An Accelerating Reduction Approach for Incomplete Decision Table Using Positive Approximation Set.

Due to the explosive growth of data collected by various sensors, it has become a difficult problem determining how to conduct feature selection more efficiently. To address this problem, we offer a fresh insight into rough set theory from the perspective of a positive approximation set. It is found that a granularity domain can be used to characterize the target knowledge, because of its form of a covering with respect to a tolerance relation. On the basis of this fact, a novel heuristic approach ARIPA is proposed to accelerate representative reduction algorithms for incomplete decision table. As a result, ARIPA in classical rough set model and ARIPA-IVPR in variable precision rough set model are realized respectively. Moreover, ARIPA is adopted to improve the computational efficiency of two existing state-of-the-art reduction algorithms. To demonstrate the effectiveness of the improved algorithms, a variety of experiments utilizing four UCI incomplete data sets are conducted. The performances of improved algorithms are compared with those of original ones as well. Numerical experiments justify that our accelerating approach enhances the existing algorithms to accomplish the reduction task more quickly. In some cases, they fulfill attribute reduction even more stably than the original algorithms do.

A Priori-Based Subarray Selection Algorithm for DOA Estimation.

A finer direction-of-arrival (DOA) estimation result needs a large and dense array; it may, however, encounter the mutual coupling effect, which degrades the performance of DOA estimation. There is a new approach to mitigating this effect by using a nonuniform array to achieve DOA estimation. In this paper, we consider a priori DOA estimation, which is easily obtained from tracking results. The a priori DOA requires us to pay close attention to the high possibility of where the DOA will appear; then, a weight according to the prior probability distribution of DOA is added to each direction, which leads the sensing matrix of DOA estimation to be near low-rank. Thus, according to the low-rank matrix approximation theory, an optimal low-rank approximate matrix is obtained and an algorithm is proposed to select the elements of the original array according to right singular vectors of the approximate matrix. After that, the impacts of different weights are analyzed, and a mixed weight is presented which has flexibility for common use. Finally, a number of numerical simulations are carried out, and the results verify the effectiveness of the proposed methods.

Two Measurement Set Partitioning Algorithms for the Extended Target Probability Hypothesis Density Filter.

The extended target probability hypothesis density (ET-PHD) filter cannot work well if the density of measurements varies from target to target, which is based on the measurement set partitioning algorithms employing the Mahalanobis distance between measurements. To tackle the problem, two measurement set partitioning approaches, the shared nearest neighbors similarity partitioning (SNNSP) and SNN density partitioning (SNNDP), are proposed in this paper. In SNNSP, the shared nearest neighbors (SNN) similarity, which incorporates the neighboring measurement information, is introduced to DP instead of the Mahalanobis distance between measurements. Furthermore, the SNNDP is developed by combining the DBSCAN algorithm with the SNN similarity together to enhance the reliability of partitions. Simulation results show that the ET-PHD filters based on the two proposed partitioning algorithms can achieve better tracking performance with less computation than the compared algorithms.

Sensor Selection for Decentralized Large-Scale Multi-Target Tracking Network.

A new optimization algorithm of sensor selection is proposed in this paper for decentralized large-scale multi-target tracking (MTT) network within a labeled random finite set (RFS) framework. The method is performed based on a marginalized δ-generalized labeled multi-Bernoulli RFS. The rule of weighted Kullback-Leibler average (KLA) is used to fuse local multi-target densities. A new metric, named as the label assignment (LA) metric, is proposed to measure the distance for two labeled sets. The lower bound of LA metric based mean square error between the labeled multi-target state set and its estimate is taken as the optimized objective function of sensor selection. The proposed bound is obtained by the information inequality to RFS measurement. Then, we present the sequential Monte Carlo and Gaussian mixture implementations for the bound. Another advantage of the bound is that it provides a basis for setting the weights of KLA. The coordinate descent method is proposed to compromise the computational cost of sensor selection and the accuracy of MTT. Simulations verify the effectiveness of our method under different signal-to- noise ratio scenarios.

Constrained Multi-Sensor Control Using a Multi-Target MSE Bound and a δ-GLMB Filter.

The existing multi-sensor control algorithms for multi-target tracking (MTT) within the random finite set (RFS) framework are all based on the distributed processing architecture, so the rule of generalized covariance intersection (GCI) has to be used to obtain the multi-sensor posterior density. However, there has still been no reliable basis for setting the normalized fusion weight of each sensor in GCI until now. Therefore, to avoid the GCI rule, the paper proposes a new constrained multi-sensor control algorithm based on the centralized processing architecture. A multi-target mean-square error (MSE) bound defined in our paper is served as cost function and the multi-sensor control commands are just the solutions that minimize the bound. In order to derive the bound by using the generalized information inequality to RFS observation, the error between state set and its estimation is measured by the second-order optimal sub-pattern assignment metric while the multi-target Bayes recursion is performed by using a δ-generalized labeled multi-Bernoulli filter. An additional benefit of our method is that the proposed bound can provide an online indication of the achievable limit for MTT precision after the sensor control. Two suboptimal algorithms, which are mixed penalty function (MPF) method and complex method, are used to reduce the computation cost of solving the constrained optimization problem. Simulation results show that for the constrained multi-sensor control system with different observation performance, our method significantly outperforms the GCI-based Cauchy-Schwarz divergence method in MTT precision. Besides, when the number of sensors is relatively large, the computation time of the MPF and complex methods is much shorter than that of the exhaustive search method at the expense of completely acceptable loss of tracking accuracy.

