Face recognition using kernel ridge regression

In this paper, we present novel ridge regression (RR) and kernel ridge regression (KRR) techniques for multivariate labels and apply the methods to the problem of face recognition. Motivated by the fact that the regular simplex vertices are separate points with highest degree of symmetry, we choose such vertices as the targets for the distinct individuals in recognition and apply RR or KRR to map the training face images into a face subspace where the training images from each individual will locate near their individual targets. We identify the new face image by mapping it into this face subspace and comparing its distance to all individual targets. An efficient cross-validation algorithm is also provided for selecting the regularization and kernel parameters. Experiments were conducted on two face databases and the results demonstrate that the proposed algorithm significantly outperforms the three popular linear face recognition techniques (Eigenfaces, Fisherfaces and Laplacianfaces) and also performs comparably with the recently developed Orthogonal Laplacianfaces with the advantage of computational speed. Experimental results also demonstrate that KRR outperforms RR as expected since KRR can utilize the nonlinear structure of the face images. Although we concentrate on face recognition in this paper, the proposed method is general and may be applied for general multi-category classification problems.

Fast cross-validation of kernel fisher discriminant classifiers

Given n training examples, the training of a Kernel Fisher Discriminant (KFD) classifier corresponds to solving a linear system of dimension n. In cross-validating KFD, the training examples are split into 2 distinct subsets for a number of times (L) wherein a subset of m examples is used for validation and the other subset of(n - m) examples is used for training the classifier. In this case L linear systems of dimension (n - m) need to be solved. We propose a novel method for cross-validation of KFD in which instead of solving L linear systems of dimension (n - m), we compute the inverse of an n × n matrix and solve L linear systems of dimension 2m, thereby reducing the complexity when L is large and/or m is small. For typical 10-fold and leave-one-out cross-validations, the proposed algorithm is approximately 4 and (^4/9n) times respectively as efficient as the naive implementations. Simulations are provided to demonstrate the efficiency of the proposed algorithms.

A fast kernel dimension reduction algorithm with applications to face recognition

This paper presents a novel dimensionality reduction algorithm for kernel based classification. In the feature space, the proposed algorithm maximizes the ratio of the squared between-class distance and the sum of the within-class variances of the training samples for a given reduced dimension. This algorithm has lower complexity than the recently reported kernel dimension reduction(KDR) for supervised learning. We conducted several simulations with large training datasets, which demonstrate that the proposed algorithm has similar performance or is marginally better compared with KDR whilst having the advantage of computational efficiency. Further, we applied the proposed dimension reduction algorithm to face recognition in which the number of training samples is very small. This proposed face recognition approach based on the new algorithm outperforms the eigenface approach based on the principle component analysis (PCA), when the training data is complete, that is, representative of the whole dataset.

Meta-analytic review of neurocognition in bipolar II disorder

Objective: The clinical distinction between bipolar II disorder (BD II) and bipolar I disorder (BD I) is not clear-cut. Cognitive functioning offers the potential to explore objective markers to help delineate this boundary. To examine this issue, we conducted a quantitative review of the cognitive profile of clinically stable patients with BD II in comparison with both patients with BD I and healthy controls.
Method: Meta-analytical methods were used to compare cognitive functioning of BD II disorder with both BD I disorder and healthy controls.
Results: Individuals with BD II were less impaired than those with BD I on verbal memory. There were also small but significant difference in
visual memory and semantic fluency. There were no significant differences in global cognition or in other cognitive domains. Patients with BD II performed poorer than controls in all cognitive domains.
Conclusion: Our findings suggest that with the exception of memory and semantic fluency, cognitive impairment in BD II is as severe as in BD I. Further studies are needed to investigate whether more severe deficits in BD I are related to neurotoxic effects of severe manic episodes on medial temporal structures or neurobiological differences from the onset of the illness.

Identification of nonlinear fMRI models using Auxiliary Particle Filter and kernel smoothing method

Hemodynamic models have a high potential in application to understanding the functional differences of the brain. However, full system identification with respect to model fitting to actual functional magnetic resonance imaging (fMRI) data is practically difficult and is still an active area of research. We present a simulation based Bayesian approach for nonlinear model based analysis of the fMRI data. The idea is to do a joint state and parameter estimation within a general filtering framework. One advantage of using Bayesian methods is that they provide a complete description of the posterior distribution, not just a single point estimate. We use an Auxiliary Particle Filter adjoined with a kernel smoothing approach to address this joint estimation problem.

Face recognition from face motion manifolds using robust kernel resistor-average distance

In this work we consider face recognition from face motion manifolds. An information-theoretic approach with Resistor-Average Distance (RAD) as a dissimilarity measure between distributions of face images is proposed. We introduce a kernel-based algorithm that retains the simplicity of the closed-form expression for the RAD between two normal distributions, while allowing for modelling of complex, nonlinear manifolds. Additionally, it is shown how errors in the face registration process can be modelled to significantly improve recognition. Recognition performance of our method is experimentally demonstrated and shown to outperform state-of-the-art algorithms. Recognition rates of 97–100% are consistently achieved on databases of 35– 90 people.