The appearance of a face is severely altered by illumination conditions that makes automatic face recognition a challenging task. In this paper we propose a Gaussian Mixture Models (GMM)-based human face identificatio...The appearance of a face is severely altered by illumination conditions that makes automatic face recognition a challenging task. In this paper we propose a Gaussian Mixture Models (GMM)-based human face identification technique built in the Fourier or frequency domain that is robust to illumination changes and does not require “illumination normalization” (removal of illumination effects) prior to application unlike many existing methods. The importance of the Fourier domain phase in human face identification is a well-established fact in signal processing. A maximum a posteriori (or, MAP) estimate based on the posterior likelihood is used to perform identification, achieving misclassification error rates as low as 2% on a database that contains images of 65 individuals under 21 different illumination conditions. Furthermore, a misclassification rate of 3.5% is observed on the Yale database with 10 people and 64 different illumination conditions. Both these sets of results are significantly better than those obtained from traditional PCA and LDA classifiers. Statistical analysis pertaining to model selection is also presented.展开更多
We investigate the structure of a large precision matrix in Gaussian graphical models by decomposing it into a low rank component and a remainder part with sparse precision matrix.Based on the decomposition,we propose...We investigate the structure of a large precision matrix in Gaussian graphical models by decomposing it into a low rank component and a remainder part with sparse precision matrix.Based on the decomposition,we propose to estimate the large precision matrix by inverting a principal orthogonal decomposition(IPOD).The IPOD approach has appealing practical interpretations in conditional graphical models given the low rank component,and it connects to Gaussian graphical models with latent variables.Specifically,we show that the low rank component in the decomposition of the large precision matrix can be viewed as the contribution from the latent variables in a Gaussian graphical model.Compared with existing approaches for latent variable graphical models,the IPOD is conveniently feasible in practice where only inverting a low-dimensional matrix is required.To identify the number of latent variables,which is an objective of its own interest,we investigate and justify an approach by examining the ratios of adjacent eigenvalues of the sample covariance matrix?Theoretical properties,numerical examples,and a real data application demonstrate the merits of the IPOD approach in its convenience,performance,and interpretability.展开更多
文摘The appearance of a face is severely altered by illumination conditions that makes automatic face recognition a challenging task. In this paper we propose a Gaussian Mixture Models (GMM)-based human face identification technique built in the Fourier or frequency domain that is robust to illumination changes and does not require “illumination normalization” (removal of illumination effects) prior to application unlike many existing methods. The importance of the Fourier domain phase in human face identification is a well-established fact in signal processing. A maximum a posteriori (or, MAP) estimate based on the posterior likelihood is used to perform identification, achieving misclassification error rates as low as 2% on a database that contains images of 65 individuals under 21 different illumination conditions. Furthermore, a misclassification rate of 3.5% is observed on the Yale database with 10 people and 64 different illumination conditions. Both these sets of results are significantly better than those obtained from traditional PCA and LDA classifiers. Statistical analysis pertaining to model selection is also presented.
文摘We investigate the structure of a large precision matrix in Gaussian graphical models by decomposing it into a low rank component and a remainder part with sparse precision matrix.Based on the decomposition,we propose to estimate the large precision matrix by inverting a principal orthogonal decomposition(IPOD).The IPOD approach has appealing practical interpretations in conditional graphical models given the low rank component,and it connects to Gaussian graphical models with latent variables.Specifically,we show that the low rank component in the decomposition of the large precision matrix can be viewed as the contribution from the latent variables in a Gaussian graphical model.Compared with existing approaches for latent variable graphical models,the IPOD is conveniently feasible in practice where only inverting a low-dimensional matrix is required.To identify the number of latent variables,which is an objective of its own interest,we investigate and justify an approach by examining the ratios of adjacent eigenvalues of the sample covariance matrix?Theoretical properties,numerical examples,and a real data application demonstrate the merits of the IPOD approach in its convenience,performance,and interpretability.
