Low-rank Nonnegative Matrix Factorization Research Articles

Underwater Image Enhancement with the Low-Rank Nonnegative Matrix Factorization Method

Due to the scattering and absorption effects in the undersea environment, underwater image enhancement is a challenging problem. To obtain the ground-truth data for training is also an open problem. So, the learning process is unavailable. In this paper, we propose a Low-Rank Nonnegative Matrix Factorization (LR-NMF) method, which only uses the degraded underwater image as input to generate the more clear and realistic image. According to the underwater image formation model, the degraded underwater image could be separated into three parts, the directed component, the back and forward scattering components. The latter two parts can be considered as scattering. The directed component is constrained to have a low rank. After that, the restored underwater image is obtained. The quantitative and qualitative analyses illustrate that the proposed method performed equivalent or better than the state-of-the-art methods. Yet, it’s simple to implement without the training process.

Monophonic and Polyphonic Wheezing Classification Based on Constrained Low-Rank Non-Negative Matrix Factorization.

The appearance of wheezing sounds is widely considered by physicians as a key indicator to detect early pulmonary disorders or even the severity associated with respiratory diseases, as occurs in the case of asthma and chronic obstructive pulmonary disease. From a physician’s point of view, monophonic and polyphonic wheezing classification is still a challenging topic in biomedical signal processing since both types of wheezes are sinusoidal in nature. Unlike most of the classification algorithms in which interference caused by normal respiratory sounds is not addressed in depth, our first contribution proposes a novel Constrained Low-Rank Non-negative Matrix Factorization (CL-RNMF) approach, never applied to classification of wheezing as far as the authors’ knowledge, which incorporates several constraints (sparseness and smoothness) and a low-rank configuration to extract the wheezing spectral content, minimizing the acoustic interference from normal respiratory sounds. The second contribution automatically analyzes the harmonic structure of the energy distribution associated with the estimated wheezing spectrogram to classify the type of wheezing. Experimental results report that: (i) the proposed method outperforms the most recent and relevant state-of-the-art wheezing classification method by approximately 8% in accuracy; (ii) unlike state-of-the-art methods based on classifiers, the proposed method uses an unsupervised approach that does not require any training.

Low-rank nonnegative matrix factorization on Stiefel manifold

Low rank is an important but ill-posed problem in the development of nonnegative matrix factorization (NMF) algorithms because the essential information is often encoded in a low-rank intrinsic data matrix, whereas noise and outliers are contained in a residue matrix. Most existing NMF approaches achieve low rank by directly specifying the dimensions of the factor matrices. A few others impose the low rank constraint on the factor matrix and use the alternating direction method of multipliers to solve the optimization problem. In contrast to previous approaches, this paper proposes a novel method for low-rank nonnegative matrix factorization on a Stiefel manifold (LNMFS), which utilizes the low rank structure of intrinsic data and transforms it into a Frobenius norm of the latent factors. To obtain orthogonal factors as distinct patterns, we further impose orthogonality constraints by assuming that the basis matrix lies on a Stiefel manifold. In addition, to improve the robustness of the data in a manifold structure, we incorporate the graph smoothness of the coefficient matrix. Finally, we develop an efficient alternative iterative algorithm to solve the optimization problem and provide proof of its convergence. Extensive experiments on real-world datasets demonstrate the superiority of the proposed method compared with other representative NMF-based algorithms.

Online/offline score informed music signal decomposition: application to minus one

In this paper, we propose a score-informed source separation framework based on non-negative matrix factorization (NMF) and dynamic time warping (DTW) that suits for both offline and online systems. The proposed framework is composed of three stages: training, alignment, and separation. In the training stage, the score is encoded as a sequence of individual occurrences and unique combinations of notes denoted as score units. Then, we proposed a NMF-based signal model where the basis functions for each score unit are represented as a weighted combination of spectral patterns for each note and instrument in the score obtained from a trained a priori over-completed dictionary. In the alignment stage, the time-varying gains are estimated at frame level by computing the projection of each score unit basis function over the captured audio signal. Then, under the assumption that only a score unit is active at a time, we propose an online DTW scheme to synchronize the score information with the performance. Finally, in the separation stage, the obtained gains are refined using local low-rank NMF and the separated sources are obtained using a soft-filter strategy. The framework has been evaluated and compared with other state-of-the-art methods for single channel source separation of small ensembles and large orchestra ensembles obtaining reliable results in terms of SDR and SIR. Finally, our method has been evaluated in the specific task of acoustic minus one, and some demos are presented.

Structurally Incoherent Low-Rank Nonnegative Matrix Factorization for Image Classification.

