Auto-weighted multi-view clustering via deep matrix decomposition

Abstract Real data are often collected from multiple channels or comprised of different representations (i.e., views). Multi-view learning provides an elegant way to analyze the multi-view data for low-dimensional representation. In recent years, several multi-view learning methods have been designed and successfully applied in various tasks. However, existing multi-view learning methods usually work in a single layer formulation. Since the mapping between the obtained representation and the original data contains rather complex hierarchical information with implicit lower-level hidden attributes, it is desirable to fully explore the hidden structures hierarchically. In this paper, a novel deep multi-view clustering model is proposed by uncovering the hierarchical semantics of the input data in a layer-wise way. By utilizing a novel collaborative deep matrix decomposition framework, the hidden representations are learned with respect to different attributes. The proposed model is able to collaboratively learn the hierarchical semantics obtained by each layer. The instances from the same class are forced to be closer layer by layer in the low-dimensional space, which is beneficial for the subsequent clustering task. Furthermore, an idea weight is automatically assigned to each view without introducing extra hyperparameter as previous methods do. To solve the optimization problem of our model, an efficient iterative updating algorithm is proposed and its convergence is also guaranteed theoretically. Our empirical study on multi-view clustering task shows encouraging results of our model in comparison to the state-of-the-art algorithms.