Results 1 
5 of
5
Normalization of Face Illumination Based on Largeand SmallScale Features
, 2009
"... Abstract—A face image can be represented by a combination of largeand smallscale features. It is wellknown that the variations of illumination mainly affect the largescalefeatures (lowfrequency components), and not so much the smallscale features. Therefore, in relevant existing methods only t ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Abstract—A face image can be represented by a combination of largeand smallscale features. It is wellknown that the variations of illumination mainly affect the largescalefeatures (lowfrequency components), and not so much the smallscale features. Therefore, in relevant existing methods only the smallscale features are extracted as illuminationinvariant features for face recognition, while the largescale intrinsic features are always ignored. In this paper, we argue that both largeand smallscale features of a face image are important for face restoration and recognition. Moreover, we suggest that illumination normalization should be performed mainly on the largescale features of a face image rather than on the original face image. A novel method of normalizing both the Smalland Largescale (S&L) features of a face image is proposed. In thismethod, a single face image isfirstdecomposed into largeand smallscale features. After that, illumination normalization is mainly performed on the largescale features, and only a minor correction is made on the smallscale features. Finally, a normalized face image is generated by combining the processed largeand smallscale features. In addition, an optional visual compensation step is suggested for improving the visual quality of the normalized image. Experiments on CMUPIE, Extended Yale B, and FRGC 2.0 face databases show that by using the proposed method significantly better recognition performance and visual results can be obtained as compared to related stateoftheart methods. Index Terms—Face recognition, illumination normalization, visual compensation. I.
TreeStructured Feature Extraction Using Mutual Information
"... Abstract — One of the most informative measures for feature extraction (FE) is mutual information (MI). In terms of MI, the optimal FE creates new features that jointly have the largest dependency on the target class. However, obtaining an accurate estimate of a highdimensional MI as well as optimi ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract — One of the most informative measures for feature extraction (FE) is mutual information (MI). In terms of MI, the optimal FE creates new features that jointly have the largest dependency on the target class. However, obtaining an accurate estimate of a highdimensional MI as well as optimizing with respect to it is not always easy, especially when only small training sets are available. In this paper, we propose an efficient treebased method for FE in which at each step a new feature is created by selecting and linearly combining two features such that the MI between the new feature and the class is maximized. Both the selection of the features to be combined and the estimation of the coefficients of the linear transform rely on estimating 2D MIs. The estimation of the latter is computationally very efficient and robust. The effectiveness of our method is evaluated on several realworld data sets. The results show that the classification accuracy obtained by the proposed method is higher than that achieved by other FE methods. Index Terms — Classification, dimensionality reduction, feature extraction, mutual information.
Preimage Problem in KernelBased Machine Learning  An intimate connection with the dimensionalityreduction problem
, 2011
"... Kernel machines have gained considerable popularity during the last 15 years, making a breakthrough in nonlinear signal processing and machine learning, thanks to extraordinary advances. This increased interest is undoubtedly driven by the practical goal of being able to easily develop efficient no ..."
Abstract
 Add to MetaCart
(Show Context)
Kernel machines have gained considerable popularity during the last 15 years, making a breakthrough in nonlinear signal processing and machine learning, thanks to extraordinary advances. This increased interest is undoubtedly driven by the practical goal of being able to easily develop efficient nonlinear algorithms. The key principle behind this, known as the kernel trick, exploits the fact that a great number of dataprocessing techniques do not explicitly depend on the data itself but rather on a similarity measure © DIGITAL STOCK & LUSPHIX between them, i.e., an inner product. To provide a nonlinear extension of these techniques, one can apply a nonlinear transformation to the data, mapping them onto some feature space. According to the kernel trick, this can be achieved by simply replacing the inner product with a reproducing kernel (i.e., positive semidefinite symmetric function), the latter corresponds to an inner product in the feature space. One consequence is that the resulting nonlinear algorithms show significant performance improvements over their linear counterparts with essentially the same computational complexity. While the nonlinear mapping from the input space to the feature space is central in kernel methods, the reverse mapping from the feature space back to the input space is also of primary interest. This is the case in many applications, including kernel principal component analysis (PCA) for signal and image denoising. Unfortunately, it turns out that the reverse mapping generally does not exist and only a few elements in the feature space have a valid preimage in the input space. The preimage problem consists of finding an approximate solution by identifying data in the input space based on their corresponding features in the highdimensional feature space. It is essentially a dimensionalityreduction problem, and both have been intimately connected in their historical evolution, as studied in this article.
Summary (English)
"... Kernel methods refer to a family of widely used nonlinear algorithms for machine learning tasks like classification, regression, and feature extraction. By exploiting the socalled kernel trick straightforward extensions of classical linear algorithms are enabled as long as the data only appear as ..."
Abstract
 Add to MetaCart
(Show Context)
Kernel methods refer to a family of widely used nonlinear algorithms for machine learning tasks like classification, regression, and feature extraction. By exploiting the socalled kernel trick straightforward extensions of classical linear algorithms are enabled as long as the data only appear as innerproducts in the model formulation. This dissertation presents research on improving the performance of standard kernel methods like kernel Principal Component Analysis and the Support Vector Machine. Moreover, the goal of the thesis has been twofold. The first part focuses on the use of kernel Principal Component Analysis for nonlinear denoising. In this context stable solution of the inverse and inherently illposed preimage problem constitutes the main challenge. It is proposed to stabilize the estimation by augmenting the cost function with either an `1or `2norm penalty, and solution schemes are derived for both approaches. The methods are experimentally validated on several biomedical data sets. Furthermore, frameworks for exploiting label information for improved denoising in the
EXPLOITING DATADEPENDENT STRUCTURE FOR IMPROVING SENSOR ACQUISITION AND INTEGRATION
, 2014
"... This thesis deals with two approaches to building efficient representations of data. The first is a study of compressive sensing and improved data acquisition. We outline the development of the theory, and proceed into its uses in matrix completion problems via convex optimization. The aim of this ..."
Abstract
 Add to MetaCart
(Show Context)
This thesis deals with two approaches to building efficient representations of data. The first is a study of compressive sensing and improved data acquisition. We outline the development of the theory, and proceed into its uses in matrix completion problems via convex optimization. The aim of this research is to prove that a general class of measurement operators, bounded norm Parseval frames, satisfy the necessary conditions for random subsampling and reconstruction. We then demonstrate an example of this theory in solving 2dimensional Fredholm integrals with partial measurements. This has large ramifications in improved acquisition of nuclear magnetic resonance spectra, for which we give several examples. The second part of this thesis studies the Laplacian Eigenmaps (LE) algorithm and its uses in data fusion. In particular, we build a natural approximate inversion algorithm for LE embeddings using L1 regularization and MDS embedding techniques. We show how this inversion, combined with feature space rotation, leads to a novel form of data reconstruction and inpainting using a priori information. We demonstrate this method on hyperspectral imagery and LIDAR. We also aim to understand and characterize the embeddings the LE algorithm gives. To this end, we characterize the order in which eigenvectors of a disjoint graph emerge and the support of those eigenvectors. We then extend this characterization to weakly connected graphs with clusters of differing sizes, utilizing the theory of invariant subspace perturbations and proving some novel results.