Projected Gradients for Subclass Discriminant Nonnegative Subspace Learning

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.

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

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.

Face and facial expression recognition is a broad research domain in machine learning domain. Non-negative matrix factorization (NMF) is a very recent technique for data decomposition and image analysis. Here we propose face identification system as well as a facial expression recognition, which is a system based on NMF. We get a significant result for face recognition. We test on CK+ and JAFFE dataset and we find the face identification accuracy is nearly 99% and 96.5% respectively. But the facial expression recognition (FER) rate is not as good as it required for the real life implementation. To increase the detection rate for facial expression recognition, our propose fusion based NMF, named as OEPA-NMF, where OEPA means Optimal Expression specific Parts Accumulation. Our experimental result shows OEPA-NMF outperforms the prevalence NMF for facial expression recognition. As face identification using NMF has a good accuracy rate, so we are not interested to apply OEPA-NMF for face identification.

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.

In this paper, we present a novel muscle synergy extraction method based on multivariate curve resolution–alternating least squares (MCR-ALS) to overcome the limitation of the nonnegative matrix factorization (NMF) method for extracting non-sparse muscle synergy, and we study its potential application for evaluating motor function of stroke survivors. Nonnegative matrix factorization (NMF) is the most widely used method for muscle synergy extraction. However, NMF is susceptible to components’ sparseness and usually provides inferior reliability, which significantly limits the promotion of muscle synergy. In this study, MCR-ALS was employed to extract muscle synergy from electromyography (EMG) data. Its performance was compared with two other matrix factorization algorithms, NMF and self-modeling mixture analysis (SMMA). Simulated data sets were utilized to explore the influences of the sparseness and noise on the extracted synergies. As a result, the synergies estimated by MCR-ALS were the most similar to true synergies as compared with SMMA and NMF. MCR-ALS was used to analyze the muscle synergy characteristics of upper limb movements performed by healthy (n = 11) and stroke (n = 5) subjects. The repeatability and intra-subject consistency were used to evaluate the performance of MCR-ALS. As a result, MCR-ALS provided much higher repeatability and intra-subject consistency as compared with NMF, which were important for the reliability of the motor function evaluation. The stroke subjects had lower intra-subject consistency and seemingly had more synergies as compared with the healthy subjects. Thus, MCR-ALS is a promising muscle synergy analysis method for motor function evaluation of stroke patients.

BackgroundIn-vivo single voxel proton magnetic resonance spectroscopy (SV 1H-MRS), coupled with supervised pattern recognition (PR) methods, has been widely used in clinical studies of discrimination of brain tumour types and follow-up of patients bearing abnormal brain masses. SV 1H-MRS provides useful biochemical information about the metabolic state of tumours and can be performed at short (< 45 ms) or long (> 45 ms) echo time (TE), each with particular advantages. Short-TE spectra are more adequate for detecting lipids, while the long-TE provides a much flatter signal baseline in between peaks but also negative signals for metabolites such as lactate. Both, lipids and lactate, are respectively indicative of specific metabolic processes taking place. Ideally, the information provided by both TE should be of use for clinical purposes. In this study, we characterise the performance of a range of Non-negative Matrix Factorisation (NMF) methods in two respects: first, to derive sources correlated with the mean spectra of known tissue types (tumours and normal tissue); second, taking the best performing NMF method for source separation, we compare its accuracy for class assignment when using the mixing matrix directly as a basis for classification, as against using the method for dimensionality reduction (DR). For this, we used SV 1H-MRS data with positive and negative peaks, from a widely tested SV 1H-MRS human brain tumour database.ResultsThe results reported in this paper reveal the advantage of using a recently described variant of NMF, namely Convex-NMF, as an unsupervised method of source extraction from SV1H-MRS. Most of the sources extracted in our experiments closely correspond to the mean spectra of some of the analysed tumour types. This similarity allows accurate diagnostic predictions to be made both in fully unsupervised mode and using Convex-NMF as a DR step previous to standard supervised classification. The obtained results are comparable to, or more accurate than those obtained with supervised techniques.ConclusionsThe unsupervised properties of Convex-NMF place this approach one step ahead of classical label-requiring supervised methods for the discrimination of brain tumour types, as it accounts for their increasingly recognised molecular subtype heterogeneity. The application of Convex-NMF in computer assisted decision support systems is expected to facilitate further improvements in the uptake of MRS-derived information by clinicians.

Facial expressions recognition and synthesis are important research fields to study how human beings reflect to environments in affective computing. With the rapid development of mathematical theory on multivariate statistics and multi-media technology especially image processing, facial expressions recognition researchers have achieved many useful results. Recently studies show that approaches to facial modeling and expressions recognition and synthesis analysis could be adapted to control security or even real-time health monitoring in the real world. Similarity, how to achieve facial expressions recognition and synthesis for independent-free mechanism is a central design in general. Based on the cognitive analysis of independent user's affective facial recognition researches we proposed an emotions composition model to dope out what are the user's new affective facial expressions. At this point, principal component, cluster and discriminate analysis were applied to show and verify independent user's affective expressions can be composited for synthesis by basic facial expressions such as happy, neutral and unhappy. Experiments were conducted to prove our models to be very significant.

