Search

Sparse subspace clustering (SSC) relies on sparse regression for accurate neighbor identification. Inspired by recent progress in compressive sensing, this paper proposes a new sparse regression scheme for SSC via two-step reweighted $\ell _{1} $ -minimization, which also generalizes a two-step $\ell _{1} $ -minimization algorithm introduced by E. J. Candès et al. in [The Annals of Statistics, vol. 42, no. 2, pp. 669–699, 2014] without incurring extra algorithmic complexity. To fully exploit the prior information offered by the computed sparse representation vector in the first step, our approach places a weight on each component of the regression vector, and solves a weighted LASSO in the second step. We propose a data weighting rule suitable for enhancing neighbor identification accuracy. Then, under the formulation of the dual problem of weighted LASSO, we study in depth the theoretical neighbor recovery rates of the proposed scheme. Specifically, an interesting connection between the locations of nonzeros of the optimal sparse solution to the weighted LASSO and the indexes of the active constraints of the dual problem is established. Afterwards, under the semi-random model, analytic probability lower/upper bounds for various neighbor recovery events are derived. Our analytic results confirm that, with the aid of data weighting and if the prior neighbor information is accurate enough, the proposed scheme with a higher probability can produce many correct neighbors and few incorrect neighbors as compared to the solution without data weighting. Computer simulations are provided to validate our analytic study and evidence the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

To strike a balance between energy efficiency and data quality control, this paper proposes a sensor censoring scheme for distributed sparse signal recovery via compressive-sensing-based wireless sensor networks. In the proposed approach, each sensor node employs a sparse sensing vector with known support for data compression, meanwhile enabling making local inference about the unknown support of the sparse signal vector of interest. This naturally leads to a ternary censoring protocol, whereby each sensor: 1) directly transmits the real-valued compressed data, if the sensing vector support is detected to be overlapped with the signal support; 2) sends a one-bit hard decision if empty support overlap is inferred; and 3) keeps silent if the measurement is judged to be uninformative. Our design then aims at minimizing the error probability that empty support overlap is decided but otherwise is true, subject to the constraints on a tolerable false-alarm probability that non-empty support overlap is decided but otherwise is true, and a target censoring rate. We derive a closed-form formula of the optimal censoring rule; a low complexity implementation using bi-section search is also developed. In addition, the average communication cost is analyzed. To aid global signal reconstruction under the proposed censoring framework, we propose a modified \ell 1 -minimization based algorithm, which exploits certain sparse nature of the hard decision vector received at the fusion center. Analytic performance guarantees, characterized in terms of the restricted isometry property, are also derived. Computer simulations are used to illustrate the performance of the proposed scheme. [ABSTRACT FROM PUBLISHER]

Various methods have been proposed for monitoring continuously varying event-region scenarios using wireless sensor networks (WSNs). However, these methods use either a centralized approach, in which a powerful control center is used to reconstruct the entire random field, or a semi-centralized approach, in which extensive real-value data exchange takes place among the sensors. By contrast, this paper proposes a two-phase distributed dynamic event-region detection scheme for WSNs characterized by a space-time Markov random field with a particular Gibbs distribution. In Phase I of the proposed scheme, each sensor makes an initial decision in accordance with its current Gaussian corrupted observation and previous decision. In Phase II, the nodes update their decisions based on the decision information received from their neighbors. Notably, the proposed scheme has a low-communication-rate characteristic, and is thus ideally suited to WSN applications. The performance of the proposed scheme is compared with that of a semicentralized detection scheme by means of computer simulations. [ABSTRACT FROM PUBLISHER]