Related papers: Exact and Heuristic Algorithms for Constrained Bic…

The primary goal in cluster analysis is to discover natural groupings of objects. The field of cluster analysis is crowded with diverse methods that make special assumptions about data and address different scientific aims. Despite its…

Given a bipartite graph, the maximum balanced biclique (\textsf{MBB}) problem, discovering a mutually connected while equal-sized disjoint sets with the maximum cardinality, plays a significant role for mining the bipartite graph and has…

Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large…

We analyze the clustering problem through a flexible probabilistic model that aims to identify an optimal partition on the sample X 1 , ..., X n. We perform exact clustering with high probability using a convex semidefinite estimator that…

Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…

We study applications of clustering (in particular, the $k$-center clustering problem) in the design of efficient and practical algorithms for computing an approximate and the exact arithmetic matrix product of two 0-1 rectangular matrices…

We present BiqBin, an exact solver for linearly constrained binary quadratic problems. Our approach is based on an exact penalty method to first efficiently transform the original problem into an instance of Max-Cut, and then to solve the…

With the aggressive scaling of VLSI technology, the explosion of layout patterns creates a critical bottleneck for DFM applications like OPC. Pattern clustering is essential to reduce data complexity, yet existing methods struggle with…

Semidefinite programming (SDP) is a powerful tool for tackling a wide range of computationally hard problems such as clustering. Despite the high accuracy, semidefinite programs are often too slow in practice with poor scalability on large…

The problem of identifying the maximum edge biclique in bipartite graphs has attracted considerable attention in bipartite graph analysis, with numerous real-world applications such as fraud detection, community detection, and online…

In sampling theory, stratification corresponds to a technique used in surveys, which allows segmenting a population into homogeneous subpopulations (strata) to produce statistics with a higher level of precision. In particular, this article…

Packing optimization is a prevalent problem that necessitates robust and efficient algorithms that are also simple to implement. One group of approaches is the raster methods, which rely on approximating the objects with pixelated…

In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor…

Contraction Clustering (RASTER) is a single-pass algorithm for density-based clustering of 2D data. It can process arbitrary amounts of data in linear time and in constant memory, quickly identifying approximate clusters. It also exhibits…

Clustering is often a challenging problem because of the inherent ambiguity in what the "correct" clustering should be. Even when the number of clusters $K$ is known, this ambiguity often still exists, particularly when there is variation…

We study here the semi-supervised $k$-clustering problem where information is available on whether pairs of objects are in the same or in different clusters. This information is either available with certainty or with a limited level of…

Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…

Clustering large, mixed data is a central problem in data mining. Many approaches adopt the idea of k-means, and hence are sensitive to initialisation, detect only spherical clusters, and require a priori the unknown number of clusters. We…

The cyclic block coordinate descent-type (CBCD-type) methods, which performs iterative updates for a few coordinates (a block) simultaneously throughout the procedure, have shown remarkable computational performance for solving strongly…

The bipartite graph structure has shown its promising ability in facilitating the subspace clustering and spectral clustering algorithms for large-scale datasets. To avoid the post-processing via k-means during the bipartite graph…