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Learning distributed representations for nodes in graphs is a crucial primitive in network analysis with a wide spectrum of applications. Linear graph embedding methods learn such representations by optimizing the likelihood of both…

Finding the reduced-dimensional structure is critical to understanding complex networks. Existing approaches such as spectral clustering are applicable only when the full network is explicitly observed. In this paper, we focus on the online…

In this paper, we propose a simple but effective method for fast image segmentation. We re-examine the locality-preserving character of spectral clustering by constructing a graph over image regions with both global and local connections.…

Molecular profiling data (e.g., gene expression) has been used for clinical risk prediction and biomarker discovery. However, it is necessary to integrate other prior knowledge like biological pathways or gene interaction networks to…

Given two input graphs, finding the largest subgraph that occurs in both, i.e., finding the maximum common subgraph, is a fundamental operator for evaluating the similarity between two graphs in graph data analysis. Existing works for…

Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…

Clustering is a well-known and important problem with numerous applications. The graph-based model is one of the typical cluster models. In the graph model, clusters are generally defined as cliques. However, such an approach might be too…

Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of…

We show, for any positive integer k, that there exists a graph in which any equitable partition of its vertices into k parts has at least ck^2/\log^* k pairs of parts which are not \epsilon-regular, where c,\epsilon>0 are absolute…

Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…

For the high dimensional data representation, nonnegative tensor ring (NTR) decomposition equipped with manifold learning has become a promising model to exploit the multi-dimensional structure and extract the feature from tensor data.…

Fox, Gromov, Lafforgue, Naor, and Pach proved a regularity lemma for semi-algebraic $k$-uniform hypergraphs of bounded complexity, showing that for each $\epsilon>0$ the vertex set can be equitably partitioned into a bounded number of parts…

Link prediction in graphs is an important task in the fields of network science and machine learning. We investigate a flexible means of regularization for link prediction based on an approximation of the Kolmogorov complexity of graphs…

Given a massive graph, how can we exploit its hierarchical structure for concisely but exactly summarizing the graph? By exploiting the structure, can we achieve better compression rates than state-of-the-art graph summarization methods?…

The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is…

Dominating Set is a well-known combinatorial optimization problem which finds application in computational biology or mobile communication. Because of its $\mathrm{NP}$-hardness, one often turns to heuristics for good solutions. Many such…

Merging the two cultures of deep and statistical learning provides insights into structured high-dimensional data. Traditional statistical modeling is still a dominant strategy for structured tabular data. Deep learning can be viewed…

In this paper we present a generalized Deep Learning-based approach for solving ill-posed large-scale inverse problems occuring in medical image reconstruction. Recently, Deep Learning methods using iterative neural networks and cascaded…

Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…

Excessive computational cost for learning large data and streaming data can be alleviated by using stochastic algorithms, such as stochastic gradient descent and its variants. Recent advances improve stochastic algorithms on convergence…