Non-negative matrix factorization (NMF) is a very popular dimensionality reduction method that has been widely used in computer vision and data clustering. However, NMF does not consider the intrinsic geometric information of a data set and also does not produce smooth and stable solutions. To resolve these problems, we propose a Graph regularized Lp Smooth Non-negative Matrix Factorization (GSNMF) method by incorporating graph regularization with Lp smooth constraint. The graph regularization can discover the hidden semantics and simultaneously respect the intrinsic geometric structure information of a data set. The Lp smooth constraint can combine the merits of isotropic (L2-norm) and anisotropic (L1-norm) diffusion smoothing, and produce a smooth and more accurate solution to the optimization problem. Experimental results on some data sets demonstrate that the proposed method outperforms related state-of-the-art NMF methods.

We apply the vectorized non-negative matrix factorization (NMF) method to the post-processing of the direct imaging data of exoplanetary systems such as circumstellar disks. NMF is an iterative approach, which first creates a nonorthogonal and non-negative basis of components using the given reference images and then models a target with the components. The constructed model is then rescaled with a factor to compensate for the contribution from the disks. We compare NMF with existing methods (classical reference differential imaging method, and the Karhunen–Loève image projection algorithm) using synthetic circumstellar disks and demonstrate the superiority of NMF: with no need of prior selection of references, NMF not only can detect fainter circumstellar disks but also better preserves their morphology and does not require forward modeling. As an application to a well-known disk example, we process the archival Hubble Space Telescope STIS coronagraphic observations of HD 181327 with different methods and compare them, and NMF is able to extract some circumstellar materials inside the primary ring for the first time. In an appendix, we mathematically investigate the stability of NMF components during the iteration and the linearity of NMF modeling.

Background: Individuals with child maltreatment (CM) experiences show alterations in emotion recognition (ER). However, previous research has mainly focused on populations with specific mental disorders, which makes it unclear whether alterations in the recognition of facial expressions are related to CM, to the presence of mental disorders or to the combination of CM and mental disorders, and on ER of emotional, rather than neutral facial expressions. Moreover, commonly, recognition of static stimulus material was researched. Objective: We assessed recognition of dynamic (closer to real life) negative, positive and neutral facial expressions in individuals characterised by CM, rather than a specific mental disorder. Moreover, we assessed whether they show a negativity bias for neutral facial expressions and whether the presence of one or more mental disorders affects recognition. Methods: Ninety-eight adults with CM experiences (CM+) and 60 non-maltreated (CM−) adult controls watched 200 non-manipulated coloured video sequences, showing 20 neutral and 180 emotional facial expressions, and indicated whether they interpreted each expression as neutral or as one of eight emotions. Results: The CM+ showed significantly lower scores in the recognition of positive, negative and neutral facial expressions than the CM− group (p < .050). Furthermore, the CM+ group showed a negativity bias for neutral facial expressions (p < .001). When accounting for mental disorders, significant effects stayed consistent, except for the recognition of positive facial expressions: individuals from the CM+ group with but not without mental disorder scored lower than controls without mental disorder. Conclusions: CM might have long-lasting influences on the ER abilities of those affected. Future research should explore possible effects of ER alterations on everyday life, including implications of the negativity bias for neutral facial expressions on emotional wellbeing and relationship satisfaction, providing a basis for interventions that improve social functioning.

Automatic recognition of facial expression remains a challenging task in computer vision, because of large amount of image data and subtle difference in facial expressions. In this paper, we present a customizable system for facial expression recognition using non-negative matrix factorization (NMF).Our system can be described in two major phases: the first phase uses preprocessing and the NMF for decomposing facial expression images into a set of basis images; the second phase incorporates dimensionality reduction and similarity to classify if an input image depicts one of the five facial expressions (i.e., normal, smile, sad, surprise, and angry) given known facial expressions as template images. Our results clearly demonstrate that the system was able to provide an effective basis for characterizing facial feature regions and reasonable classification in various facial expressions.

In this work we present a modified Nonnegative Matrix Factorization (NMF) method for learning a mixture of local SOM models. The proposed method approximates a data point with a linear combination of its k-nearest neighbor prototypes. This allows obtaining a low quantization error and at the same time keeping the interpretability of the prototypes. The results of the new method are compared with those obtained using non-negative least squares, NMF and SOM, using four benchmark data sets. Two metrics are used to assess the performance of the different approaches. The proposed k-nn NMF method obtained the lowest relative local quantization error, while keeping a global quantization error similar to the best alternative methods.KeywordsSelf Organizing MapNonnegative Matrix Factorizationk-Nearest NeighborsLinear MixtureRelative Quantization Error

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.

A rain streak in an image can degrade visual quality of that image to the human eye. Unfortunately, removing the rain streak from a single image represents a very challenging task. In this paper, a single image rain removal process based on non-negative matrix factorization is proposed. First, the rain image is broken down into a low-frequency and high-frequency part by a Gaussian filter. Therefore, the rain component, which lies mostly in the middle frequency range, can be discarded in high and low frequency domains. Next, non-negative matrix factorization (NMF) method is applied to deal with the rain streak in the low frequency domain. Finally, Canny edge detection and block copy strategy are performed separately to remove the rain component in the high frequency domain to improve image quality. In comparison with state-of-the-art approaches, the proposed method achieves competitive results without the need for an extra image database to train the dictionary.