Robust Multivariate Outlier Detection (MCD)

Robust multivariate outlier detection with the minimum covariance determinant estimates location and scatter from the most concentrated subset of cases and flags cases with large robust Mahalanobis distances.

MCD 기반 강건 다변량 이상값 탐지는 가장 밀집한 사례 부분집합으로 중심과 산포를 추정한 뒤 강건 마할라노비스 거리가 큰 사례를 표시합니다.

How can I find multivariate outliers when the outliers themselves distort the ordinary Mahalanobis distance?

이상값 때문에 일반 마할라노비스 거리가 왜곡될 때 다변량 이상값을 어떻게 찾나요?

The minimum covariance determinant estimator finds the subset of cases whose covariance matrix has the smallest determinant and uses it, after reweighting, as a robust estimate of center and scatter. Robust Mahalanobis distances are then compared with a chi-square quantile such as 0.975, which avoids the masking that hides clustered outliers in classical distances.

When to use Robust Multivariate Outlier Detection (MCD)

• You need to screen several continuous variables for multivariate outliers before modeling.
• Several outliers may be present and could mask one another.
• The bulk of the data is roughly elliptical.

When to use something else

• You only check one variable at a time; use a univariate outlier rule such as the IQR or Grubbs' test instead.
• The data form several distinct clusters; use a density-based method such as DBSCAN instead.

Assumptions and requirements

• The majority of cases come from an approximately elliptical distribution.
• Fewer than half of the cases are contaminated.
• Many more cases than variables.

What the analysis reports

• Robust Mahalanobis distances
• Chi-square cutoff and number of flagged cases
• Comparison with classical Mahalanobis distances
• Robust location estimate

How to report it

Robust Mahalanobis distances based on the minimum covariance determinant (N = [n], [p] variables) flagged [k] cases ([value]%) as multivariate outliers at the χ²([p]) 0.975 quantile.

Related methods

• Generalized ESD Outlier Test
• Isolation Forest Anomaly Detection
• DBSCAN Density Based Clustering

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