相关论文: Clustering, Hamming Embedding, Generalized LSH and…

The mechanisms by which certain training interventions, such as increasing learning rates and applying batch normalization, improve the generalization of deep networks remains a mystery. Prior works have speculated that "flatter" solutions…

The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by…

The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice.…

We examine methods for clustering in high dimensions. In the first part of the paper, we perform an experimental comparison between three batch clustering algorithms: the Expectation-Maximization (EM) algorithm, a winner take all version of…

Multibang regularization and combinatorial integral approximation decompositions are two actively researched techniques for integer optimal control. We consider a class of polyhedral functions that arise particularly as convex lower…

We present the results of a numerical study based on the analysis of the MUSIC-2 simulations, aimed at estimating the expected concentration-mass relation for the CLASH cluster sample. We study nearly 1400 halos simulated at high spatial…

We study the clustering problem for mixtures of bounded covariance distributions, under a fine-grained separation assumption. Specifically, given samples from a $k$-component mixture distribution $D = \sum_{i =1}^k w_i P_i$, where each $w_i…

Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…

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…

Maximum likelihood estimation problems are, in general, intractable optimization problems. As a result, it is common to approximate the maximum likelihood estimator (MLE) using convex relaxations. In some cases, the relaxation is tight: it…

We consider the problem of minimizing a block separable convex function (possibly nondifferentiable, and including constraints) plus Laplacian regularization, a problem that arises in applications including model fitting, regularizing…

We conduct an in-depth analysis of the Bayes risk of clustering in the context of Hidden Markov and i.i.d. models. In both settings, we identify the situations where this risk is comparable to the Bayes risk of classification and those…

The hybrid clustering-classification neural network is proposed. This network allows increasing a quality of information processing under the condition of overlapping classes due to the rational choice of a learning rate parameter and…

In this paper, we study the problem of fair sparse regression on a biased dataset where bias depends upon a hidden binary attribute. The presence of a hidden attribute adds an extra layer of complexity to the problem by combining sparse…

Heterogeneous Information Network (HIN) embedding refers to the low-dimensional projections of the HIN nodes that preserve the HIN structure and semantics. HIN embedding has emerged as a promising research field for network analysis as it…

This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special…

A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the general inverse…

We consider the Lam\'e system of linear elasticity when the inclusion has the extreme elastic constants. We show that the solutions to the Lam\'e system converge in appropriate $H^1$-norms when the shear modulus tends to infinity (the other…

Galaxy cluster mergers are representative of a wide range of physics, making them an excellent probe of the properties of dark matter and the ionized plasma of the intracluster medium. To date, most studies have focused on mergers occurring…

A method for dimension reduction with clustering, classification, or discriminant analysis is introduced. This mixture model-based approach is based on fitting generalized hyperbolic mixtures on a reduced subspace within the paradigm of…