Consistent and Specific Multi-View Subspace Clustering

Multi-view clustering has attracted intensive attention due to the effectiveness of exploiting multiple views of data. However, most existing multi-view clustering methods only aim to explore the consistency or enhance the diversity of different views. In this paper, we propose a novel multi-view subspace clustering method (CSMSC), where consistency and specificity are jointly exploited for subspace representation learning. We formulate the multi-view self-representation property using a shared consistent representation and a set of specific representations, which better fits the real-world datasets. Specifically, consistency models the common properties among all views, while specificity captures the inherent difference in each view. In addition, to optimize the nonconvex problem, we introduce a convex relaxation and develop an alternating optimization algorithm to recover the corresponding data representations. Experimental evaluations on four benchmark datasets demonstrate that the proposed approach achieves better performance over several state-of-thearts. Introduction Subspace clustering is essential to many scientific problems, e.g., representation learning (Liu and Yan 2011), motion segmentation (Rao et al. 2010) and image processing (Ma et al. 2007). Given data from multiple categories lying in a union of subspaces, clustering a dataset into categories reduces to assigning data to their respective subspaces, where each data sample is expressed by a linear combination of other samples in the same subspace. A number of subspace clustering methods have been developed in recent years (Parsons, Haque, and Liu 2004). For instance, sparse subspace clustering (Elhamifar and Vidal 2013) finds a sparse representation from the subspaces of the data. Besides, low-rank representation (Liu et al. 2013) explores the subspace structures by low-rank constraint to recover the data. After obtaining self-representation matrix of the data, spectral clustering (Ng, Jordan, and Weiss 2002) is applied to get the final clustering result. Additionally, innovation pursuit (Rahmani and Atia 2017) proposes another subspace discovery method, which identifies each subspace based on its novelty to other subspaces. ∗Corresponding author. Copyright c © 2018, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. Figure 1: Illustration of our CSMSC approach. Given data samples with V views X,X, · · · ,X , our method pursues a view-consistent self-representation matrix C and a set of view-specific self-representation matrices D,D, · · · ,D . The affinity matrix produced with C and {D}v∈[V ] will be used as input to the spectral clustering method to generate the final clustering result. Many real-world problems have representations with respect to multiple views (Blum and Mitchell 1998; Chaudhuri et al. 2009). For instance, an image is described by color, texture, edges and so on. A document can be simultaneously described by several different languages. Thus, methods only using single view information do not meet the real-world demand well. Based on a variety of theories, a lot of methods have been developed to extract comprehensive information from multiple views (Xu, Tao, and Xu 2013), including co-training (Blum and Mitchell 1998; Kumar, Rai, and Daumé 2011; Kumar and Daumé 2011), multiple kernel learning (Gönen and Alpaydın 2011) and subspace learning (Chaudhuri et al. 2009; Cao et al. 2015; Zhang et al. 2015; Xia et al. 2014). However, there are several main deficiencies for most existing methods. On one hand, single view methods do not leverage as much information as multi-view methods do. On the other hand, most multi-view methods only consider the consistency of multi-view data (Kumar and Daumé 2011; Kumar, Rai, and Daumé 2011; Zhang et al. 2015), or only explore the diversity of different subspace representations The Thirty-Second AAAI Conference on Artificial Intelligence (AAAI-18)