An application of kernel methods to variety identification based on SSR markers genetic fingerprinting

<p>Abstract</p> <p>Background</p> <p>In crop production systems, genetic markers are increasingly used to distinguish individuals within a larger population based on their genetic make-up. Supervised approaches cannot be applied directly to genotyping data due to the specific nature of those data which are neither continuous, nor nominal, nor ordinal but only partially ordered. Therefore, a strategy is needed to encode the polymorphism between samples such that known supervised approaches can be applied. Moreover, finding a minimal set of molecular markers that have optimal ability to discriminate, for example, between given groups of varieties, is important as the genotyping process can be costly in terms of laboratory consumables, labor, and time. This feature selection problem also needs special care due to the specific nature of the data used.</p> <p>Results</p> <p>An approach encoding SSR polymorphisms in a positive definite kernel is presented, which then allows the usage of any kernel supervised method. The polymorphism between the samples is encoded through the Nei-Li genetic distance, which is shown to define a positive definite kernel between the genotyped samples. Additionally, a greedy feature selection algorithm for selecting SSR marker kits is presented to build economical and efficient prediction models for discrimination. The algorithm is a filter method and outperforms other filter methods adapted to this setting. When combined with kernel linear discriminant analysis or kernel principal component analysis followed by linear discriminant analysis, the approach leads to very satisfactory prediction models.</p> <p>Conclusions</p> <p>The main advantage of the approach is to benefit from a flexible way to encode polymorphisms in a kernel and when combined with a feature selection algorithm resulting in a few specific markers, it leads to accurate and economical identification models based on SSR genotyping.</p

Non-linear and Sparse Discriminant Analysis with Data Compression

Large-sample data became prevalent as data acquisition became cheaper and easier. While a large sample size has theoretical advantages for many statistical methods, it presents computational challenges either in the form of a large number of features or a large number of training samples. We consider the two-group classification problem and adapt Linear Discriminant Analysis to the problems above. Linear Discriminant Analysis is a linear classifier and will under-fit when the true decision boundary is non-linear. To address non-linearity and sparse feature selection, we propose a kernel classifier based on the optimal scoring framework which trains a non-linear classifier. Unlike previous approaches, we provide theoretical guarantees on the expected risk consistency of the method. We also allow for feature selection by imposing structured sparsity using weighted kernels. We propose fully-automated methods for selection of all tuning parameters, and in particular adapt kernel shrinkage ideas for ridge parameter selection. Numerical studies demonstrate the superior classification performance of the proposed approach compared to existing nonparametric classifiers. We also propose automatic methods for ridge parameter selection and guassian kernel parameter selection. To address the computational challenges of a large sample size, we adapt compression to the classification setting. Sketching, or compression, is a well-studied approach to address sample reduction in regression settings, but considerably less is known about its performance in classification settings. Here we consider the computational issues due to large sample size within the discriminant analysis framework. We propose a new compression approach for reducing the number of training samples for linear and quadratic discriminant analysis, in contrast to existing compression methods which focus on reducing the number of features. We support our approach with a theoretical bound on the misclassification error rate compared to the Bayes classifier. Empirical studies confirm the significant computational gains of the proposed method and its superior predictive ability compared to random sub-sampling

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