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Approach I: Extending Conventional Outlier Detection

  • Method 1: Detect outliers in the full space, e.g., HilOut Algorithm
    • Find distance-based outliers, but use the ranks of distance instead of the absolute distance in outlier detection
    • For each object o, find its k-nearest neighbors: nn1(o), . . . , nnk(o)
    • The weight of object o:

\[ w(o)=\sum_{i=1}^{k}dist(o,nn_{i}(o)) \]

    • All objects are ranked in weight-descending order
    • Top-l objects in weight are output as outliers (l: user-specified parm)
    • Employ space-filling curves for approximation: scalable in both time and space w.r.t. data size and dimensionality
  • Method 2: Dimensionality reduction
    • Works only when in lower-dimensionality, normal instances can still be distinguished from outliers
    • PCA: Heuristically, the principal components with low variance are preferred because, on such dimensions, normal objects are likely close to each other and outliers often deviate from the majority

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