## Uncorrelated Multilinear Principal Component Analysis through Successive Variance Maximization

author: Haiping Lu, Department of Computer Science, University of Toronto
published: Aug. 7, 2008,   recorded: July 2008,   views: 1088
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# Slides

0:00 Slides Uncorrelated Multilinear Principal Component Analysis through Successive Variance Maximization Outline Tensorial Data Dimensionality Reduction Problem - 1 Dimensionality Reduction Problem - 2 Focus: Unsupervised Dimensionality Reduction-PCA - 1 Focus: Unsupervised Dimensionality Reduction-PCA - 2 Question to be Answered Focus: Unsupervised Dimensionality Reduction-PCA - 2 Question to be Answered Outline: The Proposed UMPCA Algorithm - Tensor-to-Vector Projection Notations Elementary Multilinear Projection (EMP) Tensor-to-Vector Projection (TVP) Outline: The Proposed UMPCA Algorithm - Uncorrelated Multilinear PCA (UMPCA) The UMPCA Problem Formulation - 1 The UMPCA Problem Formulation - 2 The UMPCA Problem Formulation - 3 The UMPCA Problem Formulation - 4 The UMPCA Problem Formulation - 5 The Approach of Successive Maximization The Alternating Projection Method - 1 The Alternating Projection Method - 2 The UMPCA Solution - 1 The UMPCA Solution - 2 The UMPCA Solution - 3 The UMPCA Solution - 4 Solution for p > 1 - 1 Solution for p > 1 - 2 Outline: Experimental Evaluations - Experimental Setup Experimental Setup - 1 Experimental Setup - 2 Experimental Setup - 3 Outline: Experimental Evaluations - Experimental Results Recognition Results for L = 1 Recognition Results for L = 7 Examination of Variation Captured Recognition Results for L = 7 Recognition Results for L = 1 Recognition Results for L = 7 Examination of Variation Captured Examination of Correlations Among Features Summary - Questions

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# Description

Tensorial data are frequently encountered in various machine learning tasks today and dimensionality reduction is one of their most important applications. This paper extends the classical principal component analysis (PCA) to its multilinear version by proposing a novel dimensionality reduction algorithm for tensorial data, named as uncorrelated multilinear PCA (UMPCA). UMPCA seeks a tensor-to-vector projection that captures most of the variation in the original tensorial input while producing uncorrelated features through successive variance maximization. We evaluate the proposed algorithm on a second-order tensorial problem, face recognition, and the experimental results show its superiority, especially in low-dimensional spaces, through the comparison with three other PCA-based algorithms.

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1 Haiping Lu, March 15, 2011 at 9:05 a.m.:

This work is further extended to a journal publication below:
Haiping Lu, K.N. Plataniotis and A.N. Venetsanopoulos, "Uncorrelated Multilinear Principal Component Analysis for Unsupervised Multilinear Subspace Learning", IEEE Trans. on Neural Networks, vol. 20, no. 11, pp. 1820-1836, Nov. 2009.

Its relationship with other multilinear extensions of PCA is analyzed in the following paper:
Haiping Lu, K.N. Plataniotis and A.N. Venetsanopoulos, "A Survey of Multilinear Subspace Learning for Tensor Data", Pattern Recognition, vol. 44, no. 7, pp. 1540-1551, Jul. 2011.

2 Haiping Lu, February 28, 2012 at 12:13 p.m.:

The Matlab code for UMPCA is now available at the following URL:

Data and other resources are also included.

3 Haiping Lu, March 6, 2012 at 2:59 a.m.:

The Matlab code for UMPCA (including data and resources) is also available at Matlab Central:

http://www.mathworks.com/matlabcentra...

4 Haiping Lu, March 21, 2012 at 4:06 p.m.:

The Matlab code for a closely related algorithm Uncorrelated Multilinear Discriminant Analysis (UMLDA) is also available at Matlab Central (including data and resources):

http://www.mathworks.fr/matlabcentral...