Discriminative NMF and its application to single-channel source separation

Non-negative matrix factorization (NMF) is a powerful approach to single channel audio source separation. In a supervised setting, NMF is first applied to train the basis spectra of each sound source. At test time, NMF is applied to the spectrogram of a mixture signal using the pretrained spectra. The source signals can then be separated out using a Wiener filter. A typical way to train the basis spectra of each source is to minimize the objective function of NMF. However, the basis spectra obtained in this way do not ensure that the separated signal will be optimal at test time due to the inconsistency between the objective functions for training and separation (Wiener filtering). To address this, a framework called discriminative NMF (DNMF) has recently been proposed. In in this work a multiplicative update algorithm was proposed for the basis training, however one drawback is that the convergence is not guaranteed. To overcome this drawback, this paper proposes using a majorization-minimization principle to develop a convergence-guaranteed algorithm for DNMF. Experimental results showed that the proposed algorithm outperformed standard NMF and DNMF using a multiplicative update algorithm as regards both the signal-to-distortion and signal-to-interference ratios.

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.

Non-negative subspace feature representation for few-shot learning in medical imaging

Non-negative Matrix Factorization (NMF) is among the most popular subspace methods widely used in a variety of pattern recognition applications. Recently, a discriminant NMF method that incorporates Linear Discriminant Analysis criteria and achieves an efficient decomposition of the provided data to its salient parts has been proposed. An extension of this work specialized for classification, optimized using projected gradients in order to ensure converge to a stationary limit point, resulted in a more efficient method of the latter approach. Assuming multimodality of the underlying data samples distribution and incorporating clustering discriminant inspired constraints into the NMF decomposition cost function, resulted in the Subclass Discriminant NMF algorithm which found to outperform both approaches under real life settings. In this work we review all these methods in the context of various pattern recognition problems using facial images.

We propose a new method to incorporate rich statistical priors, modeling temporal gain sequences in the solutions of nonnegative matrix factorization (NMF). The proposed method can be used for single-channel source separation (SCSS) applications. In NMF based SCSS, NMF is used to decompose the spectra of the observed mixed signal as a weighted linear combination of a set of trained basis vectors. In this work, the NMF decomposition weights are enforced to consider statistical and temporal prior information on the weight combination patterns that the trained basis vectors can jointly receive for each source in the observed mixed signal. The Hidden Markov Model (HMM) is used as a log-normalized gains (weights) prior model for the NMF solution. The normalization makes the prior models energy independent. HMM is used as a rich model that characterizes the statistics of sequential data. The NMF solutions for the weights are encouraged to increase the log-likelihood with the trained gain prior HMMs while reducing the NMF reconstruction error at the same time.

Multiplicative update algorithms are important tools for information retrieval, image processing, and pattern recognition. However, when the graph regularization is added to the cost function, different classes of sample data may be mapped to the same subspace, which leads to the increase of data clustering error rate. In this paper, an improved nonnegative matrix factorization (NMF) cost function is introduced. Based on the cost function, a class of novel graph regularized NMF algorithms is developed, which results in a class of extended multiplicative update algorithms with manifold structure regularization. Analysis shows that in the learning, the proposed algorithms can efficiently minimize the rank of the data representation matrix. Theoretical results presented in this paper are confirmed by simulations. For different initializations and data sets, variation curves of cost functions and decomposition data are presented to show the convergence features of the proposed update rules. Basis images, reconstructed images, and clustering results are utilized to present the efficiency of the new algorithms. Last, the clustering accuracies of different algorithms are also investigated, which shows that the proposed algorithms can achieve state-of-the-art performance in applications of image clustering.

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.

Nonnegative matrix factorization (NMF) by the multiplicative updates algorithm is a powerful machine learning method for decomposing a high-dimensional nonnegative matrix V into two nonnegative matrices, W and H, where V ~ WH. It has been successfully applied in the analysis and interpretation of large-scale data arising in neuroscience, computational biology, and natural language processing, among other areas. A distinctive feature of NMF is its nonnegativity constraints that allow only additive linear combinations of the data, thus enabling it to learn parts that have distinct physical representations in reality. In this letter, we describe an information-theoretic approach to NMF for signal-dependent noise based on the generalized inverse gaussian model. Specifically, we propose three novel algorithms in this setting, each based on multiplicative updates, and prove monotonicity of updates using the EM algorithm. In addition, we develop algorithm-specific measures to evaluate their goodness of fit on data. Our methods are demonstrated using experimental data from electromyography studies, as well as simulated data in the extraction of muscle synergies, and compared with existing algorithms for signal-dependent noise.

