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Related papers: An Approximation Ratio for Biclustering

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Biclustering is a powerful approach to search for patterns in data, as it can be driven by a function that measures the quality of diverse types of patterns of interest. However, due to its computational complexity, the exploration of the…

Machine Learning · Computer Science 2021-04-27 Marcin Michalak , Jesús S. Aguilar-Ruiz

This paper introduces an efficient algorithm for computing the best approximation of a given matrix onto the intersection of linear equalities, inequalities and the doubly nonnegative cone (the cone of all positive semidefinite matrices…

Optimization and Control · Mathematics 2018-03-20 Ying Cui , Defeng Sun , Kim-Chuan Toh

Correlation clustering is a central topic in unsupervised learning, with many applications in ML and data mining. In correlation clustering, one receives as input a signed graph and the goal is to partition it to minimize the number of…

Data Structures and Algorithms · Computer Science 2021-06-17 Vincent Cohen-Addad , Silvio Lattanzi , Slobodan Mitrović , Ashkan Norouzi-Fard , Nikos Parotsidis , Jakub Tarnawski

We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…

Machine Learning · Statistics 2020-03-03 Bradley S. Price , Aaron J. Molstad , Ben Sherwood

Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…

Optimization and Control · Mathematics 2017-12-27 Kun Yuan , Bicheng Ying , Xiaochuan Zhao , Ali H. Sayed

Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…

Data Structures and Algorithms · Computer Science 2019-08-07 Brian Brubach , Karthik Abinav Sankararaman , Aravind Srinivasan , Pan Xu

Microarray techniques are widely used in Gene expression analysis. These techniques are based on discovering submatrices of genes that share similar expression patterns across a set of experimental conditions with coherence constraint.…

Quantitative Methods · Quantitative Biology 2020-01-27 Bilal Taher , Muhammad. H Fares , Saeed Jalili

This article proposes a biconvex modification to convex biclustering in order to improve its performance in high-dimensional settings. In contrast to heuristics that discard a subset of noisy features a priori, our method jointly learns and…

Machine Learning · Statistics 2026-04-13 Sam Rosen , Eric C. Chi , Jason Xu

We give the first $2$-approximation algorithm for the cluster vertex deletion problem. This is tight, since approximating the problem within any constant factor smaller than $2$ is UGC-hard. Our algorithm combines the previous approaches,…

Combinatorics · Mathematics 2021-10-19 Manuel Aprile , Matthew Drescher , Samuel Fiorini , Tony Huynh

The goal of clustering is to group similar objects into meaningful partitions. This process is well understood when an explicit similarity measure between the objects is given. However, far less is known when this information is not readily…

Machine Learning · Computer Science 2020-10-12 Michaël Perrot , Pascal Mattia Esser , Debarghya Ghoshdastidar

We study the problem of approximating a matrix $\mathbf{A}$ with a matrix that has a fixed sparsity pattern (e.g., diagonal, banded, etc.), when $\mathbf{A}$ is accessed only by matrix-vector products. We describe a simple randomized…

Data Structures and Algorithms · Computer Science 2024-03-27 Noah Amsel , Tyler Chen , Feyza Duman Keles , Diana Halikias , Cameron Musco , Christopher Musco

A new fast algorithm for clustering and classification of large collections of text documents is introduced. The new algorithm employs the bipartite graph that realizes the word-document matrix of the collection. Namely, the modularity of…

Information Retrieval · Computer Science 2011-05-31 Grigory Pivovarov , Sergei Trunov

The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…

Numerical Analysis · Mathematics 2025-08-07 Chinmay Kumar Giri , Debasisha Mishra

This paper considers the problem of completing a matrix with many missing entries under the assumption that the columns of the matrix belong to a union of multiple low-rank subspaces. This generalizes the standard low-rank matrix completion…

Information Theory · Computer Science 2011-12-30 Brian Eriksson , Laura Balzano , Robert Nowak

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

Numerical Analysis · Mathematics 2014-07-01 Gil Shabat , Yaniv Shmueli , Amir Averbuch

Identifying clusters of similar objects in data plays a significant role in a wide range of applications. As a model problem for clustering, we consider the densest k-disjoint-clique problem, whose goal is to identify the collection of k…

Optimization and Control · Mathematics 2015-03-20 Brendan P. W. Ames

In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…

Optimization and Control · Mathematics 2023-05-05 Bharat Kumar , Deepmala , A. K. Das

We study the problem of graph clustering under a broad class of objectives in which the quality of a cluster is defined based on the ratio between the number of edges in the cluster, and the total weight of vertices in the cluster. We show…

Data Structures and Algorithms · Computer Science 2023-01-02 Jakub Łącki , Vahab Mirrokni , Christian Sohler

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…

Machine Learning · Computer Science 2021-04-23 Kun Li , Liang Yuan , Yunquan Zhang , Gongwei Chen

In two earlier papers, we designed a distributed deterministic asynchronous algorithm for minimizing the sum of subdifferentiable and proximable functions and a regularizing quadratic on time-varying graphs based on Dykstra's algorithm, or…

Optimization and Control · Mathematics 2018-08-23 C. H. Jeffrey Pang