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.

Prediction error estimation: a comparison of resampling methods

Abstract: Motivation: In genomic studies, thousands of features are collected on relatively few samples. One of the goals of these studies is to build classifiers to predict the outcome of future observations. There are three inherent steps to this process: feature selection, model selection and prediction assessment. With a focus on prediction assessment, we compare several methods for estimating the 'true' prediction error of a prediction model in the presence of feature selection. Results: For small studies where features are selected from thousands of candidates, the resubstitution and simple split-sample estimates are seriously biased. In these small samples, leave-one-out cross-validation (LOOCV), 10-fold cross-validation (CV) and the .632+ bootstrap have the smallest bias for diagonal discriminant analysis, nearest neighbor and classification trees. LOOCV and 10-fold CV have the smallest bias for linear discriminant analysis. Additionally, LOOCV, 5- and 10-fold CV, and the .632+ bootstrap have the lowest mean square error. The .632+ bootstrap is quite biased in small sample sizes with strong signal-to-noise ratios. Differences in performance among resampling methods are reduced as the number of specimens available increase. Contact: annette.molinaro@yale.edu Supplementary Information: A complete compilation of results and R code for simulations and analyses are available in Molinaro et al. (2005) (http://linus.nci.nih.gov/brb/TechReport.htm).

Automatic classification of single facial images

Abstract: We propose a method for automatically classifying facial images based on labeled elastic graph matching, a 2D Gabor wavelet representation, and linear discriminant analysis. Results of tests with three image sets are presented for the classification of sex, "race", and expression. A visual interpretation of the discriminant vectors is provided.

Local Gabor binary pattern histogram sequence (LGBPHS): a novel non-statistical model for face representation and recognition

Abstract: For years, researchers in face recognition area have been representing and recognizing faces based on subspace discriminant analysis or statistical learning. Nevertheless, these approaches are always suffering from the generalizability problem. This paper proposes a novel non-statistics based face representation approach, local Gabor binary pattern histogram sequence (LGBPHS), in which training procedure is unnecessary to construct the face model, so that the generalizability problem is naturally avoided. In this approach, a face image is modeled as a "histogram sequence" by concatenating the histograms of all the local regions of all the local Gabor magnitude binary pattern maps. For recognition, histogram intersection is used to measure the similarity of different LGBPHSs and the nearest neighborhood is exploited for final classification. Additionally, we have further proposed to assign different weights for each histogram piece when measuring two LGBPHSes. Our experimental results on AR and FERET face database show the validity of the proposed approach especially for partially occluded face images, and more impressively, we have achieved the best result on FERET face database.

Classifying facial actions

Abstract: The facial action coding system (FAGS) is an objective method for quantifying facial movement in terms of component actions. This paper explores and compares techniques for automatically recognizing facial actions in sequences of images. These techniques include: analysis of facial motion through estimation of optical flow; holistic spatial analysis, such as principal component analysis, independent component analysis, local feature analysis, and linear discriminant analysis; and methods based on the outputs of local filters, such as Gabor wavelet representations and local principal components. Performance of these systems is compared to naive and expert human subjects. Best performances were obtained using the Gabor wavelet representation and the independent component representation, both of which achieved 96 percent accuracy for classifying 12 facial actions of the upper and lower face. The results provide converging evidence for the importance of using local filters, high spatial frequencies, and statistical independence for classifying facial actions.

Applied Multivariate Statistical Analysis

Abstract: I Descriptive Techniques: Comparison of Batches.- II Multivariate Random Variables: A Short Excursion into Matrix Algebra Moving to Higher Dimensions Multivariate Distributions Theory of the Multinormal Theory of Estimation Hypothesis Testing.- III Multivariate Techniques: Decomposition of Data Matrices by Factors Principal Components Analysis Factor Analysis Cluster Analysis Discriminant Analysis.- Correspondence Analysis.- Canonical Correlation Analysis.- Multidimensional Scaling.- Conjoint Measurement Analysis.- Application in Finance.- Computationally Intensive Techniques.- A: Symbols and Notations.- B: Data.- Bibliography.- Index.