Semi-nonnegative Matrix Factorization Research Articles

Multi-View Clustering via Deep Matrix Factorization

Multi-View Clustering (MVC) has garnered more attention recently since many real-world data are comprised of different representations or views. The key is to explore complementary information to benefit the clustering problem. In this paper, we present a deep matrix factorization framework for MVC, where semi-nonnegative matrix factorization is adopted to learn the hierarchical semantics of multi-view data in a layer-wise fashion. To maximize the mutual information from each view, we enforce the non-negative representation of each view in the final layer to be the same. Furthermore, to respect the intrinsic geometric structure in each view data, graph regularizers are introduced to couple the output representation of deep structures. As a non-trivial contribution, we provide the solution based on alternating minimization strategy, followed by a theoretical proof of convergence. The superior experimental results on three face benchmarks show the effectiveness of the proposed deep matrix factorization model.

Semi-nonnegative Matrix Factorization Algorithm Based on Genetic Algorithm Initialization

Semi-nonnegative Matrix Factorization Algorithm Based on Genetic Algorithm Initialization

Hopfield Neural Network Approach for Supervised Nonlinear Spectral Unmixing

Nonlinear unmixing, which has attracted considerable interest from researchers and developers, has been successfully applied in many real-world hyperspectral imaging scenarios. Hopfield neural network (HNN) machine learning has already proven successful in solving the linear mixture model; this study utilized an HNN machine learning approach to solve the generalized bilinear model (GBM) optimization problem. Two HNNs were constructed in a successive manner to solve respective seminonnegative matrix factorization problems intended for abundance and nonlinear coefficient estimation. In the proposed HNN-based GBM unmixing method, both HNNs evolve to stable states after a number of iterations to obtain unmixing results related to the states of neurons. In experiments on synthetic data, the proposed method showed more efficient performance in regard to abundance estimation accuracy than other GBM optimization algorithms, especially when given reliable endmember spectra. The proposed method was also applied to real hyperspectral data and still demonstrated notable advantages despite the obvious increase in unmixing difficulty.

Directional Clustering Through Matrix Factorization.

This paper deals with a clustering problem where feature vectors are clustered depending on the angle between feature vectors, that is, feature vectors are grouped together if they point roughly in the same direction. This directional distance measure arises in several applications, including document classification and human brain imaging. Using ideas from the field of constrained low-rank matrix factorization and sparse approximation, a novel approach is presented that differs from classical clustering methods, such as seminonnegative matrix factorization, K -EVD, or k -means clustering, yet combines some aspects of all these. As in nonnegative matrix factorization and K -EVD, the matrix decomposition is iteratively refined to optimize a data fidelity term; however, no positivity constraint is enforced directly nor do we need to explicitly compute eigenvectors. As in k -means and K -EVD, each optimization step is followed by a hard cluster assignment. This leads to an efficient algorithm that is shown here to outperform common competitors in terms of clustering performance and/or computation speed. In addition to a detailed theoretical analysis of some of the algorithm's main properties, the approach is empirically evaluated on a range of toy problems, several standard text clustering data sets, and a high-dimensional problem in brain imaging, where functional magnetic resonance imaging data are used to partition the human cerebral cortex into distinct functional regions.

Learning to Detect Anomalies in Surveillance Video

Detecting anomalies in surveillance videos, that is, finding events or objects with low probability of occurrence, is a practical and challenging research topic in computer vision community. In this paper, we put forward a novel unsupervised learning framework for anomaly detection. At feature level, we propose a Sparse Semi-nonnegative Matrix Factorization (SSMF) to learn local patterns at each pixel, and a Histogram of Nonnegative Coefficients (HNC) can be constructed as local feature which is more expressive than previously used features like Histogram of Oriented Gradients (HOG). At model level, we learn a probability model which takes the spatial and temporal contextual information into consideration. Our framework is totally unsupervised requiring no human-labeled training data. With more expressive features and more complicated model, our framework can accurately detect and localize anomalies in surveillance video. We carried out extensive experiments on several benchmark video datasets for anomaly detection, and the results demonstrate the superiority of our framework to state-of-the-art approaches, validating the effectiveness of our framework.

