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

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

Speaker verification using sequence discriminant support vector machines

This paper presents a text-independent speaker verification system using support vector machines (SVMs) with score-space kernels. Score-space kernels generalize Fisher kernels and are based on underlying generative models such as Gaussian mixture models (GMMs). This approach provides direct discrimination between whole sequences, in contrast with the frame-level approaches at the heart of most current systems. The resultant SVMs have a very high dimensionality since it is related to the number of parameters in the underlying generative model. To address problems that arise in the resultant optimization we introduce a technique called spherical normalization that preconditions the Hessian matrix. We have performed speaker verification experiments using the PolyVar database. The SVM system presented here reduces the relative error rates by 34% compared to a GMM likelihood ratio system

Kernel discriminant analysis and clustering with parsimonious Gaussian process models

This work presents a family of parsimonious Gaussian process models which allow to build, from a finite sample, a model-based classifier in an infinite dimensional space. The proposed parsimonious models are obtained by constraining the eigen-decomposition of the Gaussian processes modeling each class. This allows in particular to use non-linear mapping functions which project the observations into infinite dimensional spaces. It is also demonstrated that the building of the classifier can be directly done from the observation space through a kernel function. The proposed classification method is thus able to classify data of various types such as categorical data, functional data or networks. Furthermore, it is possible to classify mixed data by combining different kernels. The methodology is as well extended to the unsupervised classification case. Experimental results on various data sets demonstrate the effectiveness of the proposed method

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

Analyze of Classification Accaptence Subsidy Food Using Kernel Discriminant

Subsidy food is government program for social protection to poor households. The aims of this program are to effort households from starve and to decrease poverty. Less precisely target of this program has negative impact. So that to successful program, it’s important to know accuracy classification of admission subsidy food. The variables classification are number of household members, number of household member in work, average expenditure capita, weighted household, and floor area. Discriminant analysis is a multivariate statistical technique which can be used to classify the new observation into a specific group. Kernel discriminant analysis is a non-parametric method which is flexible because it does not have to concern about assumption from certain distribution and equal variance matrices as in parametric discriminant analysis. The classification using the kernel discriminant analysis with the normal kernel function with optimum bandwidth 0.6 gives accurate classification 75.35%

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