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.

Practical Uses of Belief Functions

Abstract: We present examples where the use of belief functions provided sound and elegant solutions to real life problems. These are essentially characterized by ?missing' information. The examples deal with 1) discriminant analysis using a learning set where classes are only partially known; 2) an information retrieval systems handling inter-documents relationships; 3) the combination of data from sensors competent on partially overlapping frames; 4) the determination of the number of sources in a multi-sensor environment by studying the inter-sensors contradiction. The purpose of the paper is to report on such applications where the use of belief functions provides a convenient tool to handle ?messy' data problems.

Statistical Analysis and Modeling of Mass Spectrometry-Based Metabolomics Data

Abstract: Multivariate statistical techniques are used extensively in metabolomics studies, ranging from biomarker selection to model building and validation. Two model independent variable selection techniques, principal component analysis and two sample t-tests are discussed in this chapter, as well as classification and regression models and model related variable selection techniques, including partial least squares, logistic regression, support vector machine, and random forest. Model evaluation and validation methods, such as leave-one-out cross-validation, Monte Carlo cross-validation, and receiver operating characteristic analysis, are introduced with an emphasis to avoid over-fitting the data. The advantages and the limitations of the statistical techniques are also discussed in this chapter.

Identifying variables responsible for clustering in discriminant analysis of data from infrared microspectroscopy of a biological sample.

Abstract: In the biomedical field, infrared (IR) spectroscopic studies can involve the processing of data derived from many samples, divided into classes such as category of tissue (e.g., normal or cancerous) or patient identity. We require reliable methods to identify the class-specific information on which of the wavenumbers, representing various molecular groups, are responsible for observed class groupings. Employing a prostate tissue sample divided into three regions (transition zone, peripheral zone, and adjacent adenocarcinoma), and interrogated using synchrotron Fourier-transform IR microspectroscopy, we compared two statistical methods: (a) a new “cluster vector” version of principal component analysis (PCA) in which the dimensions of the dataset are reduced, followed by linear discriminant analysis (LDA) to reveal clusters, through each of which a vector is constructed that identifies the contributory wavenumbers; and (b) stepwise LDA, which exploits the fact that spectral peaks which identify certain chemical bonds extend over several wavenumbers, and which following classification via either one or two wavenumbers, checks whether the resulting predictions are stable across a range of nearby wavenumbers. Stepwise LDA is the simpler of the two methods; the cluster vector approach can indicate which of the different classes of spectra exhibit the significant differences in signal seen at the “prominent” wavenumbers identified. In situations where IR spectra are found to separate into classes, the excellent agreement between the two quite different methods points to what will prove to be a new and reliable approach to establishing which molecular groups are responsible for such separation.