Non-negative matrix factorization for speech/music separation using source dependent decomposition rank, temporal continuity term and filtering

A solution for separating speech from music signal as a single channel source separation is Non-negative Matrix Factorization (NMF). In this approach spectrogram of each source signal is factorized as multiplication of two matrices which are known as basis and weight matrices. To achieve proper estimation of signal spectrogram, weight and basis matrices are updated iteratively. To estimate distance between signal and its estimation a cost function is used usually. Different cost functions have been introduced based on Kullback-Leibler (KL) and Itakura-Saito (IS) divergences. IS divergence is scale-invariant and so it is suitable for the conditions in which the coefficients of signal have a large dynamic range, for example in music short-term spectra. Based on this IS property, in this paper, we propose to use IS divergence as cost function of NMF in the training stage for music and on the other hand we suggest to use KL divergence as NMF cost function in the training stage for speech. Moreover, in the decomposition stage, we propose to use a linear combination of these two divergences in addition to a regularization term which considers temporal continuity information as a prior knowledge. Experimental results on one hour of speech and music, shows a good trade-off between signal to inference ratio (SIR) of speech and music in comparison to conventional NMF methods.

Hyperspectral unmixing is an important technique for analyzing remote sensing images which aims to obtain a collection of endmembers and their corresponding abundances. In recent years, non-negative matrix factorization (NMF) has received extensive attention due to its good adaptability for mixed data with different degrees. The majority of existing NMF-based unmixing methods are developed by incorporating additional constraints into the standard NMF based on the spectral and spatial information of hyperspectral images. However, they neglect to exploit the nature of imbalanced pixels included in the data, which may cause the pixels mixed with imbalanced endmembers to be ignored, and thus the imbalanced endmembers generally cannot be accurately estimated due to the statistical property of NMF. To exploit the information of imbalanced samples in hyperspectral data during the unmixing procedure, in this paper, a cluster-wise weighted NMF (CW-NMF) method for the unmixing of hyperspectral images with imbalanced data is proposed. Specifically, based on the result of clustering conducted on the hyperspectral image, we construct a weight matrix and introduce it into the model of standard NMF. The proposed weight matrix can provide an appropriate weight value to the reconstruction error between each original pixel and the reconstructed pixel in the unmixing procedure. In this way, the adverse effect of imbalanced samples on the statistical accuracy of NMF is expected to be reduced by assigning larger weight values to the pixels concerning imbalanced endmembers and giving smaller weight values to the pixels mixed by majority endmembers. Besides, we extend the proposed CW-NMF by introducing the sparsity constraints of abundance and graph-based regularization, respectively. The experimental results on both synthetic and real hyperspectral data have been reported, and the effectiveness of our proposed methods has been demonstrated by comparing them with several state-of-the-art methods.

Nonnegative Matrix Factorization (NMF) has been proven to be effective in text mining. However, since NMF is a well-known unsupervised components analysis technique, the existing NMF method can not deal with prior constraints, which are beneficial to clustering or classification tasks. In this paper, we address the text clustering problem via a novel strategy, called Pairwise Constraintsguided Non-negative Matrix Factorization (PCNMF for short). Differing from the traditional NMF method, the proposed method can capture the available abundance prior constraints in original space, which result in more effective for clustering or information retrieval. Therefore, PCNMF enforces the discriminative capability in the reduced space. Utilizing the appropriate transformation, PCNMF represents as a new optimization problem, which can be efficiently solved by an iterative approach. The cluster membership of each document can be easily determined as the standard NMF. Empirical studies based on Benchmark document corpus demonstrate appealing results.

Tensorized multi-dimensional multi-view clustering based on nonnegative matrix factorization.

A locally weighted sparse graph regularized Non-Negative Matrix Factorization method

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.

The Gaussian and Gaussian-sigmoidal primaries are introduced as initialization functions in the nonnegative matrix factorization (NNMF) method to achieve more consistent error statistics. The proposed NNMF method with multiplicative update algorithm is employed for reconstruction of spectral data of Munsell and Colorchecker DC datasets from the corresponding CIEXYZ tristimulus values and the resultant achievements are compared with those obtained from PCA and the classical NNMF techniques. Both colorimetric and spectrophotometric errors between the original and the reconstructed spectra are used for the evaluation of reconstruction methods. While run to run variability of the classical NNMF method with multiplicative update algorithm is significantly remarkable, the stability of the suggested technique is fairly high, similar to the PCA method. The ensuing findings show that the embedding of Gaussian initializing vectors in NNMF method provide the all positive bases that enhance both the accuracy of Gaussian method and the reliability of NNMF technique.

As an important matrix factorization model, Nonnegative Matrix Factorization (NMF) has been widely used in information retrieval and data mining research. Standard Nonnegative Matrix Factorization is known to use the Frobenius norm to calculate the residual, making it sensitive to noises and outliers. It is desirable to use robust NMF models for practical applications, in which usually there are many data outliers. It has been studied that the 2,1, or 1-norm can be used for robust NMF formulations to deal with data outliers. However, these alternatives still suffer from the extreme data outliers. In this paper, we present a novel robust capped norm orthogonal Nonnegative Matrix Factorization model, which utilizes the capped norm for the objective to handle these extreme outliers. Meanwhile, we derive a new efficient optimization algorithm to solve the proposed non-convex non-smooth objective. Extensive experiments on both synthetic and real datasets show our proposed new robust NMF method consistently outperforms related approaches.

