We present a novel method for graph partitioning, based on reinforcement learning and graph convolutional neural networks. The new reinforcement learning based approach is used to refine a given partitioning obtained on a coarser representation of the graph, and the algorithm is applied recursively. The neural network is implemented using graph attention layers, and trained using an advantage actor critic (A2C) agent. We present two variants, one for finding an edge separator that minimizes the normalized cut or quotient cut, and one that finds a small vertex separator. The vertex separators are then used to construct a nested dissection ordering for permuting a sparse matrix so that its triangular factorization will incur less fill-in. The partitioning quality is compared with partitions obtained using METIS and Scotch, and the nested dissection ordering is evaluated in the sparse solver SuperLU. Our results show that the proposed method achieves similar partitioning quality than METIS and Scotch. Furthermore, the method generalizes from one class of graphs to another, and works well on a variety of graphs from the SuiteSparse sparse matrix collection.

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Multi-view clustering (MVC) has been extensively studied to collect multiple source information in recent years. One typical type of MVC methods is based on matrix factorization to effectively perform dimension reduction and clustering. However, the existing approaches can be further improved with following considerations: i) The current one-layer matrix factorization framework cannot fully exploit the useful data representations. ii) Most algorithms only focus on the shared information while ignore the view-specific structure leading to suboptimal solutions. iii) The partition level information has not been utilized in existing work. To solve the above issues, we propose a novel multi-view clustering algorithm via deep matrix decomposition and partition alignment. To be specific, the partition representations of each view are obtained through deep matrix decomposition, and then are jointly utilized with the optimal partition representation for fusing multi-view information. Finally, an alternating optimization algorithm is developed to solve the optimization problem with proven convergence. The comprehensive experimental results conducted on six benchmark multi-view datasets clearly demonstrates the effectiveness of the proposed algorithm against the SOTA methods.

Approximate Message Passing (AMP) algorithms have seen widespread use across a variety of applications. However, the precise forms for their Onsager corrections and state evolutions depend on properties of the underlying random matrix ensemble, limiting the extent to which AMP algorithms derived for white noise may be applicable to data matrices that arise in practice. In this work, we study more general AMP algorithms for random matrices $W$ that satisfy orthogonal rotational invariance in law, where $W$ may have a spectral distribution that is different from the semicircle and Marcenko-Pastur laws characteristic of white noise. The Onsager corrections and state evolutions in these algorithms are defined by the free cumulants or rectangular free cumulants of the spectral distribution of $W$. Their forms were derived previously by Opper, \c{C}akmak, and Winther using non-rigorous dynamic functional theory techniques, and we provide rigorous proofs. Our motivating application is a Bayes-AMP algorithm for Principal Components Analysis, when there is prior structure for the principal components (PCs) and possibly non-white noise. For sufficiently large signal strengths and any non-Gaussian prior distributions for the PCs, we show that this algorithm provably achieves higher estimation accuracy than the sample PCs.

1-planar graphs are graphs that can be drawn in the plane such that any edge intersects with at most one other edge. Ackerman showed that the edges of a 1-planar graph can be partitioned into a planar graph and a forest, and claims that the proof leads to a linear time algorithm. However, it is not clear how one would obtain such an algorithm from his proof. In this paper, we first reprove Ackerman's result (in fact, we prove a slightly more general statement) and then show that the split can be found in linear time by using an edge-contraction data structure by Holm et al.

Node classification is an important problem in graph data management. It is commonly solved by various label propagation methods that work iteratively starting from a few labeled seed nodes. For graphs with arbitrary compatibilities between classes, these methods crucially depend on knowing the compatibility matrix that must be provided by either domain experts or heuristics. Can we instead directly estimate the correct compatibilities from a sparsely labeled graph in a principled and scalable way? We answer this question affirmatively and suggest a method called distant compatibility estimation that works even on extremely sparsely labeled graphs (e.g., 1 in 10,000 nodes is labeled) in a fraction of the time it later takes to label the remaining nodes. Our approach first creates multiple factorized graph representations (with size independent of the graph) and then performs estimation on these smaller graph sketches. We define algebraic amplification as the more general idea of leveraging algebraic properties of an algorithm's update equations to amplify sparse signals. We show that our estimator is by orders of magnitude faster than an alternative approach and that the end-to-end classification accuracy is comparable to using gold standard compatibilities. This makes it a cheap preprocessing step for any existing label propagation method and removes the current dependence on heuristics.

We propose a scalable Gromov-Wasserstein learning (S-GWL) method and establish a novel and theoretically-supported paradigm for large-scale graph analysis. The proposed method is based on the fact that Gromov-Wasserstein discrepancy is a pseudometric on graphs. Given two graphs, the optimal transport associated with their Gromov-Wasserstein discrepancy provides the correspondence between their nodes and achieves graph matching. When one of the graphs has isolated but self-connected nodes ($i.e.$, a disconnected graph), the optimal transport indicates the clustering structure of the other graph and achieves graph partitioning. Using this concept, we extend our method to multi-graph partitioning and matching by learning a Gromov-Wasserstein barycenter graph for multiple observed graphs; the barycenter graph plays the role of the disconnected graph, and since it is learned, so is the clustering. Our method combines a recursive $K$-partition mechanism with a regularized proximal gradient algorithm, whose time complexity is $\mathcal{O}(K(E+V)\log_K V)$ for graphs with $V$ nodes and $E$ edges. To our knowledge, our method is the first attempt to make Gromov-Wasserstein discrepancy applicable to large-scale graph analysis and unify graph partitioning and matching into the same framework. It outperforms state-of-the-art graph partitioning and matching methods, achieving a trade-off between accuracy and efficiency.

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.

As a new classification platform, deep learning has recently received increasing attention from researchers and has been successfully applied to many domains. In some domains, like bioinformatics and robotics, it is very difficult to construct a large-scale well-annotated dataset due to the expense of data acquisition and costly annotation, which limits its development. Transfer learning relaxes the hypothesis that the training data must be independent and identically distributed (i.i.d.) with the test data, which motivates us to use transfer learning to solve the problem of insufficient training data. This survey focuses on reviewing the current researches of transfer learning by using deep neural network and its applications. We defined deep transfer learning, category and review the recent research works based on the techniques used in deep transfer learning.

We study the problem of learning to reason in large scale knowledge graphs (KGs). More specifically, we describe a novel reinforcement learning framework for learning multi-hop relational paths: we use a policy-based agent with continuous states based on knowledge graph embeddings, which reasons in a KG vector space by sampling the most promising relation to extend its path. In contrast to prior work, our approach includes a reward function that takes the accuracy, diversity, and efficiency into consideration. Experimentally, we show that our proposed method outperforms a path-ranking based algorithm and knowledge graph embedding methods on Freebase and Never-Ending Language Learning datasets.

We address the problem of learning vector representations for entities and relations in Knowledge Graphs (KGs) for Knowledge Base Completion (KBC). This problem has received significant attention in the past few years and multiple methods have been proposed. Most of the existing methods in the literature use a predefined characteristic scoring function for evaluating the correctness of KG triples. These scoring functions distinguish correct triples (high score) from incorrect ones (low score). However, their performance vary across different datasets. In this work, we demonstrate that a simple neural network based score function can consistently achieve near start-of-the-art performance on multiple datasets. We also quantitatively demonstrate biases in standard benchmark datasets, and highlight the need to perform evaluation spanning various datasets.

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