Local Component Analysis for Nonparametric Bayes Classifier

The decision boundaries of Bayes classifier are optimal because they lead to maximum probability of correct decision. It means if we knew the prior probabilities and the class-conditional densities, we could design a classifier which gives the lowest probability of error. However, in classification based on nonparametric density estimation methods such as Parzen windows, the decision regions depend on the choice of parameters such as window width. Moreover, these methods suffer from curse of dimensionality of the feature space and small sample size problem which severely restricts their practical applications. In this paper, we address these problems by introducing a novel dimension reduction and classification method based on local component analysis. In this method, by adopting an iterative cross-validation algorithm, we simultaneously estimate the optimal transformation matrices (for dimension reduction) and classifier parameters based on local information. The proposed method can classify the data with complicated boundary and also alleviate the course of dimensionality dilemma. Experiments on real data show the superiority of the proposed algorithm in term of classification accuracies for pattern classification applications like age, facial expression and character recognition. Keywords: Bayes classifier, curse of dimensionality dilemma, Parzen window, pattern classification, subspace learning.

Extended Two-Dimensional PCA for Efficient Face Representation and Recognition

In this paper a novel method called Extended Two-Dimensional PCA (E2DPCA) is proposed which is an extension to the original 2DPCA. We state that the covariance matrix of 2DPCA is equivalent to the average of the main diagonal of the covariance matrix of PCA. This implies that 2DPCA eliminates some covariance information that can be useful for recognition. E2DPCA instead of just using the main diagonal considers a radius of r diagonals around it and expands the averaging so as to include the covariance information within those diagonals. The parameter r unifies PCA and 2DPCA. r = 1 produces the covariance of 2DPCA, r = n that of PCA. Hence, by controlling r it is possible to control the trade-offs between recognition accuracy and energy compression (fewer coefficients), and between training and recognition complexity. Experiments on ORL face database show improvement in both recognition accuracy and recognition time over the original 2DPCA.

Multilinear Biased Discriminant Analysis: A Novel Method for Facial Action Unit Representation

In this paper a novel efficient method for representation of facial action units by encoding an image sequence as a fourth-order tensor is presented. The multilinear tensor-based extension of the biased discriminant analysis (BDA) algorithm, called multilinear biased discriminant analysis (MBDA), is first proposed. Then, we apply the MBDA and two-dimensional BDA (2DBDA) algorithms, as the dimensionality reduction techniques, to Gabor representations and the geometric features of the input image sequence respectively. The proposed scheme can deal with the asymmetry between positive and negative samples as well as curse of dimensionality dilemma. Extensive experiments on Cohn-Kanade database show the superiority of the proposed method for representation of the subtle changes and the temporal information involved in formation of the facial expressions. As an accurate tool, this representation can be applied to many areas such as recognition of spontaneous and deliberate facial expressions, multi modal/media human computer interaction and lie detection efforts.

Recognizing Combinations of Facial Action Units with Different Intensity Using a Mixture of Hidden Markov Models and Neural Network

Facial Action Coding System consists of 44 action units (AUs) and more than 7000 combinations. Hidden Markov models (HMMs) classifier has been used successfully to recognize facial action units (AUs) and expressions due to its ability to deal with AU dynamics. However, a separate HMM is necessary for each single AU and each AU combination. Since combinations of AU numbering in thousands, a more efficient method will be needed. In this paper an accurate real-time sequence-based system for representation and recognition of facial AUs is presented. Our system has the following characteristics: 1) employing a mixture of HMMs and neural network, we develop a novel accurate classifier, which can deal with AU dynamics, recognize subtle changes, and it is also robust to intensity variations, 2) although we use an HMM for each single AU only, by employing a neural network we can recognize each single and combination AU, and 3) using both geometric and appearance-based features, and applying efficient dimension reduction techniques, our system is robust to illumination changes and it can represent the temporal information involved in formation of the facial expressions. Extensive experiments on Cohn-Kanade database show the superiority of the proposed method, in comparison with other classifiers. Keywords: classifier design and evaluation, data fusion, facial action units (AUs), hidden Markov models (HMMs), neural network (NN).

Analysis, Interpretation, and Recognition of Facial Action Units and Expressions Using Neuro-Fuzzy Modeling

In this paper an accurate real-time sequence-based system for representation, recognition, interpretation, and analysis of the facial action units (AUs) and expressions is presented. Our system has the following characteristics: 1) employing adaptive-network-based fuzzy inference systems (ANFIS) and temporal information, we developed a classification scheme based on neuro-fuzzy modeling of the AU intensity, which is robust to intensity variations, 2) using both geometric and appearance-based features, and applying efficient dimension reduction techniques, our system is robust to illumination changes and it can represent the subtle changes as well as temporal information involved in formation of the facial expressions, and 3) by continuous values of intensity and employing top-down hierarchical rule-based classifiers, we can develop accurate human-interpretable AU-to-expression converters. Extensive experiments on Cohn-Kanade database show the superiority of the proposed method, in comparison with support vector machines, hidden Markov models, and neural network classifiers. Keywords: biased discriminant analysis (BDA), classifier design and evaluation, facial action units (AUs), hybrid learning, neuro-fuzzy modeling.