As a popular dimensionality reduction method, nonnegative matrix factorization (NMF) has been widely used in image classification. However, the NMF does not consider discriminant information from the data themselves. In addition, most NMF-based methods use the Euclidean distance as a metric, which is sensitive to noise or outliers in data. To solve these problems, in this paper, we introduce structural incoherence and low-rank to NMF and propose a novel nonnegative factorization method, called structurally incoherent low-rank NMF (SILR-NMF), in which we jointly consider structural incoherence and low-rank properties of data for image classification. For the corrupted data, we use the norm as a constraint to ensure the noise is sparse. SILR-NMF learns a clean data matrix from the noisy data by low-rank learning. As a result, the SILR-NMF can capture the global structure information of the data, which is more robust than local information to noise. By introducing the structural incoherence of the learned clean data, SILR-NMF ensures the clean data points from different classes are as independent as possible. To verify the performance of the proposed method, extensive experiments are conducted on six image databases. The experimental results demonstrate that our proposed method has substantial gain over existing NMF approaches.

Hyperspectral image restoration using framelet-regularized low-rank nonnegative matrix factorization

Hyperspectral image (HSI) restoration is a process to remove a mixture of various kinds of noise, which is a key preprocessing step to improve the performance of subsequent applications. Since the HSI has a large correlation between spectral bands and abundant geometric features in the spatial domain, thus the low-rank prior and spatial structure prior can be introduced to HSI restoration. However, many existing approaches usually directly use the nuclear norm and total variation (TV) regularization to depict the spectral-spatial priors of HSI, which inevitably requires singular value decomposition (SVD) computation and causes staircase artifacts in the image, respectively. To overcome these limitations, in this work, we propose a novel HSI restoration method named framelet-regularized low-rank nonnegative matrix factorization (F-LRNMF), in which the low-rank nonnegative matrix factorization is developed to describe that the HSI lies in a low-rank subspace. Furthermore, to decrease the staircase artifacts caused by TV regularization that directly applies to HSI, we use framelet regularization to constrain the factor whose size is much less than HSI itself. The framelet regularization can effectively preserve the details and geometric features of the restored HSI in the spatial domain. An efficient block successive upper-bound minimization (BSUM) algorithm is designed to solve the proposed optimization model. Meanwhile, we theoretically analyze that the algorithm can converge to the set of coordinate-wise minimizers. Experiments under various cases of simulated and real HSI data demonstrate the effectiveness of the proposed model and the efficiency of the numerical algorithm in terms of both quantitative and qualitative assessments.

Group Low-Rank Nonnegative Matrix Factorization With Semantic Regularizer for Hyperspectral Unmixing

In this paper, the low rank prior of abundances of hyperspectral data is explored and combined with semantic information to develop a new Group Low-rank constrained Nonnegative Matrix Factorization (GLrNMF) method for linear hyperspectral unmixing. First, hyperspectral image pixels are divided into several groups of superpixels, and then low-rank constraints are cast on them to explore the semantic geometry in both spatial and spectral domains. By incorporating semantic information into the NMF, we can recover more accurate endmembers and abundances in the linear unmixing model. Some experiments are taken on several synthetic and real hyperspectral data to investigate the performance of GLrNMF, and the results show that it can outperform some state-of-the-art unmixing results.

On the Importance of Super-Gaussian Speech Priors for Machine-Learning Based Speech Enhancement

For enhancing noisy signals, machine-learning based single-channel speech enhancement schemes exploit prior knowledge about typical speech spectral structures. To ensure a good generalization and to meet requirements in terms of computational complexity and memory consumption, certain methods restrict themselves to learning speech spectral envelopes. We refer to these approaches as machine-learning spectral envelope (MLSE)-based approaches. In this paper we show by means of theoretical and experimental analyses that for MLSE-based approaches, super-Gaussian priors allow for a reduction of noise between speech spectral harmonics which is not achievable using Gaussian estimators such as the Wiener filter. For the evaluation, we use a deep neural network (DNN)-based phoneme classifier and a low-rank nonnegative matrix factorization (NMF) framework as examples of MLSE-based approaches. A listening experiment and instrumental measures confirm that while super-Gaussian priors yield only moderate improvements for classic enhancement schemes, for MLSE-based approaches super-Gaussian priors clearly make an important difference and significantly outperform Gaussian priors.

