Sequential Logistic Principal Component Analysis (SLPCA): Dimensional Reduction in Streaming Multivariate Binary-State System

Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use profile. Principal Component Analysis (PCA), is the classical way of dimensional reduction. However, traditional PCA coincides with maximum likelihood interpretation only when data follows Gaussian distribution. The Bregman Divergence was introduced to extend PCA with maximum likelihood in exponential family distribution. In this work, we study this generalized form PCA for Bernoulli variables, which is called Logistic PCA (LPCA). We extend the batch-mode LPCA to a sequential version (SLPCA). The convergence property of this algorithm is discussed compared to the batch version (BLPCA), as well as its performance in reducing the dimension for multivariate binary-state systems. Its application in building energy end-use profile modeling is also investigated.