David Guillamet

Introducing a weighted non-negative matrix factorization for image classification

Non-negative matrix factorization (NMF) technique has been recently proposed for dimensionality reduction. NMF is capable to produce region or part based representations of objects and images. Also, a direct modification of NMF, the weighted non-negative matrix factorization (WNMF) has also been introduced to improve the NMF capabilities of representing positive local data (as color histograms). A comparison between NMF, WNMF and the well-known principal component analysis (PCA) in the context of image patch classification has been carried out and it is claimed that all these three techniques can be combined in a common and unique classifier. This contribution is an extension of a previous study and we introduce the use of the WNMF as well as a probabilistic approach to compare all the three techniques noticing a great improvement in the final recognition results.

Non-negative Matrix Factorization for Face Recognition

The computer vision problem of face classification under several ambient and unfavorable conditions is considered in this study. Changes in expression, different lighting conditions and occlusions are the relevant factors that are studied in this present contribution. Non-negative Matrix Factorization (NMF) technique is introduced in the context of face classification and a direct comparison with Principal Component Analysis (PCA) is also analyzed. Two leading techniques in face recognition are also considered in this study noticing that NMF is able to improve these techniques when a high dimensional feature space is used. Finally, different distance metrics (L1, L2 and correlation) are evaluated in the feature space defined by NMF in order to determine the best one for this specific problem. Experiments demonstrate that the correlation is the most suitable metric for this problem.

Analyzing non-negative matrix factorization for image classification

The Non-negative Matrix Factorization technique (NMF) has been recently proposed for dimensionality reduction. NMF is capable to produce a region- or part-based representation of objects and images. This paper experimentally compares NMF to Principal Component Analysis (PCA) in the context of image patch classification. A first finding is that the two techniques are complementary and that their respective performance is correlated to the with-in class scatter. This paper also analyses different techniques to combine these complementary methods. In the first combination scheme the best technique for each class is chosen and the results are merged. The second combination scheme builds a hierarchy of classifiers where again for each classification task the best technique is chosen. Additionally, incorporation of the classification results of neighboring image patches further improves the overall results.

Using an ICA representation of high dimensional data for object recognition and classification

This paper applies a Bayesian classification scheme to the problem of recognition through probabilistic modeling of high dimensional data. In this context, high dimensionality does not allow precision in the density estimation. We propose a local independent component analysis (ICA) representation of the data. The components can be assumed statistically independent and, in many cases, sparsity is observed. We show how these two characteristics can be used to simplify and add accuracy to the density estimation and develop bayesian decision within this representation. A first experiment illustrates that classification using an ICA representation is a technique that, even in low dimensions, performs comparably to standard classification techniques. The second experiment tests the ICA classification model on high dimensional data. Recognition was performed using local color histograms as salient features. It is also shown how our approach outperforms other techniques commonly used in the context of appearance-based recognition.

Using an ICA representation of local color histograms for object recognition

This paper applies a Bayesian classification scheme to the problem of object recognition through probabilistic modeling of local color histograms. In this context, the density estimation is generally performed via nonparametric kernel methods and the high dimensionality does not allow precision in the results. We propose a local independent component analysis (ICA) representation of the data. Within this representation, the components can be assumed statistically independent and, for this particular problem, sparsity of the independent components is observed. We show how these two characteristics simplify and add accuracy to the density estimation and develop a Bayesian decision scheme within this representation. We propose a set of possible density estimations for supergaussian densities, the density type associated with a sparse representation. Two experiments were performed. The first one illustrates the properties of the ICA representation for local color histograms. The second experiment tests the ICA classification model for a large set of pharmaceutical products and compares this scheme with a nonparametric technique based on Gaussian Kernels, two nearest-neighbor techniques and global histogram approach.

Determining a suitable metric when using non-negative matrix factorization

The Non-negative Matrix Factorization technique (NMF) has been recently proposed for dimensionality reduction. NMF is able to produce a region- or part-based representation of objects and images. The positive space defined with NMF lacks a suitable metric and this paper experimentally compares NMF to Principal Component Analysis (PCA) in the context of classification, trying to determine the best distance metric for NMF. This paper introduces the use of the Earth Movers Distance (EMD) as a relevant metric that takes into account the positive definition of the NMF bases, leading to better recognition results when the dimensionality of the problem is correctly chosen. PCA and NMF have also been tested under the presence of occlusions and, due to its part-based representation, NMF is able to improve on the PCA results.

A comparison of global versus local color histograms for object recognition

Global color distributions have been efficiently used as signatures for object recognition. However, these methods are very sensitive to partial occlusions and to background regions. Our approach is directed to minimize these effects by working with small neighborhoods. We compare global and local color representations on an automatic object recognition system. Local representations significantly outperformed global representations in terms of recognition rates. Local color distributions are a strong constraint when objects consist of distinctive local regions. Eigenspace techniques are applied to detect discriminant local representations and support vector machines are used during the recognition process in order to maximize the recognition rate.

Local appearance-based models using high-order statistics of image features

We propose a novel local appearance modeling method for object detection and recognition in cluttered scenes. The approach is based on the joint distribution of local feature vectors at multiple salient points and factorization with the independent component analysis (ICA). The resulting densities are simple multiplicative distributions modeled through adaptive Gaussian mixture models. This leads to computationally tractable joint probability densities, which can model high-order dependencies. Furthermore, different models are compared based on appearance, color and geometry information. Also, the combination of all of them results in a hybrid model, which obtains the best results using the COIL-100 object database. Our technique has been tested under different natural and cluttered scenes with different degrees of occlusions with promising results. Finally, a large statistical test with the MNIST digit database is used to demonstrate the improved performance obtained by explicit modeling of high-order dependencies.

Discriminant basis for object classification

This paper presents a technique to obtain a discriminant basis set in an unsupervised way. A non-negative matrix factorization (NMF) is applied over a set of color newspapers to obtain a reduced space considering only positive constraints. This method is compared with the well-known principal component analysis (PCA), obtaining promising results in the task of representing independent behaviors of the input data. With this methodology, we are able to find an ordered list of the basis functions, with it being possible to select some of them for a further discriminant task. Moreover the method can also be applied to the task of automatically extracting object classes from a set of objects.

Unsupervised Learning of Part-Based Representations

This article introduces a segmentation method to automatically extract object parts from a reduced set of images. Given a database of objects and dividing all of them using local color histograms, we obtain an object part as the conjunction of the most similar ones. The similarity measure is obtained analyzing the behaviour of a local vector with respect to the whole object database. Furthermore, the proposed technique is able to associate an energy to each object part being possible to find the most discriminant object parts. We present the non-negative matrix factorization (NMF) technique to improve the internal data representation by compacting the original local histograms (50D instead of 512D). Moreover, the NMF based projected histograms only contain a few activated components and this fact improves the clustering results with respect to the use of the original local color histograms. We present a set of experimental results validating the use of the NMF in conjunction with the clustering technique.