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Hierarchical clustering is a stronger extension of one of today's most influential unsupervised learning methods: clustering. The goal of this method is to create a hierarchy of clusters, thus constructing cluster evolutionary history and…
We present a progress on local computation algorithms for two coloring of $k$-uniform hypergraphs. We focus on instances that satisfy strengthened assumption of Local Lemma of the form $2^{1-\alpha k} (\Delta+1) e < 1$, where $\Delta$ is…
We provide a simple and novel algorithmic design technique, for which we call iterative partial rounding, that gives a tight rounding-based approximation for vertex cover with hard capacities (VC-HC). In particular, we obtain an…
We propose a theoretical framework of multi-way similarity to model real-valued data into hypergraphs for clustering via spectral embedding. For graph cut based spectral clustering, it is common to model real-valued data into graph by…
This paper proposes a new algorithm for simultaneous graph matching and clustering. For the first time in the literature, these two problems are solved jointly and synergetically without relying on any training data, which brings advantages…
We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning…
Irregular computations on unstructured data are an important class of problems for parallel programming. Graph coloring is often an important preprocessing step, e.g. as a way to perform dependency analysis for safe parallel execution. The…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
Clique-width is one of the graph complexity measures leading to polynomial special-case algorithms for generally NP-complete problems, e.g. graph colourability. The best two currently known algorithms for verifying c-colourability of graphs…
We introduce the partition function of edge-colored graph homomorphisms, of which the usual partition function of graph homomorphisms is a specialization, and present an efficient algorithm to approximate it in a certain domain. Corollaries…
Large-scale L1-regularized loss minimization problems arise in high-dimensional applications such as compressed sensing and high-dimensional supervised learning, including classification and regression problems. High-performance algorithms…
Recent developments in approximate counting have made startling progress in developing fast algorithmic methods for approximating the number of solutions to constraint satisfaction problems (CSPs) with large arities, using connections to…
Subspace clustering becomes inherently difficult near intersections, where points from different subspaces are barely separated. Most existing theoretical results address this issue by imposing separation or sampling assumptions that limit…
As the data size in Machine Learning fields grows exponentially, it is inevitable to accelerate the computation by utilizing the ever-growing large number of available cores provided by high-performance computing hardware. However, existing…
This paper studies the hierarchical clustering problem, where the goal is to produce a dendrogram that represents clusters at varying scales of a data set. We propose the ParChain framework for designing parallel hierarchical agglomerative…
Clustering a graph means identifying internally dense subgraphs which are only sparsely interconnected. Formalizations of this notion lead to measures that quantify the quality of a clustering and to algorithms that actually find…
This paper proposes a Mixed-Integer Linear Programming approach for the Soft Graph Clustering Problem. This is the first method that simultaneously allocates membership proportion for vertices that lie in multiple clusters, and that…
A pair of complementary algorithms are presented. One of the pair is a fast method for connecting graphs with an edge. The other is a fast method for removing edges from a graph. Both algorithms employ the same tree based graph…
We propose a novel approach for optimizing the graph ratio-cut by modeling the binary assignments as random variables. We provide an upper bound on the expected ratio-cut, as well as an unbiased estimate of its gradient, to learn the…
Given an edge-colored graph, the goal of the proportional fair matching problem is to find a maximum weight matching while ensuring proportional representation (with respect to the number of edges) of each color. The colors may correspond…