Carlos Eduardo Thomaz

A new ranking method for principal components analysis and its application to face image analysis

In this work, we investigate a new ranking method for principal component analysis (PCA). Instead of sorting the principal components in decreasing order of the corresponding eigenvalues, we propose the idea of using the discriminant weights given by separating hyperplanes to select among the principal components the most discriminant ones. The method is not restricted to any particular probability density function of the sample groups because it can be based on either a parametric or non-parametric separating hyperplane approach. In addition, the number of meaningful discriminant directions is not limited to the number of groups, providing additional information to understand group differences extracted from high-dimensional problems. To evaluate the discriminant principal components, separation tasks have been performed using face images and three different databases. Our experimental results have shown that the principal components selected by the separating hyperplanes allow robust reconstruction and interpretation of the data, as well as higher recognition rates using less linear features in situations where the differences between the sample groups are subtle and consequently most difficult for the standard and state-of-the-art PCA selection methods.

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 new covariance estimate for Bayesian classifiers in biometric recognition

In many biometric pattern-recognition problems, the number of training examples per class is limited, and consequently the sample group covariance matrices often used in parametric and nonparametric Bayesian classifiers are poorly estimated or singular. Thus, a considerable amount of effort has been devoted to the design of other covariance estimators, for use in limited-sample and high-dimensional classification problems. In this paper, a new covariance estimate, called the maximum entropy covariance selection (MECS) method, is proposed. It is based on combining covariance matrices under the principle of maximum uncertainty. In order to evaluate the MECS effectiveness in biometric problems, experiments on face, facial expression, and fingerprint classification were carried out and compared with popular covariance estimates, including the regularized discriminant analysis and leave-one-out covariance for the parametric classifier, and the Van Ness and Toeplitz covariance estimates for the nonparametric classifier. The results show that, in image recognition applications whenever the sample group covariance matrices are poorly estimated or ill posed, the MECS method is faster and usually more accurate than the aforementioned approaches in both parametric and nonparametric Bayesian classifiers.

Evaluating SVM and MLDA in the extraction of discriminant regions for mental state prediction

Pattern recognition methods have been successfully applied in several functional neuroimaging studies. These methods can be used to infer cognitive states, so-called brain decoding. Using such approaches, it is possible to predict the mental state of a subject or a stimulus class by analyzing the spatial distribution of neural responses. In addition it is possible to identify the regions of the brain containing the information that underlies the classification. The Support Vector Machine (SVM) is one of the most popular methods used to carry out this type of analysis. The aim of the current study is the evaluation of SVM and Maximum uncertainty Linear Discrimination Analysis (MLDA) in extracting the voxels containing discriminative information for the prediction of mental states. The comparison has been carried out using fMRI data from 41 healthy control subjects who participated in two experiments, one involving visual-auditory stimulation and the other based on bi-manual fingertapping sequences. The results suggest that MLDA uses significantly more voxels containing discriminative information (related to different experimental conditions) to classify the data. On the other hand, SVM is more parsimonious and uses less voxels to achieve similar classification accuracies. In conclusion, MLDA is mostly focused on extracting all discriminative information available, while SVM extracts the information which is sufficient for classification.

Using variance information in magnetoencephalography measures of functional connectivity

The use of magnetoencephalography (MEG) to assess long range functional connectivity across large scale distributed brain networks is gaining popularity. Recent work has shown that electrodynamic networks can be assessed using both seed based correlation or independent component analysis (ICA) applied to MEG data and further that such metrics agree with fMRI studies. To date, techniques for MEG connectivity assessment have typically used a variance normalised approach, either through the use of Pearson correlation coefficients or via variance normalisation of envelope timecourses prior to ICA. Here, we show that the use of variance information (i.e. data that have not been variance normalised) in source space projected Hilbert envelope time series yields important spatial information, and is of significant functional relevance. Further, we show that employing this information in functional connectivity analyses improves the spatial delineation of network nodes using both seed based and ICA approaches. The use of variance is particularly important in MEG since the non-independence of source space voxels (brought about by the ill-posed MEG inverse problem) means that spurious signals can exist in areas of low signal variance. We therefore suggest that this approach be incorporated into future studies.

Maximum-uncertainty linear discrimination analysis of first-episode schizophrenia subjects.

