  Principal component analysis (PCA) is a popular dimension reduction technique
for vector data. Factored PCA (FPCA) is a probabilistic extension of PCA for
matrix data, which can substantially reduce the number of parameters in PCA
while yield satisfactory performance. However, FPCA is based on the Gaussian
assumption and thereby susceptible to outliers. Although the multivariate $t$
distribution as a robust modeling tool for vector data has a very long history,
its application to matrix data is very limited. The main reason is that the
dimension of the vectorized matrix data is often very high and the higher the
dimension, the lower the breakdown point that measures the robustness. To solve
the robustness problem suffered by FPCA and make it applicable to matrix data,
in this paper we propose a robust extension of FPCA (RFPCA), which is built
upon a $t$-type distribution called matrix-variate $t$ distribution. Like the
multivariate $t$ distribution, the matrix-variate $t$ distribution can
adaptively down-weight outliers and yield robust estimates. We develop a fast
EM-type algorithm for parameter estimation. Experiments on synthetic and
real-world datasets reveal that RFPCA is compared favorably with several
related methods and RFPCA is a simple but powerful tool for matrix-valued
outlier detection.
