Recent advances in discriminant non-negative Matrix Factorization

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 objective of single-channel source separation is to accurately recover source signals from mixtures. Non-negative matrix factorization (NMF) is a popular approach for this task, yet previous NMF approaches have not optimized directly this objective, despite some efforts in this direction. Our paper introduces discriminative training of the NMF basis functions such that, given the coefficients obtained on a mixture, a desired source is optimally recovered. We approach this optimization by generalizing the model to have separate analysis and reconstruction basis functions. This generalization frees us to optimize reconstruction objectives that incorporate the filtering step and SNR performance criteria. A novel multiplicative update algorithm is presented for the optimization of the reconstruction basis functions according to the proposed discriminative objective functions. Results on the 2nd CHiME Speech Separation and Recognition Challenge task indicate significant gains in source-to-distortion ratio with respect to sparse NMF, exemplar-based NMF, as well as a previously proposed discriminative NMF criterion.

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.

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

As an effective technique for feature extraction and pattern classification Fisher linear discriminant (FLD) has been successfully applied in many fields. However, for a task with very high-dimensional data such as face images, conventional FLD technique encounters a fundamental difficulty caused by singular within-class scatter matrix. To avoid the trouble, many improvements on the feature extraction aspect of FLD have been proposed. In contrast, studies on the pattern classification aspect of FLD are quiet few. In this paper, we will focus our attention on the possible improvement on the pattern classification aspect of FLD by presenting a novel linear discriminant criterion called maximum scatter difference (MSD). Theoretical analysis demonstrates that MSD criterion is a generalization of Fisher discriminant criterion, and is the asymptotic form of discriminant criterion: large margin linear projection. The performance of MSD classifier is tested in face recognition. Experiments performed on the ORL, Yale, FERET and AR databases show that MSD classifier can compete with top-performance linear classifiers such as linear support vector machines, and is better than or equivalent to combinations of well known facial feature extraction methods, such as eigenfaces, Fisherfaces, orthogonal complementary space, nullspace, direct linear discriminant analysis, and the nearest neighbor classifier.

Discriminative nonnegative matrix factorization (DNMF) has been investigated as a promising basis-learning method for monaural source separation. To the best of our knowledge, however, no good and sound discussion has been made on quantitative definition of discriminability and it is difficult to evaluate how discriminative DNMF is actually. This paper introduces a quantitative measure to calculate how discriminative two NMF bases are. From the viewpoint of our measure, we compare three basis-learning methods of plain NMF, DNMF, and minimum-volume (min-vol) NMF. Experimental results of monaural speech separation reveal that min-vol NMF actually learns as discriminative bases as DNMF and achieves the best separation performance. This is probably because min-vol NMF can learn the most compact basis possible that can cover training data.

The methods introduced so far regarding discriminant non-negative matrix factorization (DNMF) do not guarantee convergence to a stationary limit point. In order to remedy this limitation, a novel DNMF method is presented that uses projected gradients. The proposed algorithm employs some extra modifications that make the method more suitable for classification tasks. The usefulness of the proposed technique to frontal face verification and facial expression recognition problems is demonstrated.

A novel approach to facial expression recognition (FER) based on the combination of Non-negative Matrix Factorization (NMF) and Support Vector Machine (SVM) was proposed. One key step in FER is to extract expression features from the original face images. NMF is an effective approach to extract expression features because NMF decomposition makes the reconstruction of expression images in a non-subtractive way and is much similar to the process of forming unity from parts. The proposed algorithm first processes facial expression image with histogram equalization operator. Then NMF method is used for feature dimension reduction and SVM for classification. Finally, the algorithm was implemented with Matlab and experimented in Japanese female facial expression database (JAFEE database). A recognition rate of 66.19% was obtained and showed the effectiveness of the proposed algorithm

Semi-supervised graph regularized nonnegative matrix factorization with local coordinate for image representation

Face age prediction based on face image is an important research direction in the field of face recognition, and it is also a difficult point. Non-negative matrix factorization (NMF) dimensionality reduction method can fix the number of features after dimensionality reduction. In this paper, an optimization algorithm based on NMF is proposed for improving the accuracy of age prediction based on face images. It was confirmed that the maximum performance was shown for precision 0.19 in category 1 (21-24 ages), recall 0.20 in category 5 (40-44 ages), and f1-score 0.18 in categories 1-3 (21-34 ages) and 5. In addition, the mean absolute error (MAE) of the proposed algorithm is 1.92, which is about 31.85% lower than that of other algorithms.

Dramatic growth in the volume of data made a compact and informative representation of the data highly demanded in computer vision, information retrieval, and pattern recognition. Non-negative Matrix Factorization (NMF) is used widely to provide parts-based representations by factorizing the data matrix into non-negative matrix factors. Since non-negativity constraint is not sufficient to achieve robust results, variants of NMF have been introduced to exploit the geometry of the data space. While these variants considered the local invariance based on the manifold assumption, we propose Farness preserving Non-negative Matrix Factorization (FNMF) to exploits the geometry of the data space by considering non-local invariance which is applicable to any data structure. FNMF adds a new constraint to enforce the far points (i.e., non-neighbors) in original space to stay far in the new space. Experiments on different kinds of data (e.g., Multimedia, Earth Observation) demonstrate that FNMF outperforms the other variants of NMF.

Nonnegative matrix factorization (NMF) has been successfully used in different applications including computer vision, pattern recognition and text mining. NMF aims to decompose a data matrix into the product of two matrices (respectively denoted as the basis vectors and the encoding vectors), whose entries are constrained to be nonnegative. Unlike the ordinary NMF, we propose a novel NMF, denoted as MMNMF, which considers both geometrical information and discriminative information hidden in the data. The geometrical information is discovered by minimizing the distance among the encoding vectors, while the discriminative information is uncovered by maximizing the distance among base vectors. Clustering experiments are performed on the real-world data sets of faces, images, and documents to demonstrate the effectiveness of the proposed algorithm.

Label consistency-based deep semisupervised NMF for tumor recognition

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.

Current discriminant nonnegative matrix factorization (NMF) methods either do not guarantee convergence to a stationary limit point or assume a compact data distribution inside classes, thus ignoring intra class variance in extracting discriminant data samples representations. To address both limitations, we regard that data inside each class has a multimodal distribution, forming various subclasses and perform optimization using a projected gradients framework to ensure limit point stationarity. The proposed method combines appropriate clustering-based discriminant criteria in the NMF decomposition cost function, in order to find discriminant projections that enhance class separability in the reduced dimensional projection space, thus improving classification performance. The developed algorithms have been applied to facial expression, face and object recognition, and experimental results verified that they successfully identified discriminant parts, thus enhancing recognition performance.