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We consider fast deterministic algorithms to identify the "best" linearly independent terms in multivariate mixtures and use them to compute, up to a user-selected accuracy, an equivalent representation with fewer terms. One algorithm…
We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…
The aim of this paper is twofold. First, we introduce a new class of linearizations, based on the generalization of a construction used in polynomial algebra to find the zeros of a system of (scalar) polynomial equations. We show that one…
In this study, we evaluate several classifiers and focus on selecting a minimal set of appropriate material features. Our objective is to propose and discuss general strategies for reducing the number of descriptors required for material…
Finding surface mappings with least distortion arises from many applications in various fields. Extremal Teichm\"uller maps are surface mappings with least conformality distortion. The existence and uniqueness of the extremal…
Linear constraints for a matrix polytope with no fractional vertex are investigated as intersecting research among permutation codes, rank modulations, and linear programming methods. By focusing the discussion to the block structure of…
Integration is affected by the curse of dimensionality and quickly becomes intractable as the dimensionality of the problem grows. We propose a randomized algorithm that, with high probability, gives a constant-factor approximation of a…
In this paper, we propose a novel parameterization method for genus-one and multiply connected genus-zero surfaces, called periodic conformal flattening. The conformal energy minimization technique is utilized to compute the desired…
Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters are used to promote convergence to more optimal solutions;…
Given a positive definite covariance matrix $\widehat \Sigma$, we strive to construct an optimal \emph{approximate} factor analysis model $HH^\top +D$, with $H$ having a prescribed number of columns and $D>0$ diagonal. The optimality…
Many machine learning problems require the prediction of multi-dimensional labels. Such structured prediction models can benefit from modeling dependencies between labels. Recently, several deep learning approaches to structured prediction…
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 describe a linear-time algorithm that finds a planar drawing of every graph of a simple line or pseudoline arrangement within a grid of area O(n^{7/6}). No known input causes our algorithm to use area \Omega(n^{1+\epsilon}) for any…
Majorization-minimization (MM) is a family of optimization methods that iteratively reduce a loss by minimizing a locally-tight upper bound, called a majorizer. Traditionally, majorizers were derived by hand, and MM was only applicable to a…
\emph{$K$-best enumeration}, which asks to output $k$-best solutions without duplication, is a helpful tool in data analysis for many fields. In such fields, graphs typically represent data. Thus subgraph enumeration has been paid much…
We present an ordinary differential equations approach to the analysis of algorithms for constructing $l_1$ minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is…
The design of deterministic filters can be cast as a problem of minimizing an associated cost function for an optimal control problem. Employing the min-plus linearity property of the dynamic programming operator (associated with the…
This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the…
Matrix factorization techniques have been widely used as a method for collaborative filtering for recommender systems. In recent times, different variants of deep learning algorithms have been explored in this setting to improve the task of…
Low-rank approximation with zeros aims to find a matrix of fixed rank and with a fixed zero pattern that minimizes the Euclidean distance to a given data matrix. We study the critical points of this optimization problem using algebraic…