Nonnegative Tensor Factorization Algorithms Research Articles

Efficient Nonnegative Tensor Factorization via Saturating Coordinate Descent

With the advancements in computing technology and web-based applications, data are increasingly generated in multi-dimensional form. These data are usually sparse due to the presence of a large number of users and fewer user interactions. To deal with this, the Nonnegative Tensor Factorization (NTF) based methods have been widely used. However existing factorization algorithms are not suitable to process in all three conditions of size, density, and rank of the tensor. Consequently, their applicability becomes limited. In this article, we propose a novel fast and efficient NTF algorithm using the element selection approach. We calculate the element importance using Lipschitz continuity and propose a saturation point-based element selection method that chooses a set of elements column-wise for updating to solve the optimization problem. Empirical analysis reveals that the proposed algorithm is scalable in terms of tensor size, density, and rank in comparison to the relevant state-of-the-art algorithms.

Nonnegative Tensor Factorization Approach Applied to Fission Chamber’s Output Signals Blind Source Separation

Inside nuclear reactors, gamma-rays emitted from nuclei together with the neutrons introduce unwanted backgrounds in neutron spectra. For this reason, powerful extraction methods are needed to extract useful neutron signal from recorded mixture and thus to obtain clearer neutron flux spectrum. Actually, several techniques have been developed to discriminate between neutrons and gamma-rays in a mixed radiation field. Most of these techniques, tackle using analogue discrimination methods. Others propose to use some organic scintillators to achieve the discrimination task. Recently, systems based on digital signal processors are commercially available to replace the analog systems. As alternative to these systems, we aim in this work to verify the feasibility of using a Nonnegative Tensor Factorization (NTF) to blind extract neutron component from mixture signals recorded at the output of fission chamber (WL-7657). This last have been simulated through the Geant4 linked to Garfield++ using a 252Cf neutron source. To achieve our objective of obtaining the best possible neutron-gamma discrimination, we have applied the two different NTF algorithms, which have been found to be the best methods that allow us to analyse this kind of nuclear data.

Non-negative sub-tensor ensemble factorization (NsTEF) algorithm. A new incremental tensor factorization for large data sets.

In this work we present a novel algorithm for nonnegative tensor factorization (NTF). Standard NTF algorithms are very restricted in the size of tensors that can be decomposed. Our algorithm overcomes this size restriction by interpreting the tensor as a set of sub-tensors and by proceeding the decomposition of sub-tensor by sub-tensor. This approach requires only one sub-tensor at once to be available in memory.

Fast nonnegative tensor factorization based on accelerated proximal gradient and low-rank approximation

Nonnegative tensor factorization (NTF) has been widely applied in high-dimensional nonnegative tensor data analysis. However, most of the existing algorithms suffer from slow convergence caused by the nonnegativity constraint and hence their practical applications are severely limited. In this study, we propose a new algorithm called FastNTF_APG to speed up NTF by combining accelerated proximal gradient and low-rank approximation. Experimental results demonstrate that FastNTF_APG achieves significantly higher computational efficiency than state-of-the-art NTF algorithms.

A sparse neighborhood preserving non-negative tensor factorization algorithm for facial expression recognition

In this paper, a novel sparse neighborhood preserving non-negative tensor factorization (SNPNTF) algorithm is proposed for facial expression recognition. It is derived from non-negative tensor factorization (NTF), and it works in the rank-one tensor space. A sparse constraint is adopted into the objective function, which takes the optimization step in the direction of the negative gradient, and then projects onto the sparse constrained space. To consider the spatial neighborhood structure and the class-based discriminant information, a neighborhood preserving constraint is adopted based on the manifold learning and graph preserving theory. The Laplacian graph which encodes the spatial information in the face samples and the penalty graph which considers the pre-defined class information are considered in this constraint. By using it, the obtained parts-based representations of SNPNTF vary smoothly along the geodesics of the data manifold and they are more discriminant for recognition. SNPNTF is a quadratic convex function in the tensor space, and it could converge to the optimal solution. The gradient descent method is used for the optimization of SNPNTF to ensure the convergence property. Experiments are conducted on the JAFFE database, the Cohn---Kanade database and the AR database. The results demonstrate that SNPNTF provides effective facial representations and achieves better recognition performance, compared with non-negative matrix factorization, NTF and some variant algorithms. Also, the convergence property of SNPNTF is well guaranteed.

Generalized Discriminant Orthogonal Nonnegative Tensor Factorization for Facial Expression Recognition

In order to overcome the limitation of traditional nonnegative factorization algorithms, the paper presents a generalized discriminant orthogonal non-negative tensor factorization algorithm. At first, the algorithm takes the orthogonal constraint into account to ensure the nonnegativity of the low-dimensional features. Furthermore, the discriminant constraint is imposed on low-dimensional weights to strengthen the discriminant capability of the low-dimensional features. The experiments on facial expression recognition have demonstrated that the algorithm is superior to other non-negative factorization algorithms.

Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework

We review algorithms developed for nonnegative matrix factorization (NMF) and nonnegative tensor factorization (NTF) from a unified view based on the block coordinate descent (BCD) framework. NMF and NTF are low-rank approximation methods for matrices and tensors in which the low-rank factors are constrained to have only nonnegative elements. The nonnegativity constraints have been shown to enable natural interpretations and allow better solutions in numerous applications including text analysis, computer vision, and bioinformatics. However, the computation of NMF and NTF remains challenging and expensive due the constraints. Numerous algorithmic approaches have been proposed to efficiently compute NMF and NTF. The BCD framework in constrained non-linear optimization readily explains the theoretical convergence properties of several efficient NMF and NTF algorithms, which are consistent with experimental observations reported in literature. In addition, we discuss algorithms that do not fit in the BCD framework contrasting them from those based on the BCD framework. With insights acquired from the unified perspective, we also propose efficient algorithms for updating NMF when there is a small change in the reduced dimension or in the data. The effectiveness of the proposed updating algorithms are validated experimentally with synthetic and real-world data sets.

Non-Negative Tensor Factorization Applied to Music Genre Classification

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Music genre classification techniques are typically applied to the data matrix whose columns are the feature vectors extracted from music recordings. In this paper, a feature vector is extracted using a texture window of one sec, which enables the representation of any 30 sec long music recording as a time sequence of feature vectors, thus yielding a feature matrix. Consequently, by stacking the feature matrices associated to any dataset recordings, a tensor is created, a fact which necessitates studying music genre classification using tensors. First, a novel algorithm for non-negative tensor factorization (NTF) is derived that extends the non-negative matrix factorization. Several variants of the NTF algorithm emerge by employing different cost functions from the class of Bregman divergences. Second, a novel supervised NTF classifier is proposed, which trains a basis for each class separately and employs basis orthogonalization. A variety of spectral, temporal, perceptual, energy, and pitch descriptors is extracted from 1000 recordings of the GTZAN dataset, which are distributed across 10 genre classes. The NTF classifier performance is compared against that of the multilayer perceptron and the support vector machines by applying a stratified 10-fold cross validation. A genre classification accuracy of 78.9% is reported for the NTF classifier demonstrating the superiority of the aforementioned multilinear classifier over several data matrix-based state-of-the-art classifiers. </para>