New SVD based initialization strategy for Non-negative Matrix Factorization

There are two problems need to be dealt with for Non-negative Matrix Factorization (NMF): choose a suitable rank of the factorization and provide a good initialization method for NMF algorithms. This paper aims to solve these two problems using Singular Value Decomposition (SVD). At first we extract the number of main components as the rank, actually this method is inspired from [1, 2]. Second, we use the singular value and its vectors to initialize NMF algorithm. In 2008, Boutsidis and Gollopoulos [3] provided the method titled NNDSVD to enhance initialization of NMF algorithms. They extracted the positive section and respective singular triplet information of the unit matrices {C(j)}k j=1 which were obtained from singular vector pairs. This strategy aims to use positive section to cope with negative elements of the singular vectors, but in experiments we found that even replacing negative elements by their absolute values could get better results than NNDSVD. Hence, we give another method based SVD to fulfil initialization for NMF algorithms (SVD-NMF). Numerical experiments on two face databases ORL and YALE [16, 17] show that our method is better than NNDSVD

A Unified Framework for Sparse Non-Negative Least Squares using Multiplicative Updates and the Non-Negative Matrix Factorization Problem

We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS occurs naturally in a wide variety of applications where an unknown, non-negative quantity must be recovered from linear measurements. We present a unified framework for S-NNLS based on a rectified power exponential scale mixture prior on the sparse codes. We show that the proposed framework encompasses a large class of S-NNLS algorithms and provide a computationally efficient inference procedure based on multiplicative update rules. Such update rules are convenient for solving large sets of S-NNLS problems simultaneously, which is required in contexts like sparse non-negative matrix factorization (S-NMF). We provide theoretical justification for the proposed approach by showing that the local minima of the objective function being optimized are sparse and the S-NNLS algorithms presented are guaranteed to converge to a set of stationary points of the objective function. We then extend our framework to S-NMF, showing that our framework leads to many well known S-NMF algorithms under specific choices of prior and providing a guarantee that a popular subclass of the proposed algorithms converges to a set of stationary points of the objective function. Finally, we study the performance of the proposed approaches on synthetic and real-world data.Comment: To appear in Signal Processin

Graph Regularized Nonnegative Matrix Factorization with Sparse Coding

In this paper, we propose a sparseness constraint NMF method, named graph regularized matrix factorization with sparse coding (GRNMF_SC). By combining manifold learning and sparse coding techniques together, GRNMF_SC can efficiently extract the basic vectors from the data space, which preserves the intrinsic manifold structure and also the local features of original data. The target function of our method is easy to propose, while the solving procedures are really nontrivial; in the paper we gave the detailed derivation of solving the target function and also a strict proof of its convergence, which is a key contribution of the paper. Compared with sparseness constrained NMF and GNMF algorithms, GRNMF_SC can learn much sparser representation of the data and can also preserve the geometrical structure of the data, which endow it with powerful discriminating ability. Furthermore, the GRNMF_SC is generalized as supervised and unsupervised models to meet different demands. Experimental results demonstrate encouraging results of GRNMF_SC on image recognition and clustering when comparing with the other state-of-the-art NMF methods

Advanced correlation-based character recognition applied to the Archimedes Palimpsest

