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.

A critical comparison of neural networks and discriminant analysis in lithofacies, porosity and permeability predictions

Abstract: The application of a genetic reservoir characterisation concept to the calculation of petrophysical properties requires the prediction of lithofacies followed by the assignment of petrophysical properties according to the specific lithofacies predicted. Common classification methods which fulfil this task include discriminant analysis and back-propagation neural networks. While discriminant analysis is a well-established statistical classification method back-propagation neural networks are relatively new and their performance in predicting lithofacies porosity and permeability when compared to discriminant analysis has not been widely studied. This work compares the performance of these two methods in prediction of reservoir properties by considering log and core data from a shaly glauconitic reservoir.

Sparse tensor discriminant analysis

Abstract: The classical linear discriminant analysis has undergone great development and has recently been extended to different cases. In this paper, a novel discriminant subspace learning method called sparse tensor discriminant analysis (STDA) is proposed, which further extends the recently presented multilinear discriminant analysis to a sparse case. Through introducing the L1 and L2 norms into the objective function of STDA, we can obtain multiple interrelated sparse discriminant subspaces for feature extraction. As there are no closed-form solutions, k-mode optimization technique and the L1 norm sparse regression are combined to iteratively learn the optimal sparse discriminant subspace along different modes of the tensors. Moreover, each non-zero element in each subspace is selected from the most important variables/factors, and thus STDA has the potential to perform better than other discriminant subspace methods. Extensive experiments on face databases (Yale, FERET, and CMU PIE face databases) and the Weizmann action database show that the proposed STDA algorithm demonstrates the most competitive performance against the compared tensor-based methods, particularly in small sample sizes.

Identification of human gene structure using linear discriminant functions and dynamic programming.

Abstract: Development of advanced technique to identify gene structure is one of the main challenges of the Human Genome Project Discriminant analysis was applied to the construction of recognition functions for various components of gene structure Linear discriminant functions for splice sites, 5’coding, internal exon, and 3’-coding region recognition have been developed A gene structure prediction system FGENE has been developed based on the exon recognition functions We compute a graph of mutual compatibility of different exons and present a gene structure models as paths of this directed acyclic graph For an optimal model selection we apply a variant of dynamic programming algorithm to search for the path in the graph with the maximal value of the corresponding discriminant functions Prediction by FGENE for 185 complete human gene sequences has 81% exact exon recognition accuracy and 91% accuracy at the level of individual exon nucleotides with the correlation coefficient (C) equals 090 Testing FGENE on 35 genes not used in the development of discriminant functions shows 71% accuracy of exact exon prediction and 89% at the nucleotide level (C=086) FGENE compares very favorably with the other programs currently used to predict proteincoding regions Analysis of uncharacterized human sequences based on our methods for splice site (HSPL, RNASPL),

Classification Trees as an Alternative to Linear Discriminant Analysis

Abstract: Linear discriminant analysis (LDA) is frequently used for classification/prediction problems in physical anthropology, but it is unusual to find examples where researchers consider the statistical limitations and assumptions required for this technique. In these instances, it is difficult to know whether the predictions are reliable. This paper considers a nonparametric alternative to predictive LDA: binary, recursive (or classification) trees. This approach has the advantage that data transformation is unnecessary, cases with missing predictor variables do not require special treatment, prediction success is not dependent on data meeting normality conditions or covariance homogeneity, and variable selection is intrinsic to the methodology. Here I compare the efficacy of classification trees with LDA, using typical morphometric data. With data from modern hominoids, the results show that both techniques perform nearly equally. With complete data sets, LDA may be a better choice, as is shown in this example, but with missing observations, classification trees perform outstandingly well, whereas commercial discriminant analysis programs do not predict classifications for cases with incompletely measured predictor variables and generally are not designed to address the problem of missing data. Testing of data prior to analysis is necessary, and classification trees are recommended either as a replacement for LDA or as a supplement whenever data do not meet relevant assumptions. It is highly recommended as an alternative to LDA whenever the data set contains important cases with missing predictor variables.