Nonlinear Supervised Dimensionality Reduction via Smooth Regular Embeddings

The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing methods primarily focus on the embedding of the training data, and the generalization of the embedding to initially unseen test data is rather ignored. In this work, we build on recent theoretical results on the generalization performance of supervised manifold learning algorithms. Motivated by these performance bounds, we propose a supervised manifold learning method that computes a nonlinear embedding while constructing a smooth and regular interpolation function that extends the embedding to the whole data space in order to achieve satisfactory generalization. The embedding and the interpolator are jointly learnt such that the Lipschitz regularity of the interpolator is imposed while ensuring the separation between different classes. Experimental results on several image data sets show that the proposed method outperforms traditional classifiers and the supervised dimensionality reduction algorithms in comparison in terms of classification accuracy in most settings

Rectified Gaussian Scale Mixtures and the Sparse Non-Negative Least Squares Problem

In this paper, we develop a Bayesian evidence maximization framework to solve the sparse non-negative least squares (S-NNLS) problem. We introduce a family of probability densities referred to as the Rectified Gaussian Scale Mixture (R- GSM) to model the sparsity enforcing prior distribution for the solution. The R-GSM prior encompasses a variety of heavy-tailed densities such as the rectified Laplacian and rectified Student- t distributions with a proper choice of the mixing density. We utilize the hierarchical representation induced by the R-GSM prior and develop an evidence maximization framework based on the Expectation-Maximization (EM) algorithm. Using the EM based method, we estimate the hyper-parameters and obtain a point estimate for the solution. We refer to the proposed method as rectified sparse Bayesian learning (R-SBL). We provide four R- SBL variants that offer a range of options for computational complexity and the quality of the E-step computation. These methods include the Markov chain Monte Carlo EM, linear minimum mean-square-error estimation, approximate message passing and a diagonal approximation. Using numerical experiments, we show that the proposed R-SBL method outperforms existing S-NNLS solvers in terms of both signal and support recovery performance, and is also very robust against the structure of the design matrix.Comment: Under Review by IEEE Transactions on Signal Processin

Robust Face Representation and Recognition Under Low Resolution and Difficult Lighting Conditions

This dissertation focuses on different aspects of face image analysis for accurate face recognition under low resolution and poor lighting conditions. A novel resolution enhancement technique is proposed for enhancing a low resolution face image into a high resolution image for better visualization and improved feature extraction, especially in a video surveillance environment. This method performs kernel regression and component feature learning in local neighborhood of the face images. It uses directional Fourier phase feature component to adaptively lean the regression kernel based on local covariance to estimate the high resolution image. For each patch in the neighborhood, four directional variances are estimated to adapt the interpolated pixels. A Modified Local Binary Pattern (MLBP) methodology for feature extraction is proposed to obtain robust face recognition under varying lighting conditions. Original LBP operator compares pixels in a local neighborhood with the center pixel and converts the resultant binary string to 8-bit integer value. So, it is less effective under difficult lighting conditions where variation between pixels is negligible. The proposed MLBP uses a two stage encoding procedure which is more robust in detecting this variation in a local patch. A novel dimensionality reduction technique called Marginality Preserving Embedding (MPE) is also proposed for enhancing the face recognition accuracy. Unlike Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA), which project data in a global sense, MPE seeks for a local structure in the manifold. This is similar to other subspace learning techniques but the difference with other manifold learning is that MPE preserves marginality in local reconstruction. Hence it provides better representation in low dimensional space and achieves lower error rates in face recognition. Two new concepts for robust face recognition are also presented in this dissertation. In the first approach, a neural network is used for training the system where input vectors are created by measuring distance from each input to its class mean. In the second approach, half-face symmetry is used, realizing the fact that the face images may contain various expressions such as open/close eye, open/close mouth etc., and classify the top half and bottom half separately and finally fuse the two results. By performing experiments on several standard face datasets, improved results were observed in all the new proposed methodologies. Research is progressing in developing a unified approach for the extraction of features suitable for accurate face recognition in a long range video sequence in complex environments

Infrared face recognition: a comprehensive review of methodologies and databases

Automatic face recognition is an area with immense practical potential which includes a wide range of commercial and law enforcement applications. Hence it is unsurprising that it continues to be one of the most active research areas of computer vision. Even after over three decades of intense research, the state-of-the-art in face recognition continues to improve, benefitting from advances in a range of different research fields such as image processing, pattern recognition, computer graphics, and physiology. Systems based on visible spectrum images, the most researched face recognition modality, have reached a significant level of maturity with some practical success. However, they continue to face challenges in the presence of illumination, pose and expression changes, as well as facial disguises, all of which can significantly decrease recognition accuracy. Amongst various approaches which have been proposed in an attempt to overcome these limitations, the use of infrared (IR) imaging has emerged as a particularly promising research direction. This paper presents a comprehensive and timely review of the literature on this subject. Our key contributions are: (i) a summary of the inherent properties of infrared imaging which makes this modality promising in the context of face recognition, (ii) a systematic review of the most influential approaches, with a focus on emerging common trends as well as key differences between alternative methodologies, (iii) a description of the main databases of infrared facial images available to the researcher, and lastly (iv) a discussion of the most promising avenues for future research.Comment: Pattern Recognition, 2014. arXiv admin note: substantial text overlap with arXiv:1306.160