The Archimedes Palimpsest is a manuscript containing the partial text of seven treatises by Archimedes that were copied onto parchment and bound in the tenth-century AD. This work is aimed at providing tools that allow scholars of ancient Greek mathematics to retrieve as much information as possible from images of the remaining degraded text. Acorrelation pattern recognition (CPR) system has been developed to recognize distorted versions of Greek characters in problematic regions of the palimpsest imagery, which have been obscured by damage from mold and fire, overtext, and natural aging. Feature vectors for each class of characters are constructed using a series of spatial correlation algorithms and corresponding performance metrics. Principal components analysis (PCA) is employed prior to classification to remove features corresponding to filtering schemes that performed poorly for the spatial characteristics of the selected region-of-interest. A probability is then assigned to each class, forming a character probability distribution based on relative distances from the class feature vectors to the ROI feature vector in principal component (PC) space. However, the current CPR system does not produce a single classification decision, as is common in most target detection problems, but instead has been designed to provide intermediate results that allow the user to apply his or her own decisions (or evidence) to arrive at a conclusion. To achieve this result, a probabilistic network has been incorporated into the recognition system. A probabilistic network represents a method for modeling the uncertainty in a system, and for this application, it allows information from the existing iv partial transcription and contextual knowledge from the user to be an integral part of the decision-making process. The CPR system was designed to provide a framework for future research in the area of spatial pattern recognition by accommodating a broad range of applications and the development of new filtering methods. For example, during preliminary testing, the CPR system was used to confirm the publication date of a fifteenth-century Hebrew colophon, and demonstrated success in the detection of registration markers in three-dimensional MRI breast imaging. In addition, a new correlation algorithm that exploits the benefits of linear discriminant analysis (LDA) and the inherent shift invariance of spatial correlation has been derived, implemented, and tested. Results show that this composite filtering method provides a high level of class discrimination while maintaining tolerance to withinclass distortions. With the integration of this algorithm into the existing filter library, this work completes each stage of a cyclic workflow using the developed CPR system, and provides the necessary tools for continued experimentation

Non-negative matrix factorization methods for face recognition under extreme lighting variations

Abstract-Face recognition task is of primary interest in many computer vision applications, including access control for security systems, forensic or surveillance. Most commercial biometric systems based on face recognition are claimed to perform satisfactory when the enrollment and testing process takes place under controlled environmental conditions such as constant illumination, constant pose scale, non-occluded faces or frontal view. More or less deviation from those conditions might lead to poor recognition performances or even recognition system's failure when a test identity has to be recognized under new modified testing conditions. Three non-negative matrix factorization (NMF) methods, namely, the standard one, the local NMF (LNMF) and the discriminant NMF (DNMF) are employed in this paper where their robustness against extreme lighting variations are tested for the face recognition task. Principal Component Analysis (PCA) method was also chosen as baseline. Experiments revealed that the best recognition performance is obtained with NMF, followed by DNMF and LNMF

Semantic coding by supervised dimensionality reduction

This paper addresses the problem of representing multimedia information under a compressed form that permits efficient classification. The semantic coding problem starts from a subspace method where dimensionality reduction is formulated as a matrix factorization problem. Data samples are jointly represented in a common subspace extracted from a redundant dictionary of basis functions. We first build on greedy pursuit algorithms for simultaneous sparse approximations to solve the dimensionality reduction problem. The method is extended into a supervised algorithm, which further encourages the class separability in the extraction of the most relevant features. The resulting supervised dimensionality reduction scheme provides an interesting trade-off between approximation (or compression) and discriminant feature extraction (or classification). The algorithm provides a compressed signal representation that can directly be used for multimedia data mining. The application of the proposed algorithm to image recognition problems further demonstrates classification performances that are competitive with state-of-the-art solutions in handwritten digit or face recognition. Semantic coding certainly represents an interesting solution to the challenging problem of processing huge volumes of multidimensional data in modern multimedia systems, where compressed data have to be processed and analyzed with limited computational complexity

Neighborhood Preserving Convex Nonnegative Matrix Factorization

The convex nonnegative matrix factorization (CNMF) is a variation of nonnegative matrix factorization (NMF) in which each cluster is expressed by a linear combination of the data points and each data point is represented by a linear combination of the cluster centers. When there exists nonlinearity in the manifold structure, both NMF and CNMF are incapable of characterizing the geometric structure of the data. This paper introduces a neighborhood preserving convex nonnegative matrix factorization (NPCNMF), which imposes an additional constraint on CNMF that each data point can be represented as a linear combination of its neighbors. Thus our method is able to reap the benefits of both nonnegative data factorization and the purpose of manifold structure. An efficient multiplicative updating procedure is produced, and its convergence is guaranteed theoretically. The feasibility and effectiveness of NPCNMF are verified on several standard data sets with promising results

