相关论文: New Perspectives on $k$-Support and Cluster Norms

We study Nystr\"om type subsampling approaches to large scale kernel methods, and prove learning bounds in the statistical learning setting, where random sampling and high probability estimates are considered. In particular, we prove that…

The least-squares support vector machine is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the least-squares support vector machine classifier. The…

K-means -- and the celebrated Lloyd algorithm -- is more than the clustering method it was originally designed to be. It has indeed proven pivotal to help increase the speed of many machine learning and data analysis techniques such as…

Recovering a low-rank tensor from incomplete information is a recurring problem in signal processing and machine learning. The most popular convex relaxation of this problem minimizes the sum of the nuclear norms of the unfoldings of the…

The sum of radii problem ($k$-MSR) asks, given a metric space on $n$ points, to place $k$ balls covering all points so as to minimize the sum of their radii. Despite extensive study from the perspectives of approximation and parameterized…

The widely used nuclear norm heuristic for rank minimization problems introduces a regularization parameter which is difficult to tune. We have recently proposed a method to approximate the regularization path, i.e., the optimal solution as…

Clustering is one of the most important unsupervised problems in machine learning and statistics. Among many existing algorithms, kernel k-means has drawn much research attention due to its ability to find non-linear cluster boundaries and…

Clustering is an effective technique in data mining to generate groups that are the matter of interest. Among various clustering approaches, the family of k-means algorithms and min-cut algorithms gain most popularity due to their…

The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix…

In this paper, we study the effect of different regularizers and their implications in high dimensional image classification and sparse linear unmixing. Although kernelization or sparse methods are globally accepted solutions for processing…

Unit norm finite frames are generalizations of orthonormal bases with many applications in signal processing. An important property of a frame is its coherence, a measure of how close any two vectors of the frame are to each other. Low…

Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…

We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic…

In the Non-Uniform $k$-Center problem, a generalization of the famous $k$-center clustering problem, we want to cover the given set of points in a metric space by finding a placement of balls with specified radii. In $t$-NU$k$C Problem, we…

The metric $k$-median problem is a textbook clustering problem. As input, we are given a metric space $V$ of size $n$ and an integer $k$, and our task is to find a subset $S \subseteq V$ of at most $k$ `centers' that minimizes the total…

This paper studies a regularized matrix tri-factorization \(A\approx PDQ\), where \(P\) and \(Q\) are side factors and \(D\) is a central core whose conditioning can be explicitly regularized or constrained. The formulation is a structured…

We study stochastic Cubic Newton methods for solving general possibly non-convex minimization problems. We propose a new framework, which we call the helper framework, that provides a unified view of the stochastic and variance-reduced…

Multi-task learning has been observed by many researchers, which supposes that different tasks can share a low-rank common yet latent subspace. It means learning multiple tasks jointly is better than learning them independently. In this…

This paper studies a regularized support function estimator for bounds on components of the parameter vector in the case in which the identified set is a polygon. The proposed regularized estimator has three important properties: (i) it has…

We consider spectral clustering algorithms for community detection under a general bipartite stochastic block model (SBM). A modern spectral clustering algorithm consists of three steps: (1) regularization of an appropriate adjacency or…