Alternating Direction Optimization Method Research Articles

Multi-nonlinear multi-view locality-preserving projection with similarity learning for random cross-view gait recognition

View variation is one of the greatest challenges in the field of gait recognition. Subspace learning approaches are designed to solve this issue by projecting cross-view features into a common subspace before recognition. However, similarity measures are data-dependent, which results in low accuracy when cross-view gait samples are randomly arranged. Inspired by the recent developments of data-driven similarity learning and multi-nonlinear projection, we propose a new unsupervised projection approach, called multi-nonlinear multi-view locality-preserving projections with similarity learning (M2LPP-SL). The similarity information among cross-view samples can be learned adaptively in our M2LPP-SL. Besides, the complex nonlinear structure of original data can be well preserved through multiple explicit nonlinear projection functions. Nevertheless, its performance is largely affected by the choice of nonlinear projection functions. Considering the excellent ability of kernel trick for capturing nonlinear structure information, we further extend M2LPP-SL into kernel space, and propose its multiple kernel version MKMLPP-SL. As a result, our approaches can capture linear and nonlinear structure more precisely, and also learn similarity information hidden in the multi-view gait dataset. The proposed models can be solved efficiently by alternating direction optimization method. Extensive experimental results over various view combinations on the multi-view gait database CASIA-B have demonstrated the superiority of the proposed algorithms.

A scalable and robust trust-based nonnegative matrix factorization recommender using the alternating direction method

Matrix Factorization (MF) has been proven to be an effective approach for the generation of a successful recommender system. However, most current MF-based recommenders cannot obtain high prediction accuracy due to the sparseness of the user–item matrix in collaborative filtering models. Moreover, they suffer from scalability issues when applied to large-scale real-world tasks. To tackle these issues, a social regularization method, called TrustANLF, is proposed, which incorporates users’ social trust information in a nonnegative matrix factorization framework. The proposed method integrates trust statements as an additional information source along with rating values into the recommendation model to deal with the data sparsity and cold-start issues. Moreover, the alternating direction optimization method is used for solving the trust-based nonnegative MF model in order to improve convergence speed as well as reduce computational and memory costs. To evaluate the effectiveness of the proposed method, several experiments are performed on three real-world datasets. The obtained results demonstrate the significant improvements of the proposed method over several state-of-the-art methods.

Robust Online Spectrum Prediction With Incomplete and Corrupted Historical Observations

A range of emerging applications, from adaptive spectrum sensing to proactive spectrum mobility, depend on the ability to foresee spectrum state evolution. Despite a number of studies appearing about spectrum prediction, fundamental issues still remain unresolved: 1) The existing studies do not explicitly account for anomalies, which may incur serious performance degradation; 2) they focus on the design of batch spectrum prediction algorithms, which limit the scalability to analyze massive spectrum data in real time; 3) they assume the historical data are complete, which may not hold in reality. To address these issues, we develop a Robust Online Spectrum Prediction (ROSP) framework, with incomplete and corrupted observations, in this paper. We first present data analytics of real-world spectrum measurements to reveal the correlation structures of spectrum evolution and to analyze the impact of anomalies on the rank distribution of spectrum matrices. Then, from a spectral–temporal 2-D perspective, we formulate the ROSP as a joint optimization problem of matrix completion and recovery by effectively integrating the time series forecasting techniques and develop an alternating direction optimization method to efficiently solve it. We apply ROSP to a wide range of real-world spectrum matrices of popular wireless services. Experiment results show that ROSP outperforms state-of-the-art spectrum prediction schemes.

Energy-Efficient Transceiver Design for Hybrid Sub-Array Architecture MIMO Systems

Millimeter-wave (mmWave) communication operated in frequency bands between 30 and 300 GHz has attracted extensive attention due to the potential ability of offering orders of magnitude greater bandwidths combined with further gains via beamforming and spatial multiplexing from multi-element antenna arrays. mmwave system may exploit the hybrid analog and digital precoding to achieve simultaneously the diversity, array and multiplexing gain with a lower cost of implementation. Motivated by this, in this paper, we investigate the design of hybrid precoder and combiner with sub-connected architecture, where each radio frequency chain is connected to only a subset of base station antennas from the perspective of energy efficient transmission. The problem of interest is a non-convex and NP-hard problem that is difficult to solve directly. In order to address it, we resort to design a two-layer optimization method to solve the problem of interest by exploiting jointly the interference alignment and fractional programming. First, the analog precoder and combiner are optimized via the alternating-direction optimization method where the phase shifter can be easily adjusted with an analytical structure. Then, we optimize the digital precoder and combiner based on an effective multiple-input multiple-output channel coefficient. The convergence of the proposed algorithms is proved using the monotonic boundary theorem and fractional programming theory. Extensive simulation results are given to validate the effectiveness of the presented method and to evaluate the energy efficiency performance under various system configurations.

Power allocation for two‐user cognitive multiple access channels under primary user outage constraint

SummaryWe consider a two‐user spectrum sharing cognitive radio multiple access channel (CR‐MAC) coexisting with a pair of primary users (PUs). Different from the existing works in CR‐MAC where the interference power constraint is applied to protect the PU transmission, a more advanced protection criterion over the interference power constraint, namely, PU outage constraint, is adopted in this paper not only to protect the PU transmission but also improve the performance of the CR‐MAC. Under such a constraint, as well as the transmit power constraint, and assuming that perfect channel state information (CSI) is available, two heuristic power allocation algorithms for the secondary users based on dual optimization are proposed. The objective is to maximize the ergodic sum capacity of the CR‐MAC without successive interference cancelation (SIC). One algorithm applies alternating direction optimization method to derive an iterative power allocation, while the other algorithm adopts exclusive transmission to determine the power allocation. Besides, we extend our results to the multi‐user and partial CSI scenarios. It is shown by extensive simulations that the proposed algorithm based on alternating direction optimization method always outperforms the existing algorithms based on the interference power constraint, while the proposed algorithm based on exclusive transmission outperforms the existing algorithms for medium and large values of the transmit power limit. Copyright © 2015 John Wiley & Sons, Ltd.

Restoration of Poissonian Images Using Alternating Direction Optimization

Much research has been devoted to the problem of restoring Poissonian images, namely for medical and astronomical applications. However, the restoration of these images using state-of-the-art regularizers (such as those based upon multiscale representations or total variation) is still an active research area, since the associated optimization problems are quite challenging. In this paper, we propose an approach to deconvolving Poissonian images, which is based upon an alternating direction optimization method. The standard regularization [or maximum a posteriori (MAP)] restoration criterion, which combines the Poisson log-likelihood with a (nonsmooth) convex regularizer (log-prior), leads to hard optimization problems: the log-likelihood is nonquadratic and nonseparable, the regularizer is nonsmooth, and there is a nonnegativity constraint. Using standard convex analysis tools, we present sufficient conditions for existence and uniqueness of solutions of these optimization problems, for several types of regularizers: total-variation, frame-based analysis, and frame-based synthesis. We attack these problems with an instance of the alternating direction method of multipliers (ADMM), which belongs to the family of augmented Lagrangian algorithms. We study sufficient conditions for convergence and show that these are satisfied, either under total-variation or frame-based (analysis and synthesis) regularization. The resulting algorithms are shown to outperform alternative state-of-the-art methods, both in terms of speed and restoration accuracy.