, 2022, J MACH LEARN RES, V23, P1
[9]  
Hayden E.C., 2015, Nature, V7
[10]  
He XF, 2004, ADV NEUR IN, V16, P153