[TBD]Role of discriminant function in current data science

Introduction

Laymen explanation

A doctor could perform a discriminant analysis to identify patients at high or low risk for stroke.

The analysis might classify patients into high- or low-risk groups, based on personal attributes (e.g., chololesterol level, body mass) and/or lifestyle behaviors (e.g., minutes of exercise per week, packs of cigarettes per day). If you are interested to know its relevance in current data science, then this document helps.

Technical explanation

Discriminant analysis is statistical technique used to classify observations into non-overlapping groups, based on scores on one or more quantitative predictor variables.

Discriminant function analysis (DFA) is a statistical procedure that classifies unknown individuals and the probability of their classification into a certain group (such as sex or ancestry group). Discriminant function analysis makes the assumption that the sample is normally distributed for the trait. The posterior probability and typicality probability are applied to calculate the classification probabilities (Albanese et al., 2008).

Jargons explained

The posterior probability is the probability that an unknown case belongs to a certain group based on relative Mahalanobis’ distances measuring the distance to the center or centroid of each group. The typicality probability is how likely the unknown case belongs to a group based on variability within all groups.

Real life challenges with DFA

Discriminant Function Analysis (DFA) has been used extensively in the past to derive optimal combinations of variables to differentiate groups because of its computational simplicity. However, DFA assumes that the predictors (i.e., tests included in the model) are each normally distributed and the set of predictors has a multivariate normal distribution along with homogeneous variance-covariance matrices (Harrell, 2001). These are strong statistical assumptions that are rarely met in clinical research and with performance validity measures in particular.

Fisher's LDA

It is LDA with difference that it does not make some of the assumptions of LDA such as normally distributed classes or equal class covariances.

Non-linear discriminant function??

If Co-variance matrix is class dependent, discriminant function is non-linear (ellipsoid for example)

DFA role in current data science

Neural networks also does the classification work and so, DFA is an alternate technique in current data science. This paper compares both approaches for a problem domain. This is another such paper. ANN techniques outperformed for complex problem domain of non-linear in nature(verify).

Reference

https://www.sciencedirect.com/topics/neuroscience/discriminant-function-analysis

https://stattrek.com/multiple-regression/discriminant-analysis.aspx

https://stattrek.com/multiple-regression/discriminant-analysis.aspx

https://youtu.be/_2j0cwmHKBg

http://pen.ius.edu.ba/index.php/pen/article/download/1720/702

https://www.tandfonline.com/doi/abs/10.1057/jors.1993.6

https://youtu.be/BdxbLWNtzr0?t=1513

https://en.wikipedia.org/wiki/Linear_discriminant_analysis#Fisher's_linear_discriminant