Wide and Deep Model of Multi-Source Information-Aware Recommender System

Collaborative filtering recommendation suffers from the problems of high data sparsity, poor expansibility, cold start, and the difficulty of modeling user preferences, among which data sparsity is the greatest issue. Although our previous work on matrix completion model, named low rank non-negative matrix factorization and completion algorithm (LR-NMFC) and stochastic sub-gradient based low rank matrix completion algorithm, could effectively alleviate the sparsity problem, they customarily model the linear feature interactions instead of the complex nonlinear structures between users and items when making recommendations. To better depict user preferences and item features, we deepen the linear model LR-NMFC to establish a wide and deep model, which we named Wide and Deep model of Multi-source information-Aware recommender system (WDMMA), based on multi-source information composed of user-item interaction matrix, attributes, and context. The wide part mainly handles the linear interactions between users and items, while the deep part portrays the high-order nonlinear interactions. We pre-train both the wide and the deep part using LR-NMFC in the embedding layer. In the pooling layer, we define a pooling operation, AC-pooling, which is used to model the various interactions among users, items, attributes, and context information. Upon the pooling layer, we stack some hidden layers to capture the high-order nonlinear feature interactions. Experiments on two public datasets show that WDMMA can learn complex nonlinear feature patterns successfully and effectively and is beneficial to improve the recommendation performance. Therefore, it is an effective way to consider both linear user-item interactions and multi-source information-aware nonlinear interactions in a deep learning framework when making recommendations.

Speech Enhancement Under Low SNR Conditions Via Noise Estimation Using Sparse and Low-Rank NMF with Kullback–Leibler Divergence

A key stage in speech enhancement is noise estimation which usually requires prior models for speech or noise or both. However, prior models can sometimes be difficult to obtain. In this paper, without any prior knowledge of speech and noise, sparse and low-rank nonnegative matrix factorization (NMF) with Kullback-Leibler divergence is proposed to noise and speech estimation by decomposing the input noisy magnitude spectrogram into a low-rank noise part and a sparse speech-like part. This initial unsupervised speech-noise estimation allows us to set a subsequent regularized version of NMF or convolutional NMF to reconstruct the noise and speech spectrogram, either by estimating a speech dictionary on the fly (categorized as unsupervised approaches) or by using a pre-trained speech dictionary on utterances with disjoint speakers (categorized as semi-supervised approaches). Information fusion was investigated by taking the geometric mean of the outputs from multiple enhancement algorithms. The performance of the algorithms were evaluated on five metrics (PESQ, SDR, SNR, STOI, and OVERALL) by making experiments on TIMIT with 15 noise types. The geometric means of the proposed unsupervised approaches outperformed spectral subtraction (SS), minimum mean square estimation (MMSE) under low input SNR conditions. All the proposed semi-supervised approaches showed superiority over SS and MMSE and also obtained better performance than the state-of-the-art algorithms which utilized a prior noise or speech dictionary under low SNR conditions.

Multiple Kernel Learning via Low-Rank Nonnegative Matrix Factorization for Classification of Hyperspectral Imagery

In this paper, a novel multiple kernel learning (MKL) algorithm is proposed for the classification of hyperspectral images. The proposed MKL algorithm adopts a two-step strategy to learn a multiple kernel machine. In the first step, unsupervised learning is carried out to learn a combined kernel from the predefined base kernels. In our algorithms, low-rank nonnegative matrix factorization (NMF) is used to carry out the unsupervised learning and learn an optimal combined kernel. Furthermore, the kernel NMF (KNMF) is introduced to substitute NMF for enhancing the ability of the unsupervised learning with the predefined base kernels. In the second step, the optimal kernel is embedded into the standard optimization routine of support vector machine (SVM). In addition, we address a major challenge in hyperspectral data classification, i.e., using very few labeled samples in a high-dimensional space. Experiments are conducted on three real hyperspectral datasets, and the experimental results show that the proposed algorithms, especially for KNMF-based MKL, achieve the outstanding performance for hyperspectral image classification with few labeled samples when compared with several state-of-the-art algorithms.

Email Surveillance Using Non-negative Matrix Factorization

In this study, we apply a non-negative matrix factorization approach for the extraction and detection of concepts or topics from electronic mail messages. For the publicly released Enron electronic mail collection, we encode sparse term-by-message matrices and use a low rank non-negative matrix factorization algorithm to preserve natural data non-negativity and avoid subtractive basis vector and encoding interactions present in techniques such as principal component analysis. Results in topic detection and message clustering are discussed in the context of published Enron business practices and activities, and benchmarks addressing the computational complexity of our approach are provided. The resulting basis vectors and matrix projections of this approach can be used to identify and monitor underlying semantic features (topics) and message clusters in a general or high-level way without the need to read individual electronic mail messages.

Document clustering using nonnegative matrix factorization

A methodology for automatically identifying and clustering semantic features or topics in a heterogeneous text collection is presented. Textual data is encoded using a low rank nonnegative matrix factorization algorithm to retain natural data nonnegativity, thereby eliminating the need to use subtractive basis vector and encoding calculations present in other techniques such as principal component analysis for semantic feature abstraction. Existing techniques for nonnegative matrix factorization are reviewed and a new hybrid technique for nonnegative matrix factorization is proposed. Performance evaluations of the proposed method are conducted on a few benchmark text collections used in standard topic detection studies.