Study subnetwork developing pattern of autism children by non-negative matrix factorization

The significance of Non-negative Matrix Factorization ((NMF) in the field of automatic text summarization is rapidly increasing due to its interpretation and storage capabilities. Interpretation defines the ease at which the structure of high dimensional data can be understood. While, storage capability relates to the extent of data reduction process achieved by NMF. The parametric values that serve as input to the NMF process include initialization method, rank of factorization, sparseness measure and maximum iteration. These inputs are vital to the output produced by NMF. These parameters of NMF were not been considered in the existing literature on Automatic Text Summarization (ATS). This paper sheds light specifically on sparseness of NMF when applied to ATS and the impact it makes to the quality of the summary generated. In this study on NMF algorithm that supports sparseness is treated with various degree of sparsity and its performance impact on text summary generated is compared with other NMF algorithms without sparseness constraints.

Non-negative matrix factorization (NMF) is widely used in feature extraction and dimension reduction fields. Essentially, it is an optimization problem to determine two non-negative low rank matrices \(W_{m \times k}\) and \(H_{k \times n}\) for a given matrix \(A_{m \times n}\), satisfying \(A_{m \times n} \approx W_{m \times k}H_{k \times n}\). In this paper, a novel approach to improve the image decomposing and reconstruction effects by introducing the Singular Value Decomposing (SVD)-based initialization scheme of factor matrices W and H, and another measure called choosing rule to determine the optimum value of factor rank k, are proposed. The input image is first decomposed using SVD to get its singular values and corresponding eigenvectors. Then, the number of main components as the rank value k is extracted. Then, the singular values and corresponding eigenvectors are used to initialize W and H based on selected rank k. Finally, convergent results are obtained using multiplicative and additive update rules. However, iterative NMF algorithms’ convergence is very slow on most platforms limiting its practicality. To this end, a parallel implementation frame of described improved NMF algorithm using CUDA, a tool for algorithms parallelization on massively parallel processors, i.e., many-core graphics processors, is presented. Experimental results show that our approach can get better decomposing effect than traditional NMF implementations and dramatic accelerate rate comparing to serial schemes as well as existing distributed-system implementations.

Lee and Seung proposed nonnegative matrix factorization (NMF) algorithms to decompose patterns and images for structure retrieving. The NMF algorithms have been applied to various optimization problems. However, it is difficult to prove the convergence of this class of learning algorithms. This paper presents the global minima analysis of the NMF algorithms. In the analysis, invariant set is constructed so that the non-divergence of the algorithms can be guaranteed in the set. Using the features of linear equation systems and their solutions, the fixed points and convergence properties of the update algorithms are discussed in detail. The analysis shows that, although the cost function is not convex in both A and X together, it is possible to obtain the global minima from the particular learning algorithms. For different initializations, simulations are presented to confirm the analysis results.

Characterizing sediment sources by non-negative matrix factorization of detrital geochronological data

Non-negative Matrix Factorisation (NMF) is a commonly used tool in many musical signal processing tasks, including Automatic Music Transcription (AMT). However unsupervised NMF is seen to be problematic in this context, and harmonically constrained variants of NMF have been proposed. While useful, the harmonic constraints may be constrictive in mixed signals. We have previously observed that recovery of overlapping signal elements using NMF is improved through introduction of a sparse coding step, and propose here the incorporation of a sparse coding step using the Hellinger distance into a NMF algorithm. Improved AMT results for unsupervised NMF are reported.

Nonnegative Matrix Factorization (NMF) approximates a given data matrix as a product of two low rank nonnegative matrices, usually by minimizing the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> or the KL distance between the data matrix and the matrix product. This factorization was shown to be useful for several important computer vision applications. We propose here a new NMF algorithm that minimizes the Earth Mover's Distance (EMD) error between the data and the matrix product. We propose an iterative NMF algorithm (EMD NMF) and prove its convergence. The algorithm is based on linear programming. We discuss the numerical difficulties of the EMD NMF and propose an efficient approximation. Naturally, the matrices obtained with EMD NMF are different from those obtained with L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> NMF. We discuss these differences in the context of two challenging computer vision tasks - texture classification and face recognition - and demonstrate the advantages of the proposed method.

