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Sequential or online dimensional reduction is of interests due to theexplosion of streaming data based applications and the requirement of adaptivestatistical modeling, in many emerging fields, such as the modeling of energyend-use profile. Principal Component Analysis (PCA), is the classical way ofdimensional reduction. However, traditional Singular Value Decomposition (SVD)based PCA fails to model data which largely deviates from Gaussiandistribution. The Bregman Divergence was recently introduced to achieve ageneralized PCA framework. If the random variable under dimensional reductionfollows Bernoulli distribution, which occurs in many emerging fields, thegeneralized PCA is called Logistic PCA (LPCA). In this paper, we extend thebatch LPCA to a sequential version (i.e. SLPCA), based on the sequential convexoptimization theory. The convergence property of this algorithm is discussedcompared to the batch version of LPCA (i.e. BLPCA), as well as its performancein reducing the dimension for multivariate binary-state systems. Itsapplication in building energy end-use profile modeling is also investigated.

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