Practical Predictive Analytics

Multivariate outliers

The preceding example has just given an example of looking at outliers from a univariate, or single variable, perspective. However, outliers can also occur in a multivariate or combination form. In these cases, visualizing outliers in two dimensions can be a start, but as the dimensionality increases they can be more difficult to isolate. For multivariate outliers you can use distance and influence measures such as Cook's D or Mahalanobis distances to measure how far they are from a regression line. Principal component analysis can also help by reducing the dimensionality first, and then examining the higher order principal components that could include the outliers.