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Co-clustering, that is, partitioning a numerical matrix into homogeneous submatrices, has many applications ranging from bioinformatics to election analysis. Many interesting variants of co-clustering are NP-hard. We focus on the basic…

Discrete Mathematics · Computer Science 2019-06-17 Laurent Bulteau , Vincent Froese , Sepp Hartung , Rolf Niedermeier

In this paper, we propose an unifying view of several recently proposed structured sparsity-inducing norms. We consider the situation of a model simultaneously (a) penalized by a set- function de ned on the support of the unknown parameter…

Machine Learning · Statistics 2012-05-08 Guillaume Obozinski , Francis Bach

We study exact recovery conditions for convex relaxations of point cloud clustering problems, focusing on two of the most common optimization problems for unsupervised clustering: $k$-means and $k$-median clustering. Motivations for…

Near isometric orthogonal embeddings to lower dimensions are a fundamental tool in data science and machine learning. In this paper, we present the construction of such embeddings that minimizes the maximum distortion for a given set of…

Machine Learning · Statistics 2017-12-15 Kshiteej Sheth , Dinesh Garg , Anirban Dasgupta

In the last few years, the notion of symmetry has provided a powerful and essential lens to view several optimization or sampling problems that arise in areas such as theoretical computer science, statistics, machine learning, quantum…

Data Structures and Algorithms · Computer Science 2021-09-03 Jonathan Leake , Nisheeth K. Vishnoi

In the Categorical Clustering problem, we are given a set of vectors (matrix) A={a_1,\ldots,a_n} over \Sigma^m, where \Sigma is a finite alphabet, and integers k and B. The task is to partition A into k clusters such that the median…

Data Structures and Algorithms · Computer Science 2021-04-19 Fedor V. Fomin , Petr A. Golovach , Nidhi Purohit

We consider the problem of correlation clustering on graphs with constraints on both the cluster sizes and the positive and negative weights of edges. Our contributions are twofold: First, we introduce the problem of correlation clustering…

Machine Learning · Computer Science 2015-05-25 Gregory J. Puleo , Olgica Milenkovic

Experimental mechanisms that yield the growth of homochiral copolymers over their heterochiral counterparts have been advocated by Lahav and co-workers. These chiral amplification mechanisms proceed through racemic {\beta}-sheet-controlled…

Quantitative Methods · Quantitative Biology 2012-12-19 Celia Blanco , David Hochberg

The subject of this paper is regularity-preserving aggregation of regular norms on finite-dimensional linear spaces. Regular norms were introduced in [5] and are closely related to ``type 2'' spaces [9, Chapter 9] playing important role in…

Optimization and Control · Mathematics 2024-02-13 Anatoli Juditsky , Arkadi Nemirovski

Finite mixture of skew distributions have emerged as an effective tool in modelling heterogeneous data with asymmetric features. With various proposals appearing rapidly in the recent years, which are similar but not identical, the…

Methodology · Statistics 2013-05-29 Sharon X. Lee , Geoffrey J. McLachlan

Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and…

Social and Information Networks · Computer Science 2015-07-02 David Hallac , Jure Leskovec , Stephen Boyd

We investigate new convex relaxations for the pooling problem, a classic nonconvex production planning problem in which input materials are mixed in intermediate pools, with the outputs of these pools further mixed to make output products…

Optimization and Control · Mathematics 2018-03-09 James Luedtke , Claudia D'Ambrosio , Jeff Linderoth , Jonas Schweiger

We present a comprehensive analysis of strong-lensing, weak-lensing shear and magnification data for a sample of 16 X-ray-regular and 4 high-magnification galaxy clusters selected from the CLASH survey. Our analysis combines constraints…

Cosmology and Nongalactic Astrophysics · Physics 2016-04-27 Keiichi Umetsu , Adi Zitrin , Daniel Gruen , Julian Merten , Megan Donahue , Marc Postman

We study the clustering task under anisotropic Gaussian Mixture Models where the covariance matrices from different clusters are unknown and are not necessarily the identical matrix. We characterize the dependence of signal-to-noise ratios…

Statistics Theory · Mathematics 2021-01-19 Xin Chen , Anderson Y. Zhang

We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion $\alpha$ of contaminating data to guarantee the robustness of the…

Statistics Theory · Mathematics 2008-12-18 Luis A. García-Escudero , Alfonso Gordaliza , Carlos Matrán , Agustin Mayo-Iscar

We consider the homogeneous and the non-homogeneous convex relaxations for combinatorial penalty functions defined on support sets. Our study identifies key differences in the tightness of the resulting relaxations through the notion of the…

Machine Learning · Computer Science 2018-03-08 Marwa El Halabi , Francis Bach , Volkan Cevher

We investigate generic inequalities of various contributions to the shear modulus $\mu$ in ensembles of amorphous elastic bodies. We focus first on a simple elastic network model with connectivity matrices (CMs) which are either annealed or…

Soft Condensed Matter · Physics 2025-01-07 J. P. Wittmer , H. Xu

We develop a new family of convex relaxations for $k$-means clustering based on sum-of-squares norms, a relaxation of the injective tensor norm that is efficiently computable using the Sum-of-Squares algorithm. We give an algorithm based on…

Machine Learning · Computer Science 2017-11-21 Pravesh K. Kothari , Jacob Steinhardt

In this paper, we formulate the problem of inferring a Finite Mixture Model from discrete data as an optimal transport problem with entropic regularization of parameter $\lambda\geq 0$. Our method unifies hard and soft clustering, the…

Machine Learning · Computer Science 2024-03-11 Jean-Frédéric Diebold , Nicolas Papadakis , Arnaud Dessein , Charles-Alban Deledalle

We use simulated merger trees of galaxy-cluster halos to study the effect of the halo concentration distribution on strong lensing and X-ray emission. Its log-normal shape typically found in simulations favors outliers with high…

Astrophysics · Physics 2009-11-13 C. Fedeli , M. Bartelmann , M. Meneghetti , L. Moscardini