Outlier Detection with Chi-Squared TestΒΆ

Causal Step

This step detects outliers in multivariate data by applying the modified version of Chi-Squared Test. The basic formula is as follows:

\[{\chi^2 = \sum_{i=1}^{N} \frac{(o_{i} - E_i)^2}{E_i}}\quad\text{,}\]

where \(o\) is the object to be tested and \(o_i\) is the value of \(o\) on the \(i\)th dimension. \(E_i\) is the mean value on the \(i\)th dimension among all objects. The object may be identified as an outlier if the Chi-value is larger than a threshold value.

Input Parameters

  1. Multivariate data including outliers

Output Parameters

  1. Original data with outliers marked




Chi-Squared Test


  • J. Han, M. Kamber and J. Pei, Data Mining - Concepts and Techniques, 3rd ed., Amsterdam: Morgan Kaufmann Publishers, 2012.