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.

PCA versus LDA

Abstract: In the context of the appearance-based paradigm for object recognition, it is generally believed that algorithms based on LDA (linear discriminant analysis) are superior to those based on PCA (principal components analysis). In this communication, we show that this is not always the case. We present our case first by using intuitively plausible arguments and, then, by showing actual results on a face database. Our overall conclusion is that when the training data set is small, PCA can outperform LDA and, also, that PCA is less sensitive to different training data sets.

Classification and regression trees: a powerful yet simple technique for ecological data analysis

Abstract: Classification and regression trees are ideally suited for the analysis of com- plex ecological data. For such data, we require flexible and robust analytical methods, which can deal with nonlinear relationships, high-order interactions, and missing values. Despite such difficulties, the methods should be simple to understand and give easily interpretable results. Trees explain variation of a single response variable by repeatedly splitting the data into more homogeneous groups, using combinations of explanatory var- iables that may be categorical and/or numeric. Each group is characterized by a typical value of the response variable, the number of observations in the group, and the values of the explanatory variables that define it. The tree is represented graphically, and this aids exploration and understanding. Trees can be used for interactive exploration and for description and prediction of patterns and processes. Advantages of trees include: (1) the flexibility to handle a broad range of response types, including numeric, categorical, ratings, and survival data; (2) invariance to monotonic transformations of the explanatory variables; (3) ease and ro- bustness of construction; (4) ease of interpretation; and (5) the ability to handle missing values in both response and explanatory variables. Thus, trees complement or represent an alternative to many traditional statistical techniques, including multiple regression, analysis of variance, logistic regression, log-linear models, linear discriminant analysis, and survival models. We use classification and regression trees to analyze survey data from the Australian central Great Barrier Reef, comprising abundances of soft coral taxa (Cnidaria: Octocorallia) and physical and spatial environmental information. Regression tree analyses showed that dense aggregations, typically formed by three taxa, were restricted to distinct habitat types, each of which was defined by combinations of 3-4 environmental variables. The habitat definitions were consistent with known experimental findings on the nutrition of these taxa. When used separately, physical and spatial variables were similarly strong predictors of abundances and lost little in comparison with their joint use. The spatial variables are thus effective surrogates for the physical variables in this extensive reef complex, where infor- mation on the physical environment is often not available. Finally, we compare the use of regression trees and linear models for the analysis of these data and show how linear models fail to find patterns uncovered by the trees.

Discriminant Analysis and Statistical Pattern Recognition

Abstract: Provides a systematic account of the subject area, concentrating on the most recent advances in the field. While the focus is on practical considerations, both theoretical and practical issues are explored. Among the advances covered are: regularized discriminant analysis and bootstrap-based assessment of the performance of a sample-based discriminant rule and extensions of discriminant analysis motivated by problems in statistical image analysis. Includes over 1,200 references in the bibliography.

Fisher discriminant analysis with kernels

Abstract: A non-linear classification technique based on Fisher's discriminant is proposed. The main ingredient is the kernel trick which allows the efficient computation of Fisher discriminant in feature space. The linear classification in feature space corresponds to a (powerful) non-linear decision function in input space. Large scale simulations demonstrate the competitiveness of our approach.

Methods of multivariate analysis

Abstract: Introduction. Matrix Algebra. Characterizing and Displaying Multivariate Data. The Multivariate Normal Distribution. Tests on One or Two Mean Vectors. Multivariate Analysis of Variance. Tests on Covariance Matrices. Discriminant Analysis: Description of Group Separation. Classification Analysis: Allocation of Observations to Groups. Multivariate Regression. Canonical Correlation. Principal Component Analysis. Factor Analysis. Cluster Analysis. Graphical Procedures. Tables. Answers and Hints to Problems. Data Sets and SAS Files. References. Index.