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Matrix-Variate Factor Analysis and Its Applications

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4 Author(s)
Xianchao Xie ; Dept. of Stat., Harvard Univ. Sci. Center, Cambridge, MA ; Shuicheng Yan ; Kwok, J.T. ; Huang, T.S.

Factor analysis (FA) seeks to reveal the relationship between an observed vector variable and a latent variable of reduced dimension. It has been widely used in many applications involving high-dimensional data, such as image representation and face recognition. An intrinsic limitation of FA lies in its potentially poor performance when the data dimension is high, a problem known as curse of dimensionality. Motivated by the fact that images are inherently matrices, we develop, in this brief, an FA model for matrix-variate variables and present an efficient parameter estimation algorithm. Experiments on both toy and real-world image data demonstrate that the proposed matrix-variant FA model is more efficient and accurate than the classical FA approach, especially when the observed variable is high-dimensional and the samples available are limited.

Published in:

Neural Networks, IEEE Transactions on  (Volume:19 ,  Issue: 10 )