With the advent of hands free devices, speech recognition is of utmost importance but miserably fails to be perfect in a cock-tail party environment without speech separation or speech denoising. There are various techniques available for speech separation but the one technique used nowadays is non-negative matrix factorization (NMF). Non-negative matrix factorization decomposes the mixed signal into components namely the basis functions matrix and activation or weight matrix. Speech separation using NMF is successful, if the mixed signal consists of uncorrelated sources. In this paper we revisit the concept of decomposition using NMF for vowel utterances by various speakers and analyse them to identify correlation which may exist among the basis functions. This may be useful for formulating better training bases which eventually will lead to successful speech separation.

In this study, single-channel speech source separation is carried out to separate the speech from the background music, which degrades the speech recognition performance especially in broadcast news transcription systems. Since the separation is done using single observation of the source signals, the sources have to be previously modeled using training data. Non-negative Matrix Factorization (NMF) methods are used to model the sources. In order to model the source signals, different training data sets, which contain different music and speech data, are created and the effect of the training data sets are analyzed in this study. The performances of the methods are measured not only using separation performance measure but also with speech recognition performance measures.

The nonnegative convex polyhedral cone (NCPC) learning is discussed in this paper. By exploiting the multiplicative update nonnegative quadratic programming, a multiplicative update algorithm is developed for NCPC learning. The proposed algorithm is promising for nonnegative matrix factorization (NMF) and we verify this by numerical experiments.

Object representation in the inferior temporal cortex (IT), an area of visual cortex critical for object recognition in the primate, exhibits two prominent properties: (1) objects are represented by the combined activity of columnar clusters of neurons, with each cluster representing component features or parts of objects, and (2) closely related features are continuously represented along the tangential direction of individual columnar clusters. Here we propose a learning model that reflects these properties of parts-based representation and topographic organization in a unified framework. This model is based on a nonnegative matrix factorization (NMF) basis decomposition method. NMF alone provides a parts-based representation where nonnegative inputs are approximated by additive combinations of nonnegative basis functions. Our proposed model of topographic NMF (TNMF) incorporates neighborhood connections between NMF basis functions arranged on a topographic map and attains the topographic property without losing the parts-based property of the NMF. The TNMF represents an input by multiple activity peaks to describe diverse information, whereas conventional topographic models, such as the self-organizing map (SOM), represent an input by a single activity peak in a topographic map. We demonstrate the parts-based and topographic properties of the TNMF by constructing a hierarchical model for object recognition where the TNMF is at the top tier for learning high-level object features. The TNMF showed better generalization performance over NMF for a data set of continuous view change of an image and more robustly preserving the continuity of the view change in its object representation. Comparison of the outputs of our model with actual neural responses recorded in the IT indicates that the TNMF reconstructs the neuronal responses better than the SOM, giving plausibility to the parts-based learning of the model.

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

What are the 'features' or 'parts' that our brains use to tell one thing from another? Several algorithms exist for learning object parts, and the development of the latest -- known as non-negative matrix factorization -- is now reported. This algorithm seems to decompose sets of faces into 'basis functions' that are different, and more part-like, than those found by conventional algorithms.

Non-negative Matrix Factorization (NMF) is among the most popular subspace methods widely used in a variety of image processing problems. Recently, a discriminant NMF method that incorporates Linear Discriminant Analysis criteria and achieves an efficient decomposition of the provided data to its discriminant parts has been proposed. However, this approach poses several limitations since it assumes that the underline data distribution forms compact sets which is often unrealistic. To remedy this limitation we regard that data inside each class form various number of clusters and apply a Clustering based Discriminant Analysis. The proposed method combines appropriate discriminant constraints in the NMF decomposition cost function in order to address the problem of finding discriminant projections that enhance class separability in the reduced dimensional projection space. Experimental results performed on the Cohn-Kanade database verified the effectiveness of the proposed method in the facial expression recognition task.