Edson C. Kitani

A maximum uncertainty LDA-based approach for limited sample size problems - with application to face recognition

A critical issue of applying Linear Discriminant Analysis (LDA) is both the singularity and instability of the within-class scatter matrix. In practice, particularly in image recognition applications such as face recognition, there are often a large number of pixels or pre-processed features available, but the total number of training patterns is limited and commonly less than the dimension of the feature space. In this study, a new LDA-based method is proposed. It is based on a straightforward stabilisation approach for the within-class scatter matrix. In order to evaluate its effectiveness, experiments on face recognition using the well-known ORL and FERET face databases were carried out and compared with other LDA-based methods. The classification results indicate that our method improves the LDA classification performance when the within-class scatter matrix is not only singular but also poorly estimated, with or without a Principal Component Analysis intermediate step and using less linear discriminant features. Since statistical discrimination methods are suitable not only for classification but also for characterisation of differences between groups of patterns, further experiments were carried out in order to extend the new LDA-based method to visually analyse the most discriminating hyper-plane separating two populations. The additional results based on frontal face images indicate that the new LDA-based mapping provides an intuitive interpretation of the two-group classification tasks performed, highlighting the group differences captured by the multivariate statistical approach proposed.

A Statistical Discriminant Model for Face Interpretation and Reconstruction

Multivariate statistical approaches have played an important role of recognising face images and characterizing their differences. In this paper, we introduce the idea of using a two-stage separating hyper-plane, here called statistical discriminant model (SDM), to interpret and reconstruct face images. Analogously to the well-known active appearance model proposed by Cootes et. al, SDM requires a previous alignment of all the images to a common template to minimise variations that are not necessarily related to differences between the faces. However, instead of using landmarks or annotations on the images, SDM is based on the idea of using PCA to reduce the dimensionality of the original images and a maximum uncertainty linear classifier (MLDA) to characterise the most discriminant changes between the groups of images. The experimental results based on frontal face images indicate that the SDM approach provides an intuitive interpretation of the differences between groups, reconstructing characteristics that are very subjective in human beings, such as beauty and happiness

Statistical learning approaches for discriminant features selection

Supervised statistical learning covers important models like Support Vector Machines (SVM) and Linear Discriminant Analysis (LDA). In this paper we describe the idea of using the discriminant weights given by SVM and LDA separating hyperplanes to select the most discriminant features to separate sample groups. Our method, called here as Discriminant Feature Analysis (DFA), is not restricted to any particular probability density function and the number of meaningful discriminant features is not limited to the number of groups. To evaluate the discriminant features selected, two case studies have been investigated using face images and breast lesion data sets. In both case studies, our experimental results show that the DFA approach provides an intuitive interpretation of the differences between the groups, highlighting and reconstructing the most important statistical changes between the sample groups analyzed.

Visual Interpretation of Self Organizing Maps

The design and test of a two-stage PCA+SOM methodology targeting applications on images database are presented and the result of the SOM map is analyzed by reconstructing the prototypes (codebook) of the map in terms of concrete images in the input space. This visual analysis allows us to interpret which features were used by the SOM algorithm to create a self-organizing map. Several approaches in the SOM literature study the numbers of clusters captured by the algorithm, this research work views the production of tools that help us to know which features led to self-organization. To accomplish this task, a high dimensional, complex and controlled database formed by human face images has been used. The experimental demonstration of the methodology is made through the analysis of a face database. Despite the complexity of having computations with images of faces, they are easily identified and understood by humans.

A Multi-linear Discriminant Analysis of 2D Frontal Face Images

We have designed and implemented a multi-linear discriminant method of constructing and quantifying statistically significant changes on human identity photographs. The method is based on a general multivariate two-stage linear framework that addresses the small sample size problem in high-dimensional spaces. Starting with a 2D face data set of well framed images, we determine a most characteristic direction of change by organizing the data according to the features of interest. Our goal here is to use all the facial image features simultaneously rather than separate models for texture and shape information. Our experiments show that the method does produce plausible unseen views for gender, facial expression and ageing changes. We believe that this method could be widely applied for normalization in face recognition and in identifying subjects after a lapse of time.

