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Mining Contextual Outliers I: Transform into Conventional Outlier Detection

  • If the contexts can be clearly identified, transform it to conventional outlier detection
    • Identify the context of the object using the contextual attributes
    • Calculate the outlier score for the object in the context using a conventional outlier detection method
  • Ex. Detect outlier customers in the context of customer groups
    • Contextual attributes: age group, postal code
    • Behavioral attributes: # of trans/yr, annual total trans. amount
  • Steps: (1) locate c’s context, (2) compare c with the other customers in the same group, and (3) use a conventional outlier detection method
  • If the context contains very few customers, generalize contexts
    • Ex. Learn a mixture model U on the contextual attributes, and another mixture model V of the data on the behavior attributes
    • Learn a mapping p(Vi|Uj): the probability that a data object o belonging to cluster Uj on the contextual attributes is generated by cluster Vi on the behavior attributes
    • Outlier score:

\[ S(o)=\sum_{U_{j}}p(o\epsilon U_{j})\sum_{V_{i}}p(o\epsilon V_{i})p(V_{i}|U_{j}) \]


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