Reconnaissance de visage robuste aux occultations

Face recognition is an important technology in computer vision, which often acts as an essential component in biometrics systems, HCI systems, access control systems, multimedia indexing applications, etc. Partial occlusion, which significantly changes the appearance of part of a face, cannot only cause large performance deterioration of face recognition, but also can cause severe security issues. In this thesis, we focus on the occlusion problem in automatic face recognition in non-controlled environments. Toward this goal, we propose a framework that consists of applying explicit occlusion analysis and processing to improve face recognition under different occlusion conditions. We demonstrate in this thesis that the proposed framework is more efficient than the methods based on non-explicit occlusion treatments from the literature. We identify two new types of facial occlusions, namely the sparse occlusion and dynamic occlusion. Solutions are presented to handle the identified occlusion problems in more advanced surveillance context. Recently, the emerging Kinect sensor has been successfully applied in many computer vision fields. We introduce this new sensor in the context of face recognition, particularly in presence of occlusions, and demonstrate its efficiency compared with traditional 2D cameras. Finally, we propose two approaches based on 2D and 3D to improve the baseline face recognition techniques. Improving the baseline methods can also have the positive impact on the recognition results when partial occlusion occurs.La reconnaissance faciale est une technologie importante en vision par ordinateur, avec un rôle central en biométrie, interface homme-machine, contrôle d’accès, indexation multimédia, etc. L’occultation partielle, qui change complétement l’apparence d’une partie du visage, ne provoque pas uniquement une dégradation des performances en reconnaissance faciale, mai peut aussi avoir des conséquences en termes de sécurité. Dans cette thèse, nous concentrons sur le problème des occultations en reconnaissance faciale en environnements non contrôlés. Nous proposons une séquence qui consiste à analyser de manière explicite les occultations et à fiabiliser la reconnaissance faciale soumises à diverses occultations. Nous montrons dans cette thèse que l’approche proposée est plus efficace que les méthodes de l’état de l’art opérant sans traitement explicite dédié aux occultations. Nous identifions deux nouveaux types d’occultations, à savoir éparses et dynamiques. Des solutions sont introduites pour gérer ces problèmes d’occultation nouvellement identifiés dans un contexte de vidéo surveillance avancé. Récemment, le nouveau capteur Kinect a été utilisé avec succès dans de nombreuses applications en vision par ordinateur. Nous introduisons ce nouveau capteur dans le contexte de la reconnaissance faciale, en particulier en présence d’occultations, et démontrons son efficacité par rapport aux caméras traditionnelles. Finalement, nous proposons deux approches basées 2D et 3D permettant d’améliorer les techniques de base en reconnaissance de visages. L’amélioration des méthodes de base peut alors générer un impact positif sur les résultats de reconnaissance en présence d’occultations

Self-Similarity Based Corresponding-Point Extraction from Weakly Textured Stereo Pairs

For the areas of low textured in image pairs, there is nearly no point that can be detected by traditional methods. The information in these areas will not be extracted by classical interest-point detectors. In this paper, a novel weakly textured point detection method is presented. The points with weakly textured characteristic are detected by the symmetry concept. The proposed approach considers the gray variability of the weakly textured local regions. The detection mechanism can be separated into three steps: region-similarity computation, candidate point searching, and refinement of weakly textured point set. The mechanism of radius scale selection and texture strength conception are used in the second step and the third step, respectively. The matching algorithm based on sparse representation (SRM) is used for matching the detected points in different images. The results obtained on image sets with different objects show high robustness of the method to background and intraclass variations as well as to different photometric and geometric transformations; the points detected by this method are also the complement of points detected by classical detectors from the literature. And we also verify the efficacy of SRM by comparing with classical algorithms under the occlusion and corruption situations for matching the weakly textured points. Experiments demonstrate the effectiveness of the proposed weakly textured point detection algorithm