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: 15417


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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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Reviews and comments:

Comment1 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.

Comment2 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.

Comment3 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:


Comment4 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):


Comment5 Haiping Lu, May 20, 2014 at 3:31 a.m.:

A book on this topic is published by the CRC Press

A supporting website is at

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