Uncorrelated Multilinear Principal Component Analysis through Successive Variance Maximization
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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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.
The Matlab code for UMPCA is now available at the following URL:
Data and other resources are also included.
The Matlab code for UMPCA (including data and resources) is also available at Matlab Central:
The Matlab code for a closely related algorithm Uncorrelated Multilinear Discriminant Analysis (UMLDA) is also available at Matlab Central (including data and resources):
A book on this topic is published by the CRC Press
A supporting website is at
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