Related papers: Matrix Decomposition on Graphs: A Functional View
A set of fundamental matrices relating pairs of cameras in some configuration can be represented as edges of a "viewing graph". Whether or not these fundamental matrices are generically sufficient to recover the global camera configuration…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an…
We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the…
Minimizing a sum of simple submodular functions of limited support is a special case of general submodular function minimization that has seen numerous applications in machine learning. We develop fast techniques for instances where…
High-dimensional real-world systems can often be well characterized by a small number of simultaneous low-complexity interactions. The analysis of variance (ANOVA) decomposition and the anchored decomposition are typical techniques to find…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix…
Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the…
Learning a smooth graph signal from partially observed data is a well-studied task in graph-based machine learning. We consider this task from the perspective of optimal recovery, a mathematical framework for learning a function from…
We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and…
We introduce a sampling theoretic framework for the recovery of smooth surfaces and functions living on smooth surfaces from few samples. The proposed approach can be thought of as a nonlinear generalization of union of subspace models…
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…
We consider the problem of reconstructing a low-rank matrix from a small subset of its entries. In this paper, we describe the implementation of an efficient algorithm called OptSpace, based on singular value decomposition followed by local…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
We present an approach to decomposition and factor analysis of matrices with ordinal data. The matrix entries are grades to which objects represented by rows satisfy attributes represented by columns, e.g. grades to which an image is red, a…
Functional decomposition is the process of breaking down a function $f$ into a composition $f=g(f_1,\dots,f_k)$ of simpler functions $f_1,\dots,f_k$ belonging to some class $\mathcal{F}$. This fundamental notion can be used to model…
Using graphs to model irregular information domains is an effective approach to deal with some of the intricacies of contemporary (network) data. A key aspect is how the data, represented as graph signals, depend on the topology of the…
We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks,…
We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…