text: Real-world social networks and digital platforms are comprised of individuals (nodes) that are linked to other individuals or entities through multiple types of relationships (links). Sub-networks of such a network based on each type of link correspond to distinct views of the underlying network. In real-world applications, each node is typically linked to only a small subset of other nodes. Hence, practical approaches to problems such as node labeling have to cope with the resulting sparse networks. While low-dimensional network embeddings offer a promising approach to this problem, most of the current network embedding methods focus primarily on single view networks. We introduce a novel multi-view network embedding (MVNE) algorithm for constructing low-dimensional node embeddings from multi-view networks. MVNE adapts and extends an approach to single view network embedding (SVNE) using graph factorization clustering (GFC) to the multi-view setting using an objective function that maximizes the agreement between views based on both the local and global structure of the underlying multi-view graph. Our experiments with several benchmark real-world single view networks show that GFC-based SVNE yields network embeddings that are competitive with or superior to those produced by the state-of-the-art single view network embedding methods when the embeddings are used for labeling unlabeled nodes in the networks. Our experiments with several multi-view networks show that MVNE substantially outperforms the single view methods on integrated view and the state-of-the-art multi-view methods. We further show that even when the goal is to predict labels of nodes within a single target view, MVNE outperforms its single-view counterpart suggesting that the MVNE is able to extract the information that is useful for labeling nodes in the target view from the all of the views.
  @cite_13: The Co-Training algorithm uses unlabeled examples in multiple views to bootstrap classifiers in each view, typically in a greedy manner, and operating under assumptions of view-independence and compatibility. In this paper, we propose a Co-Regularization framework where classifiers are learnt in each view through forms of multi-view regularization. We propose algorithms within this framework that are based on optimizing measures of agreement and smoothness over labeled and unlabeled examples. These algorithms naturally extend standard regularization methods like Support Vector Machines (SVM) and Regularized Least squares (RLS) for multi-view semi-supervised learning, and inherit their benefits and applicability to high-dimensional classification problems. An empirical investigation is presented that confirms the promise of this approach.
  @cite_41: 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.
  @cite_32: Real-world relations among entities can often be observed and determined by different perspectives views. For example, the decision made by a user on whether to adopt an item relies on multiple aspects such as the contextual information of the decision, the item’s attributes, the user’s profile and the reviews given by other users. Different views may exhibit multi-way interactions among entities and provide complementary information. In this paper, we introduce a multi-tensor-based approach that can preserve the underlying structure of multi-view data in a generic predictive model. Specifically, we propose structural factorization machines (SFMs) that learn the common latent spaces shared by multi-view tensors and automatically adjust the importance of each view in the predictive model. Furthermore, the complexity of SFMs is linear in the number of parameters, which make SFMs suitable to large-scale problems. Extensive experiments on real-world datasets demonstrate that the proposed SFMs outperform several state-of-the-art methods in terms of prediction accuracy and computational cost.
  @cite_0: In recent years, a great many methods of learning from multi-view data by considering the diversity of different views have been proposed. These views may be obtained from multiple sources or different feature subsets. In trying to organize and highlight similarities and differences between the variety of multi-view learning approaches, we review a number of representative multi-view learning algorithms in different areas and classify them into three groups: 1) co-training, 2) multiple kernel learning, and 3) subspace learning. Notably, co-training style algorithms train alternately to maximize the mutual agreement on two distinct views of the data; multiple kernel learning algorithms exploit kernels that naturally correspond to different views and combine kernels either linearly or non-linearly to improve learning performance; and subspace learning algorithms aim to obtain a latent subspace shared by multiple views by assuming that the input views are generated from this latent subspace. Though there is significant variance in the approaches to integrating multiple views to improve learning performance, they mainly exploit either the consensus principle or the complementary principle to ensure the success of multi-view learning. Since accessing multiple views is the fundament of multi-view learning, with the exception of study on learning a model from multiple views, it is also valuable to study how to construct multiple views and how to evaluate these views. Overall, by exploring the consistency and complementary properties of different views, multi-view learning is rendered more effective, more promising, and has better generalization ability than single-view learning.
