The greedy algorithms are efficient ways in reconstructing the sparse signal. Among all the greedy recovery algorithms for practical compressive sampling(CS), Subspace Pursuit(SP) can offer reliable recovery accuracy ...
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ISBN:
(纸本)9781612846835;9781612846828
The greedy algorithms are efficient ways in reconstructing the sparse signal. Among all the greedy recovery algorithms for practical compressive sampling(CS), Subspace Pursuit(SP) can offer reliable recovery accuracy with low costs. In this paper, the SP algorithm is optimized by reducing the complexity of the least square(LS) caculation in each iteration. The Optimized SP performs well in LTE channel estimation when compared with the other greedy algorithms. The utilization of Partial Fourier Matrix helps reduce the matrix storage in SP hardware implemention. The matrix inverse caculation is also simplified by taking advatage of the Hermite Toeplitz matrix generated from the Fourier Matrix.
This paper proposes a fast pursuit method for greedy algorithms when reconstructing multi-signals under Distributed Compressive Sensing (DCS) framework. DCS takes advantage of both intra-and inter-signal correlation s...
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ISBN:
(纸本)9781479961139
This paper proposes a fast pursuit method for greedy algorithms when reconstructing multi-signals under Distributed Compressive Sensing (DCS) framework. DCS takes advantage of both intra-and inter-signal correlation structures to reduce the measurements required for signals recovery. greedy algorithms, much faster than l(0) and l(1) minimization algorithms, are widely used in DCS. General approaches transform DCS model to Compressive Sensing (CS) model and then directly use greedy algorithms to reconstruct signals, but the recovery speed becomes very slow as the signal number n increasing. In this paper, we propose a fast pursuit method which exploits the structural features of joint measurement matrix to reduce the computational complexity form O(n(2)) to O(n) when calculating inner-product in greedy algorithms, which improves the recovery speed significantly without reducing recovery accuracy.
The paper compares different heuristics that are used by greedy algorithms for constructing of decision trees. Exact learning problem with all discrete attributes is considered that assumes absence of contradictions i...
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ISBN:
(纸本)9789898425799
The paper compares different heuristics that are used by greedy algorithms for constructing of decision trees. Exact learning problem with all discrete attributes is considered that assumes absence of contradictions in the decision table. Reference decision tables are based on 24 data sets from UCI Machine Learning Repository (Frank and Asuncion, 2010). Complexity of decision trees is estimated relative to several cost functions: depth, average depth, and number of nodes. Costs of trees built by greedy algorithms are compared with exact minimums calculated by an algorithm based on dynamic programming. The results associate to each cost function a set of potentially good heuristics that minimize it.
In this work, we study the multi-agent decision problem where agents try to coordinate to optimize a given system-level objective. While solving for the global optimum is intractable in many cases, the greedy algorith...
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ISBN:
(数字)9781665451963
ISBN:
(纸本)9781665451963
In this work, we study the multi-agent decision problem where agents try to coordinate to optimize a given system-level objective. While solving for the global optimum is intractable in many cases, the greedy algorithm is a wellstudied and efficient way to provide good approximate solutions - notably for submodular optimization problems. Executing the greedy algorithm requires the agents to be ordered and execute a local optimization based on the solutions of the previous agents. However, in limited information settings, passing the solution from the previous agents may be nontrivial, as some agents may not be able to directly communicate with each other. Thus the communication time required to execute the greedy algorithm is closely tied to the order that the agents are given. In this work, we characterize interplay between the communication complexity and agent orderings by showing that the complexity using the best ordering is O (n) and increases considerably to O (n(2)) when using the worst ordering. Motivated by this, we also propose an algorithm that can find an ordering and execute the greedy algorithm quickly, in a distributed fashion. We also show that such an execution of the greedy algorithm is advantageous over current methods for distributed submodular maximization.
In this paper, we improve greedy algorithms to recover sparse signals with complex Gaussian distributed non-zero elements, when the probability of sparsity pattern is known a priori. By exploiting this prior probabili...
