Multiple view data, which have multiple representations from different feature spaces or graph spaces, arise in various data mining applications such as information retrieval, bioinformatics and social network analysis. Since different representations could have very different statistical properties, how to learn a consensus pattern from multiple representations is a challenging problem. In this paper, we propose a general model for multiple view unsupervised learning. The proposed model introduces the concept of mapping function to make the different patterns from different pattern spaces comparable and hence an optimal pattern can be learned from the multiple patterns of multiple representations. Under this model, we formulate two specific models for two important cases of unsupervised learning, clustering and spectral dimensionality reduction; we derive an iterating algorithm for multiple view clustering, and a simple algorithm providing a global optimum to multiple spectral dimensionality reduction. We also extend the proposed model and algorithms to evolutionary clustering and unsupervised learning with side information. Empirical evaluations on both synthetic and real data sets demonstrate the effectiveness of the proposed model and algorithms.
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