Graph-Preserving Sparse Nonnegative Matrix Factorization With Application to Facial Expression Recognition
In this paper, a novel graph-preserving sparse nonnegative matrix factorization (GSNMF) algorithm is proposed for facial expression recognition. The GSNMF algorithm is derived from the original NMF algorithm by exploiting both sparse and graph-preserving properties. The latter may contain the class information of the samples. Therefore, GSNMF can be conducted as an unsupervised or a supervised dimension reduction method. A sparse representation of the facial images is obtained by minimizing the -norm of the basis images. Furthermore, according to the graph embedding theory, the neighborhood of the samples is preserved by retaining the graph structure in the mapped space. The GSNMF decomposition transforms the high-dimensional facial expression images into a locality-preserving subspace with sparse representation. To guarantee convergence, we use the projected gradient method to calculate the nonnegative solution of GSNMF. Experiments are conducted on the JAFFE database and the Cohn-Kanade database with unoccluded and partially occluded facial images. The results show that the GSNMF algorithm provides better facial representations and achieves higher recognition rates than nonnegative matrix factorization. Moreover, GSNMF is also more robust to partial occlusions than other tested methods.
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.
Multitask Sparse Nonnegative Matrix Factorization for Joint Spectral–Spatial Hyperspectral Imagery Denoising
Hyperspectral imagery (HSI) denoising is a challenging problem because of the difficulty in preserving both spectral and spatial structures simultaneously. In recent years, sparse coding, among many methods dedicated to the problem, has attracted much attention and showed state-of-the-art performance. Due to the low-rank property of natural images, an assumption can be made that the latent clean signal is a linear combination of a minority of basis atoms in a dictionary, while the noise component is not. Based on this assumption, denoising can be explored as a sparse signal recovery task with the support of a dictionary. In this paper, we propose to solve the HSI denoising problem by sparse nonnegative matrix factorization (SNMF), which is an integrated model that combines parts-based dictionary learning and sparse coding. The noisy image is used as the training data to learn a dictionary, and sparse coding is used to recover the image based on this dictionary. Unlike most HSI denoising approaches, which treat each band image separately, we take the joint spectral-spatial structure of HSI into account. Inspired by multitask learning, a multitask SNMF (MTSNMF) method is developed, in which bandwise denoising is linked across the spectral domain by sharing a common coefficient matrix. The intrinsic image structures are treated differently but interdependently within the spatial and spectral domains, which allows the physical properties of the image in both spatial and spectral domains to be reflected in the denoising model. The experimental results show that MTSNMF has superior performance on both synthetic and real-world data compared with several other denoising methods.
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