Probabilistic Relational PCA

By explicitly modeling covariance between instances as derived from the relational information, a novel probabilistic dimensionality reduction method is proposed, called Probabilistic relational PCA (PRPCA), for relational data analysis.

Abstract

Principal component analysis (PCA) has been successfully used for data analysis in many applications. Probabilistic PCA (PPCA) provides a probabilistic formulation of PCA, bringing about additional advantages such as the ability of dealing with missing data. One crucial assumption made by both PCA and PPCA is that the instances are independent and identically distributed (i.i.d.). However, it is not uncommon for some real-world data, such as web pages and research papers, to contain relation (link) structure in addition to textual content information. Different instances in such data are correlated (linked) with each other, which implies that the common i.i.d. assumption is unreasonable for such relational data. In this paper, by explicitly modeling the covariance between instances as derived from the relational information, we propose a novel probabilistic dimensionality reduction method, called probabilistic relational PCA (PRPCA), for relational data analysis. Although the i.i.d. assumption is no longer adopted in PRPCA, the learning algorithms for PRPCA can still be devised easily like those for PPCA which makes explicit use of the i.i.d. assumption. Extensive experiments on some realworld data sets show that PRPCA can effectively utilize the relational information to dramatically outperform PCA and achieve state-of-the-art performance. 1