Robust Discriminant Analysis
Also known as: robust LDA, high-breakdown discriminant analysis, MCD-based discriminant analysis, Robust Diskriminant Analizi
Robust Discriminant Analysis is a classification method that separates groups with a linear discriminant function while resisting the influence of outliers. It replaces the classical mean and covariance with a high-breakdown estimator such as the Minimum Covariance Determinant (MCD), an approach developed by Hawkins & McLachlan (1997) and Croux & Dehon (2001).
Key highlights
- Resistant to outliers and contamination: a small fraction of extreme points cannot dominate the group centres or the boundary.
- High breakdown point through the MCD estimator, so estimates stay stable even when many observations are atypical.
- Keeps the interpretable linear discriminant structure while replacing only the location and scatter estimates.
Intuition
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How it works
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When to use it
Use robust discriminant analysis to classify observations into known groups from several continuous predictors when the data may contain outliers or contamination that would distort classical LDA. It needs a reasonable sample (about 50 or more overall, with enough observations in each group) so the MCD covariance can be estimated reliably, and it assumes the predictors are multivariate continuous. It is most valuable when outliers, heavy tails, or measurement errors are a realistic concern; for clean, well-behaved data classical discriminant analysis is usually sufficient.
Strengths & limitations
- Resistant to outliers and contamination: a small fraction of extreme points cannot dominate the group centres or the boundary.
- High breakdown point through the MCD estimator, so estimates stay stable even when many observations are atypical.
- Keeps the interpretable linear discriminant structure while replacing only the location and scatter estimates.
- Needs a larger sample than classical LDA so the robust covariance can be estimated, and is unreliable below about 30 observations.
- High-leverage points can still mislead the discriminant function and may call for a bounded-influence method instead.
- Computationally heavier than ordinary discriminant analysis because the MCD subset search is iterative.
Common pitfalls
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Applications
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Frequently asked
How does this differ from classical LDA?
It keeps the same linear discriminant rule but replaces the ordinary mean and covariance with high-breakdown robust estimates (such as the MCD). This makes the boundary resistant to outliers that would distort the classical estimates.
What is the Minimum Covariance Determinant (MCD)?
MCD looks for the subset of observations whose covariance matrix has the smallest determinant and uses that clean core to estimate the centre and spread. Because outliers are left out of the core, the resulting estimates have a high breakdown point.
How much data do I need?
Plan for at least about 50 observations overall, with enough cases in each group, so the robust covariance can be estimated. Below roughly 30 observations the MCD estimate becomes unreliable and logistic regression is a safer choice.
What about high-leverage points?
Even a robust discriminant function can be misled by high-leverage points. When they are present, consider a bounded-influence approach such as robust logistic regression.
Sources
- 1.Hawkins, D. M. & McLachlan, G. J. (1997). High Breakdown Linear Discriminant Analysis. Journal of the American Statistical Association, 92(437), 136-143.
- 2.Croux, C. & Dehon, C. (2001). Robust Linear Discriminant Analysis Using S-Estimators. Canadian Journal of Statistics, 29(3), 473-493.
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Cite this page
ScholarGate. (2026, June 1). Robust Discriminant Analysis. ScholarGate. https://scholargate.app/statistics/robust-discriminant-analysis