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This paper constructs adaptive sparse grid collocation method onto arbitrary order piecewise polynomial space. The sparse grid method is a popular technique for high dimensional problems, and the associated collocation method has been well…
In recent years, network embedding methods have garnered increasing attention because of their effectiveness in various information retrieval tasks. The goal is to learn low-dimensional representations of vertexes in an information network…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
We propose an algorithmic framework for convex minimization problems of a composite function with two terms: a self-concordant function and a possibly nonsmooth regularization term. Our method is a new proximal Newton algorithm that…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
We study the recently introduced problem of finding dense common subgraphs: Given a sequence of graphs that share the same vertex set, the goal is to find a subset of vertices $S$ that maximizes some aggregate measure of the density of the…
Retrieving the most similar objects in a large-scale database for a given query is a fundamental building block in many application domains, ranging from web searches, visual, cross media, and document retrievals. State-of-the-art…
Computing over compressed data combines the space saving of data compression with efficient support for queries directly on the compressed representation. Such data structures are widely applied in text indexing and have been successfully…
Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost…
Given a network and a subset of interesting vertices whose identities are only partially known, the vertex nomination problem seeks to rank the remaining vertices in such a way that the interesting vertices are ranked at the top of the…
We describe a graph-based neural acceleration technique for nonnegative matrix factorization that builds upon a connection between matrices and bipartite graphs that is well-known in certain fields, e.g., sparse linear algebra, but has not…
In this paper, we consider convex quadratic optimization problems with indicator variables when the matrix $Q$ defining the quadratic term in the objective is sparse. We use a graphical representation of the support of $Q$, and show that if…
Consider two networks on overlapping, non-identical vertex sets. Given vertices of interest in the first network, we seek to identify the corresponding vertices, if any exist, in the second network. While in moderately sized networks graph…
We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. It…
Graphlet analysis is an approach to network analysis that is particularly popular in bioinformatics. We show how to set up a system of linear equations that relate the orbit counts and can be used in an algorithm that is significantly…
Many real-world datasets can be naturally represented as graphs, spanning a wide range of domains. However, the increasing complexity and size of graph datasets present significant challenges for analysis and computation. In response, graph…
Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…
Matching and partitioning problems are fundamentals of computer vision applications with examples in multilabel segmentation, stereo estimation and optical-flow computation. These tasks can be posed as non-convex energy minimization…
Subgraph queries also known as subgraph isomorphism search is a fundamental problem in querying graph-like structured data. It consists to enumerate the subgraphs of a data graph that match a query graph. This problem arises in many…
We introduce in this paper a new summarization method for large graphs. Our summarization approach retains only a user-specified proportion of the neighbors of each node in the graph. Our main aim is to simplify large graphs so that they…