To solve the separation of multi-source signals and detect their features from a single channel, a signal separation method using multi-constraint non-negative matrix factorization (NMF) is proposed. In view of the existing NMF algorithm not performing well in the underdetermined blind source separation, the β-divergence constraints and determinant constraints are introduced in the NMF algorithm, which can enhance local feature information and reduce redundant components by constraining the objective function. In addition, the Sine-bell window function is selected as the processing method for short-time Fourier transform (STFT), and it can preserve the overall feature distribution of the original signal. The original vibration signal is first transformed into time-frequency domain with the STFT, which describes the local characteristic of the signal from the time-frequency distribution. Then, the multi-constraint NMF is applied to reduce the dimensionality of the data and separate feature components in the low dimensional space. Meanwhile, the parameter WK is constructed to filter the reconstructed signal that recombined with the feature component in the time domain. Ultimately, the separated signals will be subjected to envelope spectrum analysis to detect fault features. The simulated and experimental results indicate the effectiveness of the proposed approach, which can realize the separation of multi-source signals and their fault diagnosis of bearings. In addition, it is also confirmed that the proposed method, juxtaposed with the NMF algorithm of the traditional objective function, is more applicable for compound fault diagnosis of the rotating machinery.

Non-negative matrix factorization (NMF) has found numerous applications, due to its ability to provide interpretable decompositions. Perhaps surprisingly, existing results regarding its uniqueness properties are rather limited, and there is much room for improvement in terms of algorithms as well. Uniqueness and computational aspects of NMF are revisited here from a geometrical point of view. Both symmetric and asymmetric NMF are considered, the former being tantamount to element-wise non-negative square-root factorization of positive semidefinite matrices. New and insightful uniqueness results are derived, e.g., it is shown that a sufficient condition for uniqueness is that the conic hull of the latent factors is a superset of a particular second-order cone. Checking this is shown to be NP-complete; yet it offers insights on latent sparsity, as is also shown in a new necessary condition, to a smaller extent. On the computational side, a new efficient algorithm for symmetric NMF is proposed which uses Procrustes rotations. Simulation results show promising performance with respect to the state-of-art. The new algorithm is also applied to a clustering problem for co-authorship data, yielding meaningful and interpretable results.

ABSTRACTHyperspectral unmixing (HU) has drawn remarkable attention because it can decompose mixed pixels into a set of endmembers and abundance fractions. And the nonnegative matrix factorization (NMF) algorithm has been widely used for solving hyperspectral spectral unmixing problem. This letter proposes a Hessian graph regularized NMF (HGNMF) algorithm, which relies upon the construction of a Hessian graph representation, to solve the hyperspectral unmixing problem. According to the HGNMF algorithm, the smoothness in the estimated abundance maps is well promoted. Moreover, the optimized problem of HGNMF algorithm is also solved by employing the multiplicative updating rules. Compared to other algorithms, the proposed HGNMF algorithm demonstrates lots of advantages based on the simulated results of the synthetic data and real data sets.

Spiny Lobster Sound Identification Based on Blind Source Separation (BSS) for Passive Acoustic Monitoring (PAM)

Nonnegative Matrix Factorization (NMF) is an unsupervised learning method that has been already applied to many applications of spectral signal unmixing. However, its efficiency in some applications strongly depends on optimization algorithms used for estimating the underlying nonnegatively constrained subproblems. In this paper, we attempt to tackle the optimization tasks with the inexact Interior-Point (IP) algorithm that has been successfully applied to image deblurring [S. Bonettini, T. Serafini, 2009]. The experiments demonstrate that the proposed NMF algorithm considerably outperforms the well-known NMF algorithms for blind unmixing of the Raman spectra.

