Feature Extraction for Electromagnetic Environment Complexity Classification Based on Non-Negative Matrix Factorization

In order to improve the fidelity and controllable of electromagnetic environment(EME) building, and build realistic EME for testing and researching the complex EME effect on the electronic information systems, this paper puts forward Equivalent building methods of complex EME based on the meta-elements. First, the paper analysis the domestic and foreign research which presents the current situation and the demand, and then puts forward the methods and expounds the core idea of basing the meta-elements to realize the equivalent EME building. Further it introduces extraction method of the electromagnetic signal environment meta-elements, and builds the description of them. In the end, it put forward the method and process to build the complex EME based on the meta-elements. This research results provide the technical support to improve the level of test EME building.

Fractal theory has been widely used for analyzing various signals in the past dew decades. However, this theory has never been employed for electromagnetic environment (EME) signal analysis. In this work, a new evaluation approach using morphological covering based fractal dimension (FD) is presented for evaluating the complexity degree of electromagnetic environment. Morphological covering based fractal dimension is a novel technique which is extended from the Minkowski-Boulingand dimension via the morphological operations. EME signals with four complexity degree are simulated to evaluate the effectiveness of the presented method. Experimental results reveal that the EME signals demonstrate fractal structures. The Morphological covering based fractal dimension has demonstrated to be an effective technique for accurate complexity degree evaluation of EME.

Feature extraction is an important research topic in hyper-spectral image (HSI) classification. However, most of feature extraction methods only extract low-level features, which makes them not perform well in the applications of HSI. In this paper, we have proposed a non-negative matrix factorization (NMF) based deep feature extraction algorithm, namely deep NMF. Deep NMF tries to construct a deep feature representation by cascading multiple NMFs. Reconstruction residual of NMF is passed layer by layer to reduce information loss. Meanwhile, passing residuals between layers can construct a feature hierarchy from coarse to fine. Furthermore, activation functions are applied between adjacent layers to enhance the ability of non-linear feature extraction. Experimental results have also shown that our algorithm is computationally efficient and effective for HSI classification.

The complex geographical environment and electromagnetic interference environment within the radar deployment position area will seriously degrade the radar detection performance. Focusing on the urgent requirement of optimizing radar deployment in complex geographic and electromagnetic environments, the environment-constrained radar position positioning optimization method is investigated. Firstly, based on the terrain and electromagnetic interference environment of radar positions, a radar position selection method under both geographic and electromagnetic environment constraints is established. Then the propagation loss under complex geographical terrain is calculated by combining the radar equations, and the detection power of target height layer and the coverage power of the focused area are used as the evaluation indicators for the superiority of radar sites. Finally, the detection range of the radar under multiple environmental constraints is visualized. The problem of complex radar operational scenarios in real systems and the single constraint considered in traditional radar equipment deployment methods is addressed. By calculating the propagation loss, terrain loss, electromagnetic loss under multiple environmental and electromagnetic constraints, and adding actual elevation and terrain data as reference, a more realistic and objective analysis of the impact of the environment around the position on the performance of radar equipment is provided, and finally the evaluation indexes and selection methods is proposed in this paper. The proposed evaluation indexes and selection methods and visualization can provide accurate, reliable and intuitive strategies for optimizing the deployment of radar equipment under multiple constraints.

Non-negative Matrix Factorization (NMF) has been frequently applied to image feature extraction and clustering. Especially in image clustering tasks, it can achieve the similar or better performance than most of the matrix factorization algorithms due to its parts-based representations in the brain. However, the features extracted by NMF are not sparse and localized enough and the error of factorization is not small enough. Semi-tensor product of matrices (STP) is a novel operation of matrix multiplication, it is a generalization of the conventional matrix product for allowing the dimensions of factor matrices to be unequal. STP can manage the data hierarchically and the inverse process of STP can separate the data hierarchically. Based on this character of STP, we propose the Non-Negative Matrix Semi-Tensor Factorization (NMSTF). In this algorithm, we use the inverse process of Semi-Tensor Product of matrices for non-negative matrix factorization. This algorithm effectively optimizes the above two problems in NMF. While achieving similar even better performance on image clustering tasks, the size of features extracted by STNMF is at least 50 % smaller than the ones’ extracted by NMF and the error of factorization reduces 30 % in average.

