Learning Inter- and Intra-manifolds for Matrix Factorization-based Multi-Aspect Data Clustering

Abstract--Clustering on the data with multiple aspects, such as multi-view or multi-type relational data, has become popular in recent years due to their wide applicability. The approach using manifold learning with the Nonnegative Matrix Factorization (NMF) framework, that learns the accurate low-rank representation of the multidimensional data, has shown effectiveness. We propose to include the inter-manifold in the NMF framework, utilizing the distance information of data points of different data types (or views) to learn the diverse manifold for data clustering. Empirical analysis reveals that the proposed method can find partial representations of various interrelated types and select useful features during clustering. Results on several datasets demonstrate that the proposed method outperforms the state-of-the-art multi-aspect data clustering methods in both accuracy and efficiency. This can be (1) multi-view data where samples For instance, in Figure 1.a, three intra-type relationship are represented by multiple views; or (2) multi-type matrices will store intra-similarities between Webpages, relational data (MTRD) where samples are represented by between Terms and between Hyperlinks, and three interrelationships different data types and their inherent relationships.