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ISBN:
(纸本)9781538670484
In this paper, we improve greedy algorithms to recover sparse signals with complex Gaussian distributed non-zero elements, when the probability of sparsity pattern is known a priori. By exploiting this prior probability, we derive a correction function that minimizes the probability of incorrect selection of a support index at each iteration of the orthogonal matching pursuit (OMP). In particular, we employ the order statistics of exponential distribution to create the correction function. Simulation results demonstrate that the correction function significantly improves the recovery performance of OMP and subspace pursuit (SP) for random Gaussian and Bernoulli measurement matrices.
The paper examines four weak relaxed greedy algorithms for finding approximate sparse solutions of convex optimization problems in a Banach space. First, we present a review of primal results on the convergence rate o...
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ISBN:
(纸本)9783319729268;9783319729251
The paper examines four weak relaxed greedy algorithms for finding approximate sparse solutions of convex optimization problems in a Banach space. First, we present a review of primal results on the convergence rate of the algorithms based on the geometric properties of the objective function. Then, using the ideas of [16], we define the duality gap and prove that the duality gap is a certificate for the current approximation to the optimal solution. Finally, we find estimates of the dependence of the duality gap values on the number of iterations for weak greedy algorithms.
The problem of sparse signal reconstruction in the presence of possibly impulsive noise is studied. The state-of-the-art greedy algorithms, Iterative Hard Thresholding (IHT), Orthogonal Matching Pursuit (OMP), and Com...
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ISBN:
(纸本)9781467310680
The problem of sparse signal reconstruction in the presence of possibly impulsive noise is studied. The state-of-the-art greedy algorithms, Iterative Hard Thresholding (IHT), Orthogonal Matching Pursuit (OMP), and Compressive Sampling Matching Pursuit (CoSaMP) are robustified in order to cope with impulsive noise environments and outliers. We employ robust weighting of the residuals and replace the least-squares estimates byM-estimates of regression. Also a robust M-estimation based ridge regression is considered and shown to possess high potential when utilized in CS algorithms.
For many complex combinatorial optimization problems, obtaining good solutions quickly is of value either by itself or as part of an exact algorithm. greedy algorithms to obtain such solutions are known for many probl...
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ISBN:
(纸本)9780769539706
For many complex combinatorial optimization problems, obtaining good solutions quickly is of value either by itself or as part of an exact algorithm. greedy algorithms to obtain such solutions are known for many problems. In this paper we present stochastic greedy algorithms which are perturbed versions of standard greedy algorithms, and report on experiments using learned and standard probability distributions conducted on knapsack problems and single machine sequencing problems. The results indicate that the approach produces solutions significantly closer to optimal than the standard greedy approach, and runs quite fast. It can thus be seen in the space of approximate algorithms as falling between the very quick greedy approaches and the relatively slower soft computing approaches like genetic algorithms and simulated annealing.
greedy algorithms provide a fast and often also effective solution to many combinatorial optimization problems. However, it is well known that they sometimes lead to low quality solutions on certain instances. In this...
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ISBN:
(纸本)9781450356183
greedy algorithms provide a fast and often also effective solution to many combinatorial optimization problems. However, it is well known that they sometimes lead to low quality solutions on certain instances. In this paper, we explore the use of randomness in greedy algorithms for the minimum vertex cover and dominating set problem and compare the resulting performance against their deterministic counterpart. Our algorithms are based on a parameter. which allows to explore the spectrum between uniform and deterministic greedy selection in the steps of the algorithm and our theoretical and experimental investigations point out the benefits of incorporating randomness into greedy algorithms for the two considered combinatorial optimization problems.
We show how to leverage quantum annealers (QAs) to better select candidates in greedy algorithms. Unlike conventional greedy algorithms that employ problem-specific heuristics for making locally optimal choices at eac...
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ISBN:
(数字)9781665427920
ISBN:
(纸本)9781665427920
We show how to leverage quantum annealers (QAs) to better select candidates in greedy algorithms. Unlike conventional greedy algorithms that employ problem-specific heuristics for making locally optimal choices at each stage, we use QAs that sample from the ground state of a problem-dependent Hamiltonians at cryogenic temperatures and use retrieved samples to estimate the probability distribution of problem variables. More specifically, we look at each spin of the Ising model as a random variable and contract all problem variables whose corresponding uncertainties are negligible. Our empirical results on a D-Wave 2000Q quantum processor demonstrate that the proposed quantum-assisted greedy algorithm (QAGA) scheme can find notably better solutions compared to the state-of-the-art techniques in the realm of quantum annealing.
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