Positron emission tomography (PET) is an important imaging technique to visualize a number of functions in the brain or human body. For reconstructing PET images from the sinogram data, an inverse problem has to be solved using numerical optimizations such as expectation-maximization (EM)-based methods. However, the standard EM method suffers from measurement noise added in the sinogram data. In this paper, we propose a new simultaneous PET image reconstruction and parts extraction method using constrained non-negative matrix factorization. In contrast that the many existing methods reconstruct a single PET image independently, we reconstruct the time-series of PET images simultaneously from the time-series of sinograms using non-negative matrix factorization. Furthermore, we impose the smoothness constraint for the temporal feature, and the exclusive LASSO-based sparseness constraint for the spatial feature for robust image reconstruction and physically meaningful feature extraction.

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.

Non-negative matrix factorization (NMF) has been one of the most popular methods for feature learning in the field of machine learning and computer vision. Most existing works directly apply NMF on high-dimensional image datasets for computing the effective representation of the raw images. However, in fact, the common essential information of a given class of images is hidden in their low rank parts. For obtaining an effective low-rank data representation, we in this paper propose a non-negative low-rank matrix factorization (NLMF) method for image clustering. For the purpose of improving its robustness for the data in a manifold structure, we further propose a graph regularized NLMF by incorporating the manifold structure information into our proposed objective function. Finally, we develop an efficient alternating iterative algorithm to learn the low-dimensional representation of low-rank parts of images for clustering. Alternatively, we also incorporate robust principal component analysis into our proposed scheme. Experimental results on four image datasets reveal that our proposed methods outperform four representative methods.

Feature extraction and classification of electroencephalogram (EEG) signal for normal and epileptic patients is one of the most challenging research areas in the field of biomedical signal processing. Epileptic seizures are manifestations of epilepsy. Several techniques have been used for feature extraction and classification of EEG in last decades. In this article, non-negative matrix factorization (NMF) has been used for feature extraction of EEG signals and the classifiers used are Artificial Neural Network (ANN) and support vector machine (SVM). For NMF, fast Fourier transform (FFT) is used for feature extraction of the EEG signal. Performances of classifiers are measured on the parameters: accuracy, sensitivity and specificity. It has been observed that NMF gives satisfactory results for feature extraction and classification of EEG signal.

In this work, we will consider the dimension reduction of the set of time series, such as economic data, to find the meaningful basis vector for the set of data, and indicate which data use which basis vector. Usually each of the time series is analyzed independently in economics but here we will analyze the set of time series simultaneously. Since some of the economic data are measured as positive values and we want to decompose them as a mixture of the parts, we will apply non-negative matrix factorization to the economic data. Non-negative matrix factorization can compress dimensions by approximating a non-negative matrix with the product of two non-negative matrices. The two non-negative matrices are called the coefficient matrix and the basis matrix, and the basis matrix can be considered as a dimensionally compressed matrix. If the standard non-negative matrix factorization is used for economic data, the basis matrix may not be smooth. We think that the basis vectors should be smooth except a few special economical incidents. In the proposed method, a Graph-based non-negative matrix factorization is introduced to regularize the basis matrix of the time series. A path graph for representing the time series of economic data is incorporated into the non-negative matrix factorization as regularization. As a result, basis vectors that maintains the time series of economic data are decomposed. Furthermore, we propose to introduce a sparsity in the non-negative matrix factorization. Traditionally, the sparsity incorporated into non-negative matrix factorization has been used for basis vectors. However, the proposed method introduces the sparsity for coefficient vectors. Thus the proposed method, which simultaneously incorporates the sparsity for the coefficient vectors and the smoothness for the basis vectors, can extract the smooth basis vectors and the original economical data are approximated as the weighted sum of the few bases vectors. This allows us to discover economic trends and the best-fit trends for each data at the same time.