  @cite_5: 
  @cite_31: Multi-view clustering has become a widely studied problem in the area of unsupervised learning. It aims to integrate multiple views by taking advantages of the consensus and complimentary information from multiple views. Most of the existing works in multi-view clustering utilize the vector-based representation for features in each view. However, in many real-world applications, instances are represented by graphs, where those vector-based models cannot fully capture the structure of the graphs from each view. To solve this problem, in this paper we propose a Multi-view Clustering framework on graph instances with Graph Embedding (MCGE). Specifically, we model the multi-view graph data as tensors and apply tensor factorization to learn the multi-view graph embeddings, thereby capturing the local structure of graphs. We build an iterative framework by incorporating multi-view graph embedding into the multi-view clustering task on graph instances, jointly performing multi-view clustering and multi-view graph embedding simultaneously. The multi-view clustering results are used for refining the multi-view graph embedding, and the updated multi-view graph embedding results further improve the multi-view clustering. Extensive experiments on two real brain network datasets (i.e., HIV and Bipolar) demonstrate the superior performance of the proposed MCGE approach in multi-view connectome analysis for clinical investigation and application.
  @cite_20: In many clustering problems, we have access to multiple views of the data each of which could be individually used for clustering. Exploiting information from multiple views, one can hope to find a clustering that is more accurate than the ones obtained using the individual views. Often these different views admit same underlying clustering of the data, so we can approach this problem by looking for clusterings that are consistent across the views, i.e., corresponding data points in each view should have same cluster membership. We propose a spectral clustering framework that achieves this goal by co-regularizing the clustering hypotheses, and propose two co-regularization schemes to accomplish this. Experimental comparisons with a number of baselines on two synthetic and three real-world datasets establish the efficacy of our proposed approaches.
  @cite_10: Graph classification has traditionally focused on graphs generated from a single feature view. In many applications, it is common to have useful information from different channels views to describe objects, which naturally results in a new representation with multiple graphs generated from different feature views being used to describe one object. In this paper, we formulate a new Multi-Graph-View learning task for graph classification, where each object to be classified contains graphs from multiple graph-views. This problem setting is essentially different from traditional single-graph-view graph classification, where graphs are from one single feature view. To solve the problem, we propose a Cross Graph-View Sub graph Feature based Learning (gCGVFL) algorithm that explores an optimal set of sub graphs, across multiple graph-views, as features to represent graphs. Specifically, we derive an evaluation criterion to estimate the discriminative power and the redundancy of sub graph features across all views, and assign proper weight values to each view to indicate its importance for graph classification. The iterative cross graph-view sub graph scoring and graph-view weight updating form a closed loop to find optimal sub graphs to represent graphs for multi-graph-view learning. Experiments and comparisons on real-world tasks demonstrate the algorithm's performance.
  @cite_12: Multi-view learning or learning with multiple distinct feature sets is a rapidly growing direction in machine learning with well theoretical underpinnings and great practical success. This paper reviews theories developed to understand the properties and behaviors of multi-view learning and gives a taxonomy of approaches according to the machine learning mechanisms involved and the fashions in which multiple views are exploited. This survey aims to provide an insightful organization of current developments in the field of multi-view learning, identify their limitations, and give suggestions for further research. One feature of this survey is that we attempt to point out specific open problems which can hopefully be useful to promote the research of multi-view machine learning.
summary: There is a growing body of recent works on multi-view learning algorithms, e.g., @cite_41 @cite_10 @cite_31 , that attempt to integrate information across the multiple views to optimize the predictive performance of the classifier (see @cite_0 @cite_12 ). Some multi-view learning methods seek to maximize the agreement between views using regularization @cite_13 @cite_20 whereas others seek to optimally selecting subsets of features from different views for each prediction task @cite_5 @cite_32 However, these methods were not designed for network embedding. Most of the existing multi-view learning algorithms are either not directly applicable to multi-view networks or are not designed to cope with high degrees of data sparsity, a key challenge in modeling real-world multi-view networks.