Discriminant Analysis

Abstract

Discriminant analysis (DA) is a pattern recognition technique that has been widely applied in medical studies. It allows multivariate observations ("patterns" or points in multidimensional space) to be allocated to previously defined groups (diagnostic categories). The relationships between DA and other multivariate statistical techniques of interest in medical studies will be briefly discussed. The main emphasis is on linear discriminant functions (LDF). The theoretic assumptions underlying DA using LDFs will be presented, and the effect of violations to these assumptions will be reviewed in detail. Alternative methods will be presented when violations cause serious problems. It has been shown that the familiar LDF is fairly robust to departures from the assumptions. The application of the LDF in less than ideal situations therefore often does not cause much harm (if the violations are not too grotesque). Another set of problems reviewed is how to estimate the misallocation probabilities when using discriminant functions. The selection of the "best" subset of variables out of the complete set will be discussed. Practical guide lines are given based on the theoretic studies reviewed. When possible, available computer programs for various problems of DA will be indicated. The review does not aim at covering all medical studies where DA has been applied, since emphasis is on the practical conclusions of the theory of DA.

Proton magnetic resonance spectroscopy of cerebrospinal fluid in neurodegenerative disease: Indication of glial energy impairment in Huntington chorea, but not Parkinson disease

“…Analysis of the subgroups of Parkinson patients did not indicate any differences in any parameter (not shown), and the patients were subsequently considered as a combined group. The data for the various metabolites and age were also tested to find out how many cases would be correctly classified into their respective groups by discriminant analysis (Solberg, 1978).…”

A molecular risk score based on 4 functional pathways for advanced classical Hodgkin lymphoma

“…Univariate regression analysis was performed with treatment response (F vs U) as the dependent variable to identify genes significantly associated (P Ͻ .05) with outcome. In addition, final gene selection analysis was performed by cross-validation with the use of 3 prediction algorithms (http://tnasas.bioinfo.cnio.es/): diagonal linear discriminant analysis, 19 support vector machines, 20 and K-nearest neighbor. 21 Cross validation was used to test the classification ability of the initial set of significant genes to choose the strongest predictor genes, which were classified into functional groups on the basis of their known biologic relationship and their coregulated expression as estimated by the Pearson correlation coefficient.…”

Response diversity of Arabidopsis thaliana ecotypes in elevated [CO2] in the field

“…Multivariate statistical analysis was performed using PCA (Principal Component Analysis), and LDA (Linear Discriminant Analysis) (Sharma 1996;Jobson 1992;Solberg 1978;Catchpole et al 2005). PCA was used as a way to explore the key variables in metabolite groups and lines.…”