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This article is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components <i>exactly</i> by solving a very… (More)

—In this paper, we study the problem of recovering a low-rank matrix (the principal components) from a high-dimensional data matrix despite both small entry-wise noise and gross sparse errors. Recently, it has been shown that a convex program, named Principal Component Pursuit (PCP), can recover the low-rank matrix when the data matrix is corrupted by gross… (More)

- Xiaodong Li
- GECCO
- 2004

This paper proposes an improved particle swarm optimizer using the notion of species to determine its neighbourhood best values, for solving multimodal optimization problems. In the proposed species-based PSO (SPSO), the swarm population is divided into species sub-populations based on their similarity. Each species is grouped around a dominating particle… (More)

We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x ∈ C n about which we have phaseless samples of the form y r = ⟨a r , x⟩⟩ (knowledge of the phase of these samples would yield a linear system). This paper develops a non-convex formulation of the phase retrieval problem as… (More)

—This paper proposes an improved particle swarm optimizer using the notion of species to determine its neighborhood best values for solving multimodal optimization problems and for tracking multiple optima in a dynamic environment. In the proposed species-based particle swam optimization (SPSO), the swarm population is divided into species subpopulations… (More)

This note shows that we can recover any complex vector x 0 ∈ C n exactly from on the order of n quadratic equations of the form ||a i , x 0 | by using a semidefinite program known as PhaseLift. This improves upon earlier bounds in [3], which required the number of equations to be at least on the order of n log n. Further, we show that exact recovery holds… (More)

—Orthogonal frequency division multiplexing (OFDM) is an attractive technique for wireless communication applications. However, an OFDM signal has a large peak-to-mean envelope power ratio, which can result in significant distortion when passed through a nonlinear device, such as a transmitter power amplifier. We investigate, through extensive computer… (More)

—This paper presents a new cooperative coevolving particle swarm optimization (CCPSO) algorithm in an attempt to address the issue of scaling up particle swarm optimization (PSO) algorithms in solving large-scale optimization problems (up to 2000 real-valued variables). The proposed CCPSO2 builds on the success of an early CCPSO that employs an effective… (More)

Niching techniques play an important role in evolutionary algorithms. Existing niching methods often require user-specified parameters, limiting their usefulness. This paper proposes a niching method for Particle Swarm Optimisation (PSO) where population statistics are used to adaptively determine the niching parameters during a run. The proposed niching… (More)