Related papers: Analysis of the Self Projected Matching Pursuit Al…
In this work we address the problem of recovering sparse solutions to non linear inverse problems. We look at two variants of the basic problem, the synthesis prior problem when the solution is sparse and the analysis prior problem where…
In text classification, the problem of overfitting arises due to the high dimensionality, making regularization essential. Although classic regularizers provide sparsity, they fail to return highly accurate models. On the contrary,…
Orthogonal matching pursuit (OMP) is a greedy algorithm widely used for the recovery of sparse signals from compressed measurements. In this paper, we analyze the number of iterations required for the OMP algorithm to perform exact recovery…
We propose a fast greedy algorithm to compute sparse representations of signals from continuous dictionaries that are factorizable, i.e., with atoms that can be separated as a product of sub-atoms. Existing algorithms strongly reduce the…
We study the problem of selecting a subset of vectors from a large set, to obtain the best signal representation over a family of functions. Although greedy methods have been widely used for tackling this problem and many of those have been…
Learning of low-rank matrices is fundamental to many machine learning applications. A state-of-the-art algorithm is the rank-one matrix pursuit (R1MP). However, it can only be used in matrix completion problems with the square loss. In this…
Spare representation of signals has received significant attention in recent years. Based on these developments, a sparse representation-based classification (SRC) has been proposed for a variety of classification and related tasks,…
The orthogonal matching pursuit (OMP) algorithm is a commonly used algorithm for recovering $K$-sparse signals $\x\in \mathbb{R}^{n}$ from linear model $\y=\A\x$, where $\A\in \mathbb{R}^{m\times n}$ is a sensing matrix. A fundamental…
It is a survey on recent results in constructive sparse approximation. Three directions are discussed here: (1) Lebesgue-type inequalities for greedy algorithms with respect to a special class of dictionaries, (2) constructive sparse…
Isometry pursuit is a convex algorithm for identifying orthonormal column-submatrices of wide matrices. It consists of a novel normalization method followed by multitask basis pursuit. Applied to Jacobians of putative coordinate functions,…
Many clustering applications in machine learning and data mining rely on solving metric-constrained optimization problems. These problems are characterized by $O(n^3)$ constraints that enforce triangle inequalities on distance variables…
We formulate and analyze a generic sequential resource access problem arising in a variety of engineering fields, where a user disposes a number of heterogeneous computing, communication, or storage resources, each characterized by the…
A key problem in multiobjective linear programming is to find the set of all efficient extreme points in objective space. In this paper we introduce oriented projective geometry as an efficient and effective framework for solving this…
We study sparse approximate solutions to convex optimization problems. It is known that in many engineering applications researchers are interested in an approximate solution of an optimization problem as a linear combination of elements…
We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but…
We present a greedy algorithm for computing selected eigenpairs of a large sparse matrix $H$ that can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a small number of its…
Orthogonal matching pursuit (OMP) is a widely used algorithm for recovering sparse high dimensional vectors in linear regression models. The optimal performance of OMP requires \textit{a priori} knowledge of either the sparsity of…
Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the…
Sparse Subspace Clustering (SSC) is a state-of-the-art method for clustering high-dimensional data points lying in a union of low-dimensional subspaces. However, while $\ell_1$ optimization-based SSC algorithms suffer from high…
This work addresses approximate nearest neighbor search applied in the domain of large-scale image retrieval. Within the group testing framework we propose an efficient off-line construction of the search structures. The linear-time…