Exploring and Understanding the High Dimensional and Sparse Image Face Space: a Self-Organized Manifold Mapping

Face recognition has motivated several research studies in the last years owing not only to its applicability and multidisciplinary inherent characteristics, but also to its important role in human relationship. Despite extensive studies on face recognition, a number of related problems has still remained challenging in this research topic. It is well known that humans can overcome any computer program in the task of face recognition when artefacts are present such as changes in pose, illumination, occlusion, aging and etc. For instance, young children can robustly identify their parents, friends and common social groups without any previous explicit teaching or learning. Some recent research in Neuroscience (Kandel et al., 2000; Bakker et al., 2008) has shown that there is some new information about how humans deal with such high dimensional and sparse visual recognition task, indicating that the brain does not memorize all details of the visual stimuli (images) to perform face recognition (Brady et al., 2008). Instead, our associative memory tends to work essentially on the most expressive information (Bakker et al., 2008; Oja, 1982). In fact, theoretical models (Treves and Rolls, 1994; O’Reilly and Rudy, 2001; Norman and O’Reilly, 2003) have indicated that the ability of our memory relies on the capability of orthogonalizing (pattern separation) and completing (pattern prototyping) partial patterns in order to encode, store and recall information (O’Reily and McClelland, 1994; Kuhl et al., 2010). Therefore, subspace learning techniques have a close biological inspiration and reasonability in terms of computational methods to possibly exploring and understanding the human behaviour of recognizing faces. The aim of this chapter is to study the non-supervised subspace learning called SelfOrganizing Map (SOM) (Kohonen, 1982; Kohonen, 1990) based on the principle of prototyping face image observations. Our idea with this study is not only to seek a low dimensional Euclidean embedding subspace of a set of face samples that describes the intrinsic similarities of the data (Kitani et al., 2006; Giraldi et al., 2008; Thomaz et al., 2009; Kitani et al., 2010), but also to explore an alternative mapping representation based on manifold models topologically constrained.

Learning Embedded Data Structure with Self-Organizing Maps

Self-Organizing Map (SOM) is undoubtedly one of the most famous and successful artificial neural network approaches. Since the SOM is related with the Vector Quantization learning process, minimizing error quantization and maximizing topology preservation can be concurrent tasks. Besides, even with some metrics, sometimes the analysis of the map results depends on the user and poses an additional difficulty when the user deals with high dimensional data. This work discusses a proposal of relocating the voted map units after the training phase in order to minimize the quantization error and evaluate the impact in the topology preservation. The idea is to enhance the visualization of embedded data structure from input samples using the SOM.

SOMM – self-organized manifold mapping

The Self Organizing Map (SOM) [1] proposed by Kohonen has proved to be remarkable in terms of its range of applications. It can be used for high dimensional space visualization, pattern recognition, input space dimensionality reduction and for generating prototyping to extrapolate information. Basically, tasks conducted by the SOM method are closely related with input space mapping in order to preserve topological and metric relationship between samples. These maps are meant to create a low dimensional output representation of high dimensional input space. Although maps higher than two dimensions can be created by SOM, it is common to work with the limit of one or two dimensions. This work presents a methodology named SOMM (Self-Organized Manifold Mapping) that can be useful to discover structures and clusters of input dataset using the SOM map as a representation of data distribution structure.

Discriminant Component Analysis and Self-Organized Manifold Mapping for Exploring and Understanding Image Face Spaces

Face recognition is a multidisciplinary field that involves subjects in neuroscience, computer science and statistical learning. Some recent research in neuroscience has indicated that the ability of our memory relies on the capability of orthogonalizing (pattern separation) and completing (pattern prototyping) partial patterns in order to encode, store and recall information. From a computational viewpoint, pattern separation can be cast in the subspace learning area while pattern prototyping is closer to manifold learning methods. So, subspace (or manifold) learning techniques have a close biological inspiration and reasonability in terms of computational methods to possibly exploring and understanding the human behavior of recognizing faces. Therefore, the aim of this paper is threefold. Firstly, we review some theoretical aspects about perceptual and cognitive processes related to the mechanisms of pattern separation and pattern prototyping. Then, the paper presents the basic idea of manifold learning and its relationship with subspace learning with focus on the dimensionality reduction problem. Finally, we present the Discriminant Principal Component Analysis (DPCA) and the Self-Organized Manifold Mapping (SOMM) algorithm to exemplify respectively pattern separation and completion techniques. We show experimental results to demonstrate the effectiveness of DPCA and SOMM algorithms on well-framed face image analysis.

Fine-tuning of the SOMkNN classifier

Classification is an important data mining task used in decision-making processes. Techniques such as Artificial Neural Networks (ANN) and Statistics are used to help in an automatic classification. In a previous work, we proposed a method for classification problems based on Self-Organizing Maps ANN (SOM) and k Nearest Neighbor (kNN) statistical classifier. The SOMkNN classifier, as we call this combination, is much faster than the traditional kNN and it keeps equivalent rates results. We propose a fine-tuning for this classifier here, which consists of a neuron relocation of the SOM map. The experiments presented compare SOMkNN with and without fine-tuning. Experiments using 8 databases, 6 of which are available in the UCI repository, the fine-tuning results are an improvement classification rate in 7 databases and in the last one the result is the same. The results indicate a trend of classification rate improvement with the application of the fine tuning technique. The gain in rate is approximately 1.2% and experiments were performed in order to correlate the results.