Linear discriminant analysis

About: Linear discriminant analysis is a research topic. Over the lifetime, 18361 publications have been published within this topic receiving 603195 citations. The topic is also known as: Linear discriminant analysis & LDA.

Ensemble-based discriminant learning with boosting for face recognition

Abstract: In this paper, we propose a novel ensemble-based approach to boost performance of traditional Linear Discriminant Analysis (LDA)-based methods used in face recognition. The ensemble-based approach is based on the recently emerged technique known as "boosting". However, it is generally believed that boosting-like learning rules are not suited to a strong and stable learner such as LDA. To break the limitation, a novel weakness analysis theory is developed here. The theory attempts to boost a strong learner by increasing the diversity between the classifiers created by the learner, at the expense of decreasing their margins, so as to achieve a tradeoff suggested by recent boosting studies for a low generalization error. In addition, a novel distribution accounting for the pairwise class discriminant information is introduced for effective interaction between the booster and the LDA-based learner. The integration of all these methodologies proposed here leads to the novel ensemble-based discriminant learning approach, capable of taking advantage of both the boosting and LDA techniques. Promising experimental results obtained on various difficult face recognition scenarios demonstrate the effectiveness of the proposed approach. We believe that this work is especially beneficial in extending the boosting framework to accommodate general (strong/weak) learners.

Analyzing microarray data using cluster analysis

Abstract: As pharmacogenetics researchers gather more detailed and complex data on gene polymorphisms that effect drug metabolizing enzymes, drug target receptors and drug transporters, they will need access to advanced statistical tools to mine that data. These tools include approaches from classical biostatistics, such as logistic regression or linear discriminant analysis, and supervised learning methods from computer science, such as support vector machines and artificial neural networks. In this review, we present an overview of another class of models, cluster analysis, which will likely be less familiar to pharmacogenetics researchers. Cluster analysis is used to analyze data that is not a priori known to contain any specific subgroups. The goal is to use the data itself to identify meaningful or informative subgroups. Specifically, we will focus on demonstrating the use of distance-based methods of hierarchical clustering to analyze gene expression data.

Neural networks and genetic algorithms for bankruptcy predictions

Abstract: We are focusing on three alternative techniques-linear discriminant analysis, logit analysis and genetic algorithms-that can be used to empirically select predictors for neural networks in failure prediction. The selected techniques all have different assumptions about the relationships between the independent variables. Linear discriminant analysis is based on linear combination of independent variables, logit analysis uses the logistical cumulative function and genetic algorithms is a global search procedure based on the mechanics of natural selection and natural genetics. In an empirical test all three selection methods chose different bankruptcy prediction variables. The best prediction results were achieved when using genetic algorithms.

Combining reconstructive and discriminative subspace methods for robust classification and regression by subsampling

Abstract: Linear subspace methods that provide sufficient reconstruction of the data, such as PCA, offer an efficient way of dealing with missing pixels, outliers, and occlusions that often appear in the visual data. Discriminative methods, such as LDA, which, on the other hand, are better suited for classification tasks, are highly sensitive to corrupted data. We present a theoretical framework for achieving the best of both types of methods: an approach that combines the discrimination power of discriminative methods with the reconstruction property of reconstructive methods which enables one to work on subsets of pixels in images to efficiently detect and reject the outliers. The proposed approach is therefore capable of robust classification with a high-breakdown point. We also show that subspace methods, such as CCA, which are used for solving regression tasks, can be treated in a similar manner. The theoretical results are demonstrated on several computer vision tasks showing that the proposed approach significantly outperforms the standard discriminative methods in the case of missing pixels and images containing occlusions and outliers.

On Discrimination Using Qualitative Variables

Abstract: The use of a linear function for discriminating with dichotomous variables is discussed and evaluated. Four such functions are considered: Fisher's linear discriminant function, two functions based upon a logistic model, and a function based upon the assumption of mutual independence of the variables. The evaluation of these functions as well as of a completely general multinomial procedure is carried out within the context of a 1st order interaction model by means of computer experiments. The product moment correlation of the optimal function with the linear function under evaluation plays a central role as a criterion for judging the relative merits of the procedures considered.