Related papers: A Note on Archetypal Analysis and the Approximatio…
We study the convex-hull problem in a probabilistic setting, motivated by the need to handle data uncertainty inherent in many applications, including sensor databases, location-based services and computer vision. In our framework, the…
This paper is concerned with the low-rank approximation for large-scale nonsymmetric matrices. Inspired by the classical Nystrom method, which is a popular method to find the low-rank approximation for symmetric positive semidefinite…
We propose an algorithm for solving nonlinear convex programs defined in terms of a symmetric positive semidefinite matrix variable $X$. This algorithm rests on the factorization $X=Y Y^T$, where the number of columns of Y fixes the rank of…
We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or…
Convex clustering has recently garnered increasing interest due to its attractive theoretical and computational properties, but its merits become limited in the face of high-dimensional data. In such settings, pairwise affinity terms that…
Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample…
We propose a clustering-based generalized low rank approximation method, which takes advantage of appealing features from both the generalized low rank approximation of matrices (GLRAM) and cluster analysis. It exploits a more general form…
Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…
This paper investigates contextual word representation models from the lens of similarity analysis. Given a collection of trained models, we measure the similarity of their internal representations and attention. Critically, these models…
This paper concerns a fundamental class of convex matrix optimization problems. It presents the first algorithm that uses optimal storage and provably computes a low-rank approximation of a solution. In particular, when all solutions have…
Automated per-instance algorithm selection and configuration have shown promising performances for a number of classic optimization problems, including satisfiability, AI planning, and TSP. The techniques often rely on a set of features…
In this article we utilise abstract convexity theory in order to unify and generalize many different concepts from nonsmooth analysis. We introduce the concepts of abstract codifferentiability, abstract quasidifferentiability and abstract…
Convex clustering is a recent stable alternative to hierarchical clustering. It formulates the recovery of progressively coalescing clusters as a regularized convex problem. While convex clustering was originally designed for handling…
Structured low-rank approximation is the problem of minimizing a weighted Frobenius distance to a given matrix among all matrices of fixed rank in a linear space of matrices. We study exact solutions to this problem by way of computational…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…
This paper considers a restriction to non-negative matrix factorization in which at least one matrix factor is stochastic. That is, the elements of the matrix factors are non-negative and the columns of one matrix factor sum to 1. This…
A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and…
We introduce a novel exploratory technique, termed biarchetype analysis, which extends archetype analysis to simultaneously identify archetypes of both observations and features. This innovative unsupervised machine learning tool aims to…
In this paper, we introduce an unsupervised learning approach to automatically discover, summarize, and manipulate artistic styles from large collections of paintings. Our method is based on archetypal analysis, which is an unsupervised…