Guitar string separation is a novel and complicated task. Guitar notes are not pure steady-state signals, hence, we hypothesize that neither Non-Negative Matrix Factorization (NMF) nor Non-Negative Matrix Factor Deconvolution (NMFD) are optimal for separating them. Therefore, we separate steady-state and transient parts using Harmonic-Percussive Separation (HPS) as a preprocessing step. Then, we use NMF for factorizing the harmonic part and NMFD for deconvolving the percussive part. We make use of a hexaphonic guitar dataset which allows for objective evaluation. In addition, we compare several types of time-frequency mask and introduce an intuitive way to combine a binary mask with a ratio mask. We show that the HPS mask type has an effect on source estimation. Our proposed method achieved results comparable to NMF without HPS. Finally, we show that the optimal mask at the final separation stage depends on the estimation algorithm.

In this paper, a novel supervised feature extraction method is presented. The method employs discriminant analysis in the features derived by non-negative matrix factorization (NMF). In this way, a two phase discriminant feature extraction procedure is implemented, namely NMF plus linear discriminant analysis (LDA). The introduced method has been applied to the problem of frontal face verification using the well known XM2VTS database, where a better performance than NMF, eigenfaces and Fisherfaces has been achieved

Deep Learning Artificial Neural Networks has pushed forward researches in the field of pattern recognition, furthermore in human handwriting recognition. From online to offline approach, signature verification, writing or writer identification, segmentation or features extraction, a multitude of Artificial Neural Networks (ANNs) models are applied in the process. This paper focuses on the literature review of human handwriting recognition with ANN's over the last decade. We propose an exploratory analysis of 294 research papers collected from five indexed research engines: ACM Digital Library, IEEE digital library, Science Direct, Scopus and Web of Science. Our aim is to provide a research papers distribution across years and journals, a Keywords frequency analysis using cloud visualization, and a Natural Language Processing Topic Modeling using Non-Negative Matrix Factorization (NMF). The results of this study show that the number of research papers reached noticeably a peak in the 2010 with 44 published papers; also Pattern Recognition was the top publishing journal with 12 published papers. As for the topic modeling using NMF we obtained 3 topics listed as follows: 1) Feature Extraction and segmentation techniques for Handwritten Texts Recognition; 2) Signature Verification in Biometric security for Off-line Authentication; 3) Assessment Systems for Student Identification

Nonnegative Matrix Factorization (NMF), as a popular feature extraction technique, has recently attracted increasing attentions in high-dimensional data analysis, due to the strong ability of dimension reduction and semantic representation. In order to utilize the partial label information in practice, several semi-supervised NMF methods have been proposed. However, existing semi-supervised NMF variants only consider the global label constraint of data, but ignore the local label information embedded in geometric structure, which is very crucial for data representation. To address the above issue, we propose an improved NMF method, namely local and global regularized semi-supervised NMF (LGNMF), by considering the local and global label constraints simultaneously. Specifically, the local label constraint is depicted in a graph, which is pre-computed by metric learning. In addition, to explore the global label information, we construct an indicator matrix to restrict the coefficient matrix in LGNMF. For the formulated LGNMF, a multiplicative update rule (MUR) is developed. Extensive experiments on several real datasets demonstrate the superiority of the proposed method over the state-of-the-art methods in terms of clustering accuracy and normalized mutual information.

In this letter, we consider the nonnegative matrix factorization (NMF) problem and several NMF variants. Two approaches based on DC (difference of convex functions) programming and DCA (DC algorithm) are developed. The first approach follows the alternating framework that requires solving, at each iteration, two nonnegativity-constrained least squares subproblems for which DCA-based schemes are investigated. The convergence property of the proposed algorithm is carefully studied. We show that with suitable DC decompositions, our algorithm generates most of the standard methods for the NMF problem. The second approach directly applies DCA on the whole NMF problem. Two algorithms-one computing all variables and one deploying a variable selection strategy-are proposed. The proposed methods are then adapted to solve various NMF variants, including the nonnegative factorization, the smooth regularization NMF, the sparse regularization NMF, the multilayer NMF, the convex/convex-hull NMF, and the symmetric NMF. We also show that our algorithms include several existing methods for these NMF variants as special versions. The efficiency of the proposed approaches is empirically demonstrated on both real-world and synthetic data sets. It turns out that our algorithms compete favorably with five state-of-the-art alternating nonnegative least squares algorithms.