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.
Xie
Xianchao
X
Department of Statistics, Harvard University Science Center, Cambridge, MA 02138-2901, USA. xxie@fas.harvard.edu
Yan
Shuicheng
S
Kwok
James T
JT
Huang
Thomas S
TS
D001185:Artificial Intelligence; D001699:Biometry / Q000379:methods*; D005145:Face / Q000033:anatomy & histology*; D005163:Factor Analysis, Statistical; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D015999:Multivariate Analysis; D010363:Pattern Recognition, Automated / Q000379:methods*