Recent techniques of image analysis brought the possibility to recognize subjects based on discriminative image features. We performed a magnetic resonance imaging (MRI)-based classification study to assess its usefulness for outcome prediction of first-episode schizophrenia patients (FES). We included 39 FES patients and 39 healthy controls (HC) and performed the maximum-uncertainty linear discrimination analysis (MLDA) of MRI brain intensity images. The classification accuracy index (CA) was correlated with the Positive and Negative Syndrome Scale (PANSS) and the Global Assessment of Functioning scale (GAF) at 1-year follow-up. The rate of correct classifications of patients with poor and good outcomes was analyzed using chi-square tests. MLDA classification was significantly better than classification by chance. Leave-one-out accuracy was 72%. CA correlated significantly with PANSS and GAF scores at the 1-year follow-up. Moreover, significantly more patients with poor outcome than those with good outcome were classified correctly. MLDA of brain MR intensity features is, therefore, able to correctly classify a significant number of FES patients, and the discriminative features are clinically relevant for clinical presentation 1 year after the first episode of schizophrenia. The accuracy of the current approach is, however, insufficient to be used in clinical practice immediately. Several methodological issues need to be addressed to increase the usefulness of this classification approach.

Using a Maximum Uncertainty LDA-Based Approach to Classify and Analyse MR Brain Images

Multivariate statistical learning techniques that analyse all voxels simultaneously have been used to classify and describe MR brain images. Most of these techniques have overcome the difficulty of dealing with the inherent high dimensionality of 3D brain image data by using pre-processed segmented images or a number of specific features. However, an intuitive way of mapping the classification results back into the original image domain for further interpretation remains challenging. In this paper, we introduce the idea of using Principal Components Analysis (PCA) plus the maximum uncertainty Linear Discriminant Analysis (LDA) based approach to classify and analyse magnetic resonance (MR) images of the brain. It avoids the computation costs inherent in commonly used optimisation processes, resulting in a simple and efficient implementation for the maximisation and interpretation of the Fisher’s classification results. In order to demonstrate the effectiveness of the approach, we have used two MR brain data sets. The first contains images of 17 schizophrenic patients and 5 controls, and the second is composed of brain images of 12 preterm infants at term equivalent age and 12 term controls. The results indicate that the two-stage linear classifier not only makes clear the statistical differences between the control and patient samples, but also provides a simple method of analysing the results for further medical research.

Mobile Robot Path Planning Using Genetic Algorithms

Genetic Algorithms (GAs) have demonstrated to be effective procedures for solving multicriterion optimization problems. These algorithms mimic models of natural evolution and have the ability to adaptively search large spaces in near-optimal ways. One direct application of this intelligent technique is in the area of evolutionary robotics, where GAs are typically used for designing behavioral controllers for robots and autonomous agents. In this paper we describe a new GA path-planning approach that proposes the evolution of a chromosome attitudes structure to control a simulated mobile robot, called Khepera. These attitudes define the basic robot actions to reach a goal location, performing straight motion and avoiding obstacles. The GA fitness function, employed to teach robot’s movements, was engineered to achieve this type of behavior in spite of any changes in Khepera’s goals and environment. The results obtained demonstrate the controller’s adaptability, displaying near-optimal paths in different configurations of the environment.

Identification of psychopathic individuals using pattern classification of MRI images

Background: Psychopathy is a disorder of personality characterized by severe impairments of social conduct, emotional experience, and interpersonal behavior. Psychopaths consistently violate social norms and bring considerable financial, emotional, or physical harm to others and to society as a whole. Recent developments in analysis methods of magnetic resonance imaging (MRI), such as voxel-based-morphometry (VBM), have become major tools to understand the anatomical correlates of this disorder. Nevertheless, the identification of psychopathy by neuroimaging or other neurobiological tools (e.g., genetic testing) remains elusive. Methods/Principal findings: The main aim of this study was to develop an approach to distinguish psychopaths from healthy controls, based on the integration between pattern recognition methods and gray matter quantification. We employed support vector machines (SVM) and maximum uncertainty linear discrimination analysis (MLDA), with a feature-selection algorithm. Imaging data from 15 healthy controls and 15 psychopathic individuals (7 women in each group) were analyzed with SPM2 and the optimized VBM preprocessing routines. Participants were scanned with a 1.5 Tesla MRI system. Both SVM and MLDA achieved an overall leave-one-out accuracy of 80%, but SVM mapping was sparser than using MLDA. The superior temporal sulcus/gyrus (bilaterally) was identified as a region containing the most relevant information to separate the two groups. Conclusion/significance: These results indicate that gray matter quantitative measures contain robust information to predict high psychopathy scores in individual subjects. The methods employed herein might prove useful as an adjunct to the established clinical and neuropsychological measures in patient screening and diagnostic accuracy.

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 paper, a maximum uncertainty 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 results indicate that our method im-proves 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.