Zuyuan Yang

Blind Spectral Unmixing Based on Sparse Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a widely used method for blind spectral unmixing (SU), which aims at obtaining the endmembers and corresponding fractional abundances, knowing only the collected mixing spectral data. It is noted that the abundance may be sparse (i.e., the endmembers may be with sparse distributions) and sparse NMF tends to lead to a unique result, so it is intuitive and meaningful to constrain NMF with sparseness for solving SU. However, due to the abundance sum-to-one constraint in SU, the traditional sparseness measured by L0/L1-norm is not an effective constraint any more. A novel measure (termed as S-measure) of sparseness using higher order norms of the signal vector is proposed in this paper. It features the physical significance. By using the S-measure constraint (SMC), a gradient-based sparse NMF algorithm (termed as NMF-SMC) is proposed for solving the SU problem, where the learning rate is adaptively selected, and the endmembers and abundances are simultaneously estimated. In the proposed NMF-SMC, there is no pure index assumption and no need to know the exact sparseness degree of the abundance in prior. Yet, it does not require the preprocessing of dimension reduction in which some useful information may be lost. Experiments based on synthetic mixtures and real-world images collected by AVIRIS and HYDICE sensors are performed to evaluate the validity of the proposed method.

Online Blind Source Separation Using Incremental Nonnegative Matrix Factorization With Volume Constraint

Online blind source separation (BSS) is proposed to overcome the high computational cost problem, which limits the practical applications of traditional batch BSS algorithms. However, the existing online BSS methods are mainly used to separate independent or uncorrelated sources. Recently, nonnegative matrix factorization (NMF) shows great potential to separate the correlative sources, where some constraints are often imposed to overcome the non-uniqueness of the factorization. In this paper, an incremental NMF with volume constraint is derived and utilized for solving online BSS. The volume constraint to the mixing matrix enhances the identifiability of the sources, while the incremental learning mode reduces the computational cost. The proposed method takes advantage of the natural gradient based multiplication updating rule, and it performs especially well in the recovery of dependent sources. Simulations in BSS for dual-energy X-ray images, online encrypted speech signals, and high correlative face images show the validity of the proposed method.

Nonnegative Blind Source Separation by Sparse Component Analysis Based on Determinant Measure

The problem of nonnegative blind source separation (NBSS) is addressed in this paper, where both the sources and the mixing matrix are nonnegative. Because many real-world signals are sparse, we deal with NBSS by sparse component analysis. First, a determinant-based sparseness measure, named D-measure, is introduced to gauge the temporal and spatial sparseness of signals. Based on this measure, a new NBSS model is derived, and an iterative sparseness maximization (ISM) approach is proposed to solve this model. In the ISM approach, the NBSS problem can be cast into row-to-row optimizations with respect to the unmixing matrix, and then the quadratic programming (QP) technique is used to optimize each row. Furthermore, we analyze the source identifiability and the computational complexity of the proposed ISM-QP method. The new method requires relatively weak conditions on the sources and the mixing matrix, has high computational efficiency, and is easy to implement. Simulation results demonstrate the effectiveness of our method.

Minimum-Volume-Constrained Nonnegative Matrix Factorization: Enhanced Ability of Learning Parts

Nonnegative matrix factorization (NMF) with minimum-volume-constraint (MVC) is exploited in this paper. Our results show that MVC can actually improve the sparseness of the results of NMF. This sparseness is L0-norm oriented and can give desirable results even in very weak sparseness situations, thereby leading to the significantly enhanced ability of learning parts of NMF. The close relation between NMF, sparse NMF, and the MVC_NMF is discussed first. Then two algorithms are proposed to solve the MVC_NMF model. One is called quadratic programming_MVC_NMF (QP_MVC_NMF) which is based on quadratic programming and the other is called negative glow_MVC_NMF (NG_MVC_NMF) because it uses multiplicative updates incorporating natural gradient ingeniously. The QP_MVC_NMF algorithm is quite efficient for small-scale problems and the NG_MVC_NMF algorithm is more suitable for large-scale problems. Simulations show the efficiency and validity of the proposed methods in applications of blind source separation and human face images analysis.

Mixing Matrix Estimation From Sparse Mixtures With Unknown Number of Sources

In blind source separation, many methods have been proposed to estimate the mixing matrix by exploiting sparsity. However, they often need to know the source number a priori, which is very inconvenient in practice. In this paper, a new method, namely nonlinear projection and column masking (NPCM), is proposed to estimate the mixing matrix. A major advantage of NPCM is that it does not need any knowledge of the source number. In NPCM, the objective function is based on a nonlinear projection and its maxima just correspond to the columns of the mixing matrix. Thus a column can be estimated first by locating a maximum and then deflated by a masking operation. This procedure is repeated until the evaluation of the objective function decreases to zero dramatically. Thus the mixing matrix and the number of sources are estimated simultaneously. Because the masking procedure may result in some small and useless local maxima, particle swarm optimization (PSO) is introduced to optimize the objective function. Feasibility and efficiency of PSO are also discussed. Comparative experimental results show the efficiency of NPCM, especially in the cases where the number of sources is unknown and the sources are relatively less sparse.

