Network analysis of human brain connectivity is critically important for understanding brain function and disease states. Embedding a brain network as a whole graph instance into a meaningful low-dimensional representation can be used to investigate disease mechanisms and inform therapeutic interventions. Moreover, by exploiting information from multiple neuroimaging modalities or views, we are able to obtain an embedding that is more useful than the embedding learned from an individual view. Therefore, multi-view multi-graph embedding becomes a crucial task. Currently, only a few studies have been devoted to this topic, and most of them focus on the vector-based strategy which will cause structural information contained in the original graphs lost. As a novel attempt to tackle this problem, we propose Multi-view Multi-graph Embedding (M2E) by stacking multi-graphs into multiple partially-symmetric tensors and using tensor techniques to simultaneously leverage the dependencies and correlations among multi-view and multi-graph brain networks. Extensive experiments on real HIV and bipolar disorder brain network datasets demonstrate the superior performance of M2E on clustering brain networks by leveraging the multi-view multi-graph interactions.
Multi-view graph embedding and hub detection have both become widely studied problems in the area of graph learning. Both graph embedding and hub detection relate to the node clustering structure of graphs. The multi-view graph embedding usually implies the node clustering structure of the graph based on the multiple views, while hubs are the boundary-spanning nodes across different node clusters in the graph and thus may potentially influence the clustering structure of the graph. However, none of the existing works considered joint learning the multi-view embeddings and the hubs from multi-view graph data. In this paper, we propose to incorporate the hub detection task into the multi-view graph embedding framework so that the two tasks could benefit from each other. Specifically, we propose an auto-weighted framework of Multi-view Graph Embedding with Hub Detection (MVGE-HD) for brain network analysis. The MVGE-HD framework learns a unified graph embedding across all the views while reducing the potential influence of the hubs on blurring the boundaries between node clusters in the graph, thus leading to a clear and discriminative node clustering structure for the graph. We apply MVGE-HD on two real multi-view brain network datasets (i.e., HIV and Bipolar). The experimental results demonstrate the superior performance of the proposed framework in brain network analysis for clinical investigation and application. Many real-world datasets are comprised of different representations or views which often provide information complementary to each other. To integrate information from multiple views in the unsupervised setting, multiview clustering algorithms have been developed to cluster multiple views simultaneously to derive a solution which uncovers the common latent structure shared by multiple views. In this paper, we propose a novel NMFbased multi-view clustering algorithm by searching for a factorization that gives compatible clustering solutions across multiple views. The key idea is to formulate a joint matrix factorization process with the constraint that pushes clustering solution of each view towards a common consensus instead of fixing it directly. The main challenge is how to keep clustering solutions across different views meaningful and comparable. To tackle this challenge, we design a novel and effective normalization strategy inspired by the connection between NMF and PLSA. Experimental results on synthetic and several real datasets demonstrate the effectiveness of our approach. We propose a spectral clustering algorithm for the multi-view setting where we have access to multiple views of the data, each of which can be independently used for clustering. Our spectral clustering algorithm has a flavor of co-training, which is already a widely used idea in semi-supervised learning. We work on the assumption that the true underlying clustering would assign a point to the same cluster irrespective of the view. Hence, we constrain our approach to only search for the clusterings that agree across the views. Our algorithm does not have any hyperparameters to set, which is a major advantage in unsupervised learning. We empirically compare with a number of baseline methods on synthetic and real-world datasets to show the efficacy of the proposed algorithm. With advances in data collection technologies, multiple data sources are assuming increasing prominence in many applications. Clustering from multiple data sources has emerged as a topic of critical significance in the data mining and machine learning community. Different data sources provide different levels of necessarily detailed knowledge. Thus, combining multiple data sources is pivotal to facilitate the clustering process. However, in reality, the data usually exhibits heterogeneity and incompleteness. The key challenge is how to effectively integrate information from multiple heterogeneous sources in the presence of missing data. Conventional methods mainly focus on clustering heterogeneous data with full information in all sources or at least one source without missing values. In this paper, we propose a more general framework T-MIC (Tensor based Multi-source Incomplete data Clustering) to integrate multiple incomplete data sources. Specifically, we first use the kernel matrices to form an initial tensor across all the multiple sources. Then we formulate a joint tensor factorization process with the sparsity constraint and use it to iteratively push the initial tensor towards a quality-driven exploration of the latent factors by taking into account missing data uncertainty. Finally, these factors serve as features to clustering. Extensive experiments on both synthetic and real datasets demonstrate that our proposed approach can effectively boost clustering performance, even with large amounts of missing data.  Graph-based approaches have been successful in unsupervised and semi-supervised learning. In this paper, we focus on the real-world applications where the same instance can be represented by multiple heterogeneous features. The key point of utilizing the graph-based knowledge to deal with this kind of data is to reasonably integrate the different representations and obtain the most consistent manifold with the real data distributions. In this paper, we propose a novel framework via the reformulation of the standard spectral learning model, which can be used for multiview clustering and semisupervised tasks. Unlike other methods in the literature, the proposed methods can learn an optimal weight for each graph automatically without introducing an additive parameter as previous methods do. Furthermore, our objective under semisupervised learning is convex and the global optimal result will be obtained. Extensive empirical results on different real-world data sets demonstrate that the proposed methods achieve comparable performance with the state-of-the-art approaches and can be used more practically.