Identifying glass defects through machine visual has a vital importance for the efficient production of high quality glass. In this paper, a method based on the combination of Non-negative Matrix Factorization (NMF) and Sparse Representation Classification (SRC) was proposed for the identification of glass defects. According to the properties of glass defect image, NMF algorithm is used to decompose a defect image into one base image and another weighted coefficient matrix, so the defect image is characterized by the coefficient matrix. Then, SRC algorithm is used to classify glass defects. Simulation results show that, with NMF and SRC, glass defects images could be effectively identified.

Non-negative matrix factorization (NMF) provides a lower rank approximation of a matrix. Due to nonnegativity imposed on the factors, it gives a latent structure that is often more physically meaningful than other lower rank approximations such as singular value decomposition (SVD). Most of the algorithms proposed in literature for NMF have been based on minimizing the Frobenius norm. This is partly due to the fact that the minimization problem based on the Frobenius norm provides much more flexibility in algebraic manipulation than other divergences. In this paper we propose a fast NMF algorithm that is applicable to general Bregman divergences. Through Taylor series expansion of the Bregman divergences, we reveal a relationship between Bregman divergences and Euclidean distance. This key relationship provides a new direction for NMF algorithms with general Bregman divergences when combined with the scalar block coordinate descent method. The proposed algorithm generalizes several recently proposed methods for computation of NMF with Bregman divergences and is computationally faster than existing alternatives. We demonstrate the effectiveness of our approach with experiments conducted on artificial as well as real world data.

Autism is hypothesized to result in a cortical excitatory and inhibitory imbalance driven by inhibitory interneuron dysfunction, which is associated with the generation of gamma oscillations. On the other hand, impaired motor control has been widely reported in autism. However, no study has focused on the gamma oscillations during motor control in autism. In the present study, we investigated the motor-related gamma oscillations in autism using magnetoencephalography. Magnetoencephalographic signals were recorded from 14 right-handed human children with autism (5 female), aged 5–7 years, and age- and IQ-matched 15 typically developing children during a motor task using their right index finger. Consistent with previous studies, the autism group showed a significantly longer button response time and reduced amplitude of motor-evoked magnetic fields. We observed that the autism group exhibited a low peak frequency of motor-related gamma oscillations from the contralateral primary motor cortex, and these were associated with the severity of autism symptoms. The autism group showed a reduced power of motor-related gamma oscillations in the bilateral primary motor cortex. A linear discriminant analysis using the button response time and gamma oscillations showed a high classification performance (86.2% accuracy). The alterations of the gamma oscillations in autism might reflect the cortical excitatory and inhibitory imbalance. Our findings provide an important clue into the behavioral and neurophysiological alterations in autism and a potential biomarker for autism.SIGNIFICANCE STATEMENT Currently, the diagnosis of autism has been based on behavioral assessments, and a crucial issue in the diagnosis of autism is to identify objective and quantifiable clinical biomarkers. A key hypothesis of the neurophysiology of autism is an excitatory and inhibitory imbalance in the brain, which is associated with the generation of gamma oscillations. On the other hand, motor deficits have also been widely reported in autism. This is the first study to demonstrate low motor performance and altered motor-related gamma oscillations in autism, reflecting a brain excitatory and inhibitory imbalance. Using these behavioral and neurophysiological parameters, we classified autism and control group with good accuracy. This work provides important information on behavioral and neurophysiological alterations in patients with autism.

Nonnegative matrix factorization (NMF) is a widely-used method for multivariate analysis of nonnegative data, the goal of which is decompose a data matrix into a basis matrix and an encoding variable matrix with all of these matrices allowed to have only nonnegative elements. In this paper we present simple algorithms for orthogonal NMF, where orthogonality constraints are imposed on basis matrix or encoding matrix. We develop multiplicative updates directly from the true gradient (natural gradient) in Stiefel manifold, whereas existing algorithms consider additive orthogonality constraints. Numerical experiments on face image data for a image representation task show that our orthogonal NMF algorithm preserves the orthogonality, while the goodness-of-fit (GOF) is minimized. We also apply our orthogonal NMF to a clustering task, showing that it works better than the original NMF, which is confirmed by experiments on several UCI repository data sets.