Robust multivariate L1 principal component analysis and dimensionality reduction

Further to our recent work on the robust L1 PCA we introduce a new version of robust PCA model based on the so-called multivariate Laplace distribution (called L1 distribution) proposed in Eltoft et al. [2006. On the multivariate Laplace distribution. IEEE Signal Process. Lett. 13(5), 300-303]. Due to the heavy tail and high component dependency characteristics of the multivariate L1 distribution, the proposed model is expected to be more robust against data outliers and fitting component dependency. Additionally, we demonstrate how a variational approximation scheme enables effective inference of key parameters in the probabilistic multivariate L1-PCA model. By doing so, a tractable Bayesian inference can be achieved based on the variational EM-type algorithm.