Matrix-Variate Factor Analysis and Its Applications

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.