Dual Sensor Control Scheme for Multi-Target Tracking.

Sensor control is a challenging issue in the field of multi-target tracking. It involves multi-target state estimation and the optimal control of the sensor. To maximize the overall utility of the surveillance system, we propose a dual sensor control scheme. This work is formulated in the framework of partially observed Markov decision processes (POMDPs) with Mahler’s finite set statistics (FISST). To evaluate the performance associated with each control action, a key element is to design an appropriate metric. From a task-driven perspective, we utilize a metric to minimize the posterior distance between the sensor and the target. This distance-related metric promotes the design of a dual sensor control scheme. Moreover, we introduce a metric to maximize the predicted average probability of detection, which will improve the efficiency by avoiding unnecessary update processes. Simulation results indicate that the performance of the proposed algorithm is significantly superior to the existing methods.

Multi-Target Joint Detection and Estimation Error Bound for the Sensor with Clutter and Missed Detection.

The error bound is a typical measure of the limiting performance of all filters for the given sensor measurement setting. This is of practical importance in guiding the design and management of sensors to improve target tracking performance. Within the random finite set (RFS) framework, an error bound for joint detection and estimation (JDE) of multiple targets using a single sensor with clutter and missed detection is developed by using multi-Bernoulli or Poisson approximation to multi-target Bayes recursion. Here, JDE refers to jointly estimating the number and states of targets from a sequence of sensor measurements. In order to obtain the results of this paper, all detectors and estimators are restricted to maximum a posteriori (MAP) detectors and unbiased estimators, and the second-order optimal sub-pattern assignment (OSPA) distance is used to measure the error metric between the true and estimated state sets. The simulation results show that clutter density and detection probability have significant impact on the error bound, and the effectiveness of the proposed bound is verified by indicating the performance limitations of the single-sensor probability hypothesis density (PHD) and cardinalized PHD (CPHD) filters for various clutter densities and detection probabilities.

Convergence analysis of deterministic discrete time system of a unified self-stabilizing algorithm for PCA and MCA.

Unified algorithms for principal and minor components analysis can be used to extract principal components and if altered simply by the sign, it can also serve as a minor component extractor. Obviously, the convergence of these algorithms is an essential issue in practical applications. This paper studies the convergence of a unified PCA and MCA algorithm via a corresponding deterministic discrete-time (DDT) system and some sufficient conditions to guarantee convergence are obtained. Simulations are carried out to further illustrate the theoretical results achieved.

A unified self-stabilizing neural network algorithm for principal and minor components extraction.

Recently, many unified learning algorithms have been developed for principal component analysis and minor component analysis. These unified algorithms can be used to extract principal components and, if altered simply by the sign, can also serve as a minor component extractor. This is of practical significance in the implementations of algorithms. This paper proposes a unified self-stabilizing neural network learning algorithm for principal and minor components extraction, and studies the stability of the proposed unified algorithm via the fixed-point analysis method. The proposed unified self-stabilizing algorithm for principal and minor components extraction is extended for tracking the principal subspace (PS) and minor subspace (MS). The averaging differential equation and the energy function associated with the unified algorithm for tracking PS and MS are given. It is shown that the averaging differential equation will globally asymptotically converge to an invariance set, and the corresponding energy function exhibit a unique global minimum attained if and only if its state matrices span the PS or MS of the autocorrelation matrix of a vector data stream. It is concluded that the proposed unified algorithm for tracking PS and MS can efficiently track an orthonormal basis of the PS or MS. Simulations are carried out to further illustrate the theoretical results achieved.

A self-stabilizing MSA algorithm in high-dimension data stream.

Minor subspace analysis (MSA) is a statistical method for extracting the subspace spanned by all the eigenvectors associated with the minor eigenvalues of the autocorrelation matrix of a high-dimension vector sequence. In this paper, we propose a self-stabilizing neural network learning algorithm for tracking minor subspace in high-dimension data stream. Dynamics of the proposed algorithm are analyzed via a corresponding deterministic continuous time (DCT) system and stochastic discrete time (SDT) system methods. The proposed algorithm provides an efficient online learning for tracking the MS and can track an orthonormal basis of the MS. Computer simulations are carried out to confirm the theoretical results.

On the discrete-time dynamics of a class of self-stabilizing MCA extraction algorithms.

The minor component analysis (MCA) deals with the recovery of the eigenvector associated to the smallest eigenvalue of the autocorrelation matrix of the input dada, and it is a very important tool for signal processing and data analysis. This brief analyzes the convergence and stability of a class of self-stabilizing MCA algorithms via a deterministic discrete-time (DDT) method. Some sufficient conditions are obtained to guarantee the convergence of these learning algorithms. Simulations are carried out to further illustrate the theoretical results achieved. It can be concluded that these self-stabilizing algorithms can efficiently extract the minor component (MC), and they outperform some existing MCA methods.