Structure constrained semi-nonnegative matrix factorization for EEG-based motor imagery classification

BackgroundElectroencephalogram (EEG) provides a non-invasive approach to measure the electrical activities of brain neurons and has long been employed for the development of brain-computer interface (BCI). For this purpose, various patterns/features of EEG data need to be extracted and associated with specific events like cue-paced motor imagery. However, this is a challenging task since EEG data are usually non-stationary time series with a low signal-to-noise ratio. New methodIn this study, we propose a novel method, called structure constrained semi-nonnegative matrix factorization (SCS-NMF), to extract the key patterns of EEG data in time domain by imposing the mean envelopes of event-related potentials (ERPs) as constraints on the semi-NMF procedure. The proposed method is applicable to general EEG time series, and the extracted temporal features by SCS-NMF can also be combined with other features in frequency domain to improve the performance of motor imagery classification. ResultsReal data experiments have been performed using the SCS-NMF approach for motor imagery classification, and the results clearly suggest the superiority of the proposed method. Comparison with existing methodsComparison experiments have also been conducted. The compared methods include ICA, PCA, Semi-NMF, Wavelets, EMD and CSP, which further verified the effectivity of SCS-NMF. ConclusionsThe SCS-NMF method could obtain better or competitive performance over the state of the art methods, which provides a novel solution for brain pattern analysis from the perspective of structure constraint.

Exact and Heuristic Algorithms for Semi-Nonnegative Matrix Factorization

Given a matrix $M$ (not necessarily nonnegative) and a factorization rank $r$, semi-nonnegative matrix factorization (semi-NMF) looks for a matrix $U$ with $r$ columns and a nonnegative matrix $V$ with $r$ rows such that $UV$ is the best possible approximation of $M$ according to some metric. In this paper, we study the properties of semi-NMF from which we develop exact and heuristic algorithms. Our contribution is threefold. First, we prove that the error of a semi-NMF of rank $r$ has to be smaller than the best unconstrained approximation of rank $r-1$. This leads us to a new initialization procedure based on the singular value decomposition (SVD) with a guarantee on the quality of the approximation. Second, we propose an exact algorithm (that is, an algorithm that finds an optimal solution), also based on the SVD, for a certain class of matrices (including nonnegative irreducible matrices) from which we derive an initialization for matrices not belonging to that class. Numerical experiments illustrate that this second approach performs extremely well, and allows us to compute optimal semi-NMF decompositions in many situations. Finally, we analyze the computational complexity of semi-NMF proving its NP-hardness, already in the rank-one case (that is, for $r = 1$), and we show that semi-NMF is sometimes ill-posed (that is, an optimal solution does not exist).

Nonlinear Unmixing of Hyperspectral Data Using Semi-Nonnegative Matrix Factorization

Nonlinear spectral mixture models have recently received particular attention in hyperspectral image processing. In this paper, we present a novel optimization method of nonlinear unmixing based on a generalized bilinear model (GBM), which considers the second-order scattering of photons in a spectral mixture model. Semi-nonnegative matrix factorization (semi-NMF) is used for the optimization to process a whole image in matrix form. When endmember spectra are given, the optimization of abundance and interaction abundance fractions converge to a local optimum by alternating update rules with simple implementation. The proposed method is evaluated using synthetic datasets considering its robustness for the accuracy of endmember extraction and spectral complexity, and shows smaller errors in abundance fractions rather than conventional methods. GBM-based unmixing using semi-NMF is applied to the analysis of an airborne hyperspectral image taken over an agricultural field with many endmembers, and it visualizes the impact of a nonlinear interaction on abundance maps at reasonable computational cost.

Command Generation Techniques for a Pin Array using the SVD and the SNMF

This paper presents two command generation techniques for improving the surface generation time of a pin array device, specifically a prototype called Digital Clay. The procedures use singular value decomposition (SVD) and semi-nonnegative matrix factorization (SNMF) to create intermediate surfaces that sum to a desired surface. Although the focus is on pin array control, the techniques can apply to any system with a set of subsystems coupled by the row-column input method. The row-column method allows multiple actuators to be controlled by a few inputs. Current procedures for systems using the row-column method are too slow for many applications. Recent work has improved the time response of these systems using simultaneous feedback control but can potentially create unwanted oscillatory behavior. This paper describes command generation techniques using the SVD and SNMF that maintain the improvement in time without the oscillations. Simulation results compare the two procedures to the line scanning technique used in previous work on pin arrays.

A Long-Term Care Plan for North Carolina

Multivariate time series from neural electrophysiological recordings are a rich source of information about neural processing systems and require appropriate methods for proper analysis. Current methods for mapping brain function in these data using neural decoding aggregate information across space and time in limited ways, rarely incorporating spatial dependence across recording locations. We propose Shrinkage Classification for Overlapping Time Series (SCOTS), a neural decoding method that maps brain function, while accounting for spatio-temporal dependence, through interpretable dimensionality reduction and classification of multivariate neural time series. SCOTS has two components: first, overlapping clustering from sparse semi-nonnegative matrix factorization gives a data-driven aggregation of neural information across space; second, wavelet-transformed nearest shrunken centroids with sparse group lasso performs multi-class classification with selection of informative clusters and time intervals. We demonstrate use of SCOTS by applying it to human intracranial electrophysiological and MEG data collected while participants viewed visual stimuli from a range of categories. The method reveals the dynamic activation of brain regions with sensitivity to different object categories, giving insight into spatio-temporal contributions of these neural processing systems.