Projection-Pursuit-Based Method for Blind Separation of Nonnegative Sources

This paper presents a projection pursuit (PP) based method for blind separation of nonnegative sources. First, the available observation matrix is mapped to construct a new mixing model, in which the inaccessible source matrix is normalized to be column-sum-to-1. Then, the PP method is proposed to solve this new model, where the mixing matrix is estimated column by column through tracing the projections to the mapped observations in specified directions, which leads to the recovery of the sources. The proposed method is much faster than Chans method, which has similar assumptions to ours, due to the usage of optimal projection. It is also more advantageous in separating cross-correlated sources than the independence- and uncorrelation-based methods, as it does not employ any statistical information of the sources. Furthermore, the new method does not require the mixing matrix to be nonnegative. Simulation results demonstrate the superior performance of our method.

Adaptive Method for Nonsmooth Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is an emerging tool for meaningful low-rank matrix representation. In NMF, explicit constraints are usually required, such that NMF generates desired products (or factorizations), especially when the products have significant sparseness features. It is known that the ability of NMF in learning sparse representation can be improved by embedding a smoothness factor between the products. Motivated by this result, we propose an adaptive nonsmooth NMF (Ans-NMF) method in this paper. In our method, the embedded factor is obtained by using a data-related approach, so it matches well with the underlying products, implying a superior faithfulness of the representations. Besides, due to the usage of an adaptive selection scheme to this factor, the sparseness of the products can be separately constrained, leading to wider applicability and interpretability. Furthermore, since the adaptive selection scheme is processed through solving a series of typical linear programming problems, it can be easily implemented. Simulations using computer-generated data and real-world data show the advantages of the proposed Ans-NMF method over the state-of-the-art methods.

On the Security of Compressed Sensing-Based Signal Cryptosystem

With the development of the cyber-physical systems (CPS), the security analysis of the data therein becomes more and more important. Recently, due to the advantage of joint encryption and compression for data transmission in CPS, the emerging compressed sensing (CS)-based cryptosystem has attracted much attention, where security is of extreme importance. The existing methods only analyze the security of the plaintext under the assumption that the key is absolutely safe. However, for sparse plaintext, the prior sparsity knowledge of the plaintext could be exploited to partly retrieve the key, and then the plaintext, from the ciphertext. So, the existing methods do not provide a satisfactory security analysis. In this paper, it is conducted in the information theory frame, where the plaintext sparsity feature and the mutual information of the ciphertext, key, and plaintext are involved. In addition, the perfect secrecy criteria (Shannon-sense and Wyner-sense) are extended to measure the security. While the security level is given, the illegal access risk is also discussed. It is shown that the CS-based cryptosystem achieves the extended Wyner-sense perfect secrecy, but when the key is used repeatedly, both the plaintext and the key could be conditionally accessed.

An Efficient MAC Protocol With Adaptive Energy Harvesting for Machine-to-Machine Networks

In a machine-to-machine network, the throughput performance plays a very important role. Recently, an attractive energy harvesting technology has shown great potential to the improvement of the network throughput, as it can provide consistent energy for wireless devices to transmit data. Motivated by that, an efficient energy harvesting-based medium access control (MAC) protocol is designed in this paper. In this protocol, different devices first harvest energy adaptively and then contend the transmission opportunities with energy level related priorities. Then, a new model is proposed to obtain the optimal throughput of the network, together with the corresponding hybrid differential evolution algorithm, where the involved variables are energy-harvesting time, contending time, and contending probability. Analytical and simulation results show that the network based on the proposed MAC protocol has greater throughput than that of the traditional methods. In addition, as expected, our scheme has less transmission delay, further enhancing its superiority.

Nonorthogonal Approximate Joint Diagonalization With Well-Conditioned Diagonalizers

To make the results reasonable, existing joint diagonalization algorithms have imposed a variety of constraints on diagonalizers. Actually, those constraints can be imposed uniformly by minimizing the condition number of diagonalizers. Motivated by this, the approximate joint diagonalization problem is reviewed as a multiobjective optimization problem for the first time. Based on this, a new algorithm for nonorthogonal joint diagonalization is developed. The new algorithm yields diagonalizers which not only minimize the diagonalization error but also have as small condition numbers as possible. Meanwhile, degenerate solutions are avoided strictly. Besides, the new algorithm imposes few restrictions on the target set of matrices to be diagonalized, which makes it widely applicable. Primary results on convergence are presented and we also show that, for exactly jointly diagonalizable sets, no local minima exist and the solutions are unique under mild conditions. Extensive numerical simulations illustrate the performance of the algorithm and provide comparison with other leading diagonalization methods. The practical use of our algorithm is shown for blind source separation (BSS) problems, especially when ill-conditioned mixing matrices are involved.