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

Sparse multinomial kernel discriminant analysis (sMKDA)

Dimensionality reduction via canonical variate analysis (CVA) is important for pattern recognition and has been extended variously to permit more flexibility, e.g. by "kernelizing" the formulation. This can lead to over-fitting, usually ameliorated by regularization. Here, a method for sparse, multinomial kernel discriminant analysis (sMKDA) is proposed, using a sparse basis to control complexity. It is based on the connection between CVA and least-squares, and uses forward selection via orthogonal least-squares to approximate a basis, generalizing a similar approach for binomial problems. Classification can be performed directly via minimum Mahalanobis distance in the canonical variates. sMKDA achieves state-of-the-art performance in terms of accuracy and sparseness on 11 benchmark datasets

Neural Class-Specific Regression for face verification

Face verification is a problem approached in the literature mainly using nonlinear class-specific subspace learning techniques. While it has been shown that kernel-based Class-Specific Discriminant Analysis is able to provide excellent performance in small- and medium-scale face verification problems, its application in today's large-scale problems is difficult due to its training space and computational requirements. In this paper, generalizing our previous work on kernel-based class-specific discriminant analysis, we show that class-specific subspace learning can be cast as a regression problem. This allows us to derive linear, (reduced) kernel and neural network-based class-specific discriminant analysis methods using efficient batch and/or iterative training schemes, suited for large-scale learning problems. We test the performance of these methods in two datasets describing medium- and large-scale face verification problems.Comment: 9 pages, 4 figure

A Simple Iterative Algorithm for Parsimonious Binary Kernel Fisher Discrimination

By applying recent results in optimization theory variously known as optimization transfer or majorize/minimize algorithms, an algorithm for binary, kernel, Fisher discriminant analysis is introduced that makes use of a non-smooth penalty on the coefficients to provide a parsimonious solution. The problem is converted into a smooth optimization that can be solved iteratively with no greater overhead than iteratively re-weighted least-squares. The result is simple, easily programmed and is shown to perform, in terms of both accuracy and parsimony, as well as or better than a number of leading machine learning algorithms on two well-studied and substantial benchmarks

Direct kernel biased discriminant analysis: a new content-based image retrieval relevance feedback algorithm

In recent years, a variety of relevance feedback (RF) schemes have been developed to improve the performance of content-based image retrieval (CBIR). Given user feedback information, the key to a RF scheme is how to select a subset of image features to construct a suitable dissimilarity measure. Among various RF schemes, biased discriminant analysis (BDA) based RF is one of the most promising. It is based on the observation that all positive samples are alike, while in general each negative sample is negative in its own way. However, to use BDA, the small sample size (SSS) problem is a big challenge, as users tend to give a small number of feedback samples. To explore solutions to this issue, this paper proposes a direct kernel BDA (DKBDA), which is less sensitive to SSS. An incremental DKBDA (IDKBDA) is also developed to speed up the analysis. Experimental results are reported on a real-world image collection to demonstrate that the proposed methods outperform the traditional kernel BDA (KBDA) and the support vector machine (SVM) based RF algorithms

Quadratic Projection Based Feature Extraction with Its Application to Biometric Recognition

This paper presents a novel quadratic projection based feature extraction framework, where a set of quadratic matrices is learned to distinguish each class from all other classes. We formulate quadratic matrix learning (QML) as a standard semidefinite programming (SDP) problem. However, the con- ventional interior-point SDP solvers do not scale well to the problem of QML for high-dimensional data. To solve the scalability of QML, we develop an efficient algorithm, termed DualQML, based on the Lagrange duality theory, to extract nonlinear features. To evaluate the feasibility and effectiveness of the proposed framework, we conduct extensive experiments on biometric recognition. Experimental results on three representative biometric recogni- tion tasks, including face, palmprint, and ear recognition, demonstrate the superiority of the DualQML-based feature extraction algorithm compared to the current state-of-the-art algorithm