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Greedy algorithm
About: Greedy algorithm is a research topic. Over the lifetime, 15347 publications have been published within this topic receiving 393945 citations.
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TL;DR: This paper provides new results on computing simultaneous sparse approximations of multichannel signals over redundant dictionaries using two greedy algorithms, p-thresholding and p-SOMP, and shows that, if the dictionary satisfies a uniform uncertainty principle, the probability that simultaneous OMP fails to recover any sufficiently sparse set of atoms gets increasingly smaller as the number of channels increases.
Abstract: This paper provides new results on computing simultaneous sparse approximations of multichannel signals over redundant dictionaries using two greedy algorithms. The first one, p-thresholding, selects the S atoms that have the largest p-correlation while the second one, p-simultaneous matching pursuit (p-SOMP), is a generalisation of an algorithm studied by Tropp in (Signal Process. 86:572–588, 2006). We first provide exact recovery conditions as well as worst case analyses of all algorithms. The results, expressed using the standard cumulative coherence, are very reminiscent of the single channel case and, in particular, impose stringent restrictions on the dictionary. We unlock the situation by performing an average case analysis of both algorithms. First, we set up a general probabilistic signal model in which the coefficients of the atoms are drawn at random from the standard Gaussian distribution. Second, we show that under this model, and with mild conditions on the coherence, the probability that p-thresholding and p-SOMP fail to recover the correct components is overwhelmingly small and gets smaller as the number of channels increases. Furthermore, we analyse the influence of selecting the set of correct atoms at random. We show that, if the dictionary satisfies a uniform uncertainty principle (Candes and Tao, IEEE Trans. Inf. Theory, 52(12):5406–5425, 2006), the probability that simultaneous OMP fails to recover any sufficiently sparse set of atoms gets increasingly smaller as the number of channels increases.
232 citations
TL;DR: An efficient algorithm for the inference of stochastic block models in large networks, capable of delivering results which are indistinguishable from the more exact and numerically expensive MCMC method in many artificial and empirical networks, despite being much faster.
Abstract: We present an efficient algorithm for the inference of stochastic block models in large networks. The algorithm can be used as an optimized Markov chain Monte Carlo (MCMC) method, with a fast mixing time and a much reduced susceptibility to getting trapped in metastable states, or as a greedy agglomerative heuristic, with an almost linear O(Nln2N) complexity, where N is the number of nodes in the network, independent of the number of blocks being inferred. We show that the heuristic is capable of delivering results which are indistinguishable from the more exact and numerically expensive MCMC method in many artificial and empirical networks, despite being much faster. The method is entirely unbiased towards any specific mixing pattern, and in particular it does not favor assortative community structures.
231 citations
TL;DR: A natural Greedy heuristic for the maximum volume problem is studied and it is shown that if the optimal solution selects k columns, then Greedy will select @W(k/logk) columns, providing a logk approximation.
230 citations
TL;DR: In this article, a greedy heuristic and a genetic algorithm are proposed for the solution to the integrated problem of inventory-level-dependent demand inventory model and product assortment and shelf-space allocation.
229 citations
TL;DR: A new greedy algorithm which is called the orthogonal super greedy algorithm (OSGA), called OSGA, is built and it is observed that OSGA is times simpler (more efficient) than OMP.
Abstract: The general theory of greedy approximation is well developed. Much less is known about how specific features of a dictionary can be used to our advantage. In this paper, we discuss incoherent dictionaries. We build a new greedy algorithm which is called the orthogonal super greedy algorithm (OSGA). We show that the rates of convergence of OSGA and the orthogonal matching pursuit (OMP) with respect to incoherent dictionaries are the same. Based on the analysis of the number of orthogonal projections and the number of iterations, we observed that OSGA is times simpler (more efficient) than OMP. Greedy approximation is also a fundamental tool for sparse signal recovery. The performance of orthogonal multimatching pursuit, a counterpart of OSGA in the compressed sensing setting, is also analyzed under restricted isometry property conditions.
227 citations