In this paper, we propose a novel scheme to supervised nonnegative matrix factorization (NMF). We formulate the supervised NMF as a sparse optimization problem assuming the availability of a set of basis vectors, some of which are irrelevant to a given matrix to be decomposed. The proposed scheme is presented in the context of music transcription and musical instrument recognition. In addition to the nonnegativity constraint, we introduce three regularization terms: (i) a block ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm to select relevant basis vectors, and (ii) a temporal-continuity term plus the popular ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm to estimate correct activation vectors. We present a state-of-the-art convex-analytic iterative solver which ensures global convergence. The number of basis vectors to be actively used is obtained as a consequence of optimization. Simulation results show the efficacy of the proposed scheme both in the case of perfect/imperfect basis matrices.

In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the optimization problem underlying NMF, showing for the first time that non-trivial NMF solutions always exist and that the optimization problem is actually convex, by using the theory of Completely Positive Factorization. We subsequently explore four novel approaches to finding globally-optimal NMF solutions using various ideas from convex optimization. We then develop a new method, isometric NMF (isoNMF), which preserves non-negativity while also providing an isometric embedding, simultaneously achieving two properties which are helpful for interpretation. Though it results in a more difficult optimization problem, we show experimentally that the resulting method is scalable and even achieves more compact spectra than standard NMF.

Understanding the evolving user session profile is key to maintaining service performance levels. Clustering techniques have been used to automatically discover typical user profiles from Web access logs. But it is a challenging problem that many clustering algorithms yield poor results because the session vectors are usually high dimensional and sparse. Although standard non-negative matrix factorization (SNMF) can be used in reducing the dimensionality of the session-URL matrix, the clustering results is not precise, because the basis vectors SNMF gets are not orthogonal and usually redundancy. In this paper, we apply local nonnegative matrix factorization (LNMF), which get basis vectors as orthogonal as possible, to reduce the dimensionality of the session-URL matrix. The experiment results show that LNMF performs better than SNMF for mining typical user session profile.

Obtaining an optimum data representation is a challenging issue that arises in many intellectual data processing techniques such as data mining, pattern recognition, and gene clustering. Many existing methods formulate this problem as a nonnegative matrix factorization (NMF) approximation problem. The standard NMF uses the least square loss function, which is not robust to outlier points and noises and fails to utilize prior label information to enhance the discriminability of representations. In this study, we develop a novel matrix factorization method called robust semisupervised nonnegative local coordinate factorization by integrating robust NMF, a robust local coordinate constraint, and local spline regression into a unified framework. We use the l2,1 norm for the loss function of the NMF and a local coordinate constraint term to make our method insensitive to outlier points and noises. In addition, we exploit the local and global consistencies of sample labels to guarantee that data representation is compact and discriminative. An efficient multiplicative updating algorithm is deduced to solve the novel loss function, followed by a strict proof of the convergence. Several experiments conducted in this study on face and gene datasets clearly indicate that the proposed method is more effective and robust compared to the state-of-the-art methods.

Standard nonnegative matrix factorization (NMF) is a powerful algorithm for data analysis and processing. In this paper, we improve the standard NMF and propose a supervised NMF algorithm that uses labeled samples for model training. The new NMF can identify the label of samples and achieve clustering. Using the clustering property of the supervised NMF algorithm, fault detection and isolation (FDI) is developed when both fault-free samples and all types of faulty samples are available for model training. Finally, the effectiveness of the proposed FDI approach is verified by an experiment on FDI of the penicillin fermentation process (PFP).

In this letter, we develop a multichannel blind source separation algorithm based on a beamspace transform and the multichannel nonnegative matrix factorization (NMF) method. The conventional multichannel NMF algorithm performs well with multichannel mixing data, but there is still room for enhancement in multichannel real-world recording data. In this letter, we consider a beamspace-time-frequency domain data model for multichannel NMF method, and enhance the conventional method using a beamspace transform. Our decomposition algorithm is applied to 2-channel and 4-channel unsupervised audio source separation, using a dataset from the international Signal Separation Evaluation Campaign 2010 (SiSEC 2010). Our algorithm shows a better performance than the conventional NMF method in an evaluation results.

본 논문은 시간 연속성을 갖는 비음수 행렬 분해(Nonnegative Matrix Factorization, NMF)를 이용하여 잡음에 열화된 음성 신호의 음질을 개선하는 문제를 다룬다. 음성과 잡음 신호는 포아송 분포로 모델되며, NMF의 기본 벡터와 이득 벡터는 감마 분포로 모델된다. 이득 벡터의 시간 연속성은 음질 개선에 중요한 영향을 미치는 것으로 알려져 있다. 본 논문에서 시간의 연속성은 이득 벡터를 감마-마르코프 연쇄(Gamma-Markov chain, GMC) 사전 분포로 모델함으로써 이루어진다. 실험 결과는 제안된 알고리즘이 잡음 신호의 시간 연속성을 효과적으로 모델하는 것을 보여준다. In this paper, speech enhancement using nonnegative matrix factorization with temporal continuity has been addressed. Speech and noise signals are modeled as Possion distributions, and basis vectors and gain vectors of NMF are modeled as Gamma distributions. Temporal continuity of the gain vector is known to be critical to the quality of enhanced speech signals. In this paper, temporal continiuty is implemented by adopting Gamma-Markov chain priors for noise gain vectors during the separation phase. Simulation results show that the Gamma-Markov chain models temporal continuity of noise signals and track changes in noise effectively.