Blind Source Separation by Nonnegative Matrix Factorization with Minimum-Volume Constraint

Recently, nonnegative matrix factorization (NMF) attracts more and more attentions for the promising of wide applications. A problem that still remains is that, however, the factors resulted from it may not necessarily be realistically interpretable. Some constraints are usually added to the standard NMF to generate such interpretive results. In this paper, a minimum-volume constrained NMF is proposed and an efficient multiplicative update algorithm is developed based on the natural gradient optimization. The proposed method can be applied to the blind source separation (BSS) problem, a hot topic with many potential applications, especially if the sources are mutually dependent. Simulation results of BSS for images show the superiority of the proposed method.

Blind extraction using fractional lower-order statistics

In traditional method to blindly extract interesting source signals sequentially, the second-order or higher-order statistics of signals are often utilized. However, for impulsive sources, both of the second-order and higher-order statistics may degenerate. Therefore, it is necessary to exploit new method for the blind extraction of impulsive sources. Based on the best compression-reconstruction principle, a novel model is proposed in this work, together with the corresponding algorithm. The proposed method can be used for blind extraction of sources which are distributed from alpha stable process. Simulations are given to illustrate availability and robustness of our algorithm.

Blind source separation by fully nonnegative constrained iterative volume maximization

Blind source separation (BSS) has been widely discussed in many real applications. Recently, under the assumption that both of the sources and the mixing matrix are nonnegative, Wang develop an amazing BSS method by using volume maximization. However, the algorithm that they have proposed can guarantee the nonnegativities of the sources only, but cannot obtain a nonnegative mixing matrix necessarily. In this letter, by introducing additional constraints, a method for fully nonnegative constrained iterative volume maximization (FNCIVM) is proposed. The result is with more interpretation, while the algorithm is based on solving a single linear programming problem. Numerical experiments with synthetic signals and real-world images are performed, which show the effectiveness of the proposed method.

On blind separability based on the temporal predictability method

This letter discusses blind separability based on temporal predictability (Stone, 2001; Xie, He, & Fu, 2005). Our results show that the sources are separable using the temporal predictability method if and only if they have different temporal structures (i.e., autocorrelations). Consequently, the applicability and limitations of the temporal predictability method are clarified. In addition, instead of using generalized eigendecomposition, we suggest using joint approximate diagonalization algorithms to improve the robustness of the method. A new criterion is presented to evaluate the separation results. Numerical simulations are performed to demonstrate the validity of the theoretical results.

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.

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.