Current Slide

• Multivariate data: A data set involving two or more attributes or variables
• Transform the multivariate outlier detection task into a univariate outlier detection problem
• Method 1. Compute Mahalaobis distance
• Let ō be the mean vector for a multivariate data set. Mahalaobis distance for an object o to ō is
  \[ MDist(o, \bar{o}) = (o-\bar{o})^{T} S^{(-1)}(o-\bar{o}) \]
  where S is the covariance matrix
• Use the Grubb's test on this measure to detect outliers
• Method 2. Use χ2 –statistic:

\[ X^{2} = \sum_{i=1}^{n}\frac{(o_{i}-E_{i})^{2}}{E_{i}} \]

• where Ei is the mean of the i-dimension among all objects, and n is the dimensionality
• If χ2 –statistic is large, then object oi is an outlier