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Approach III: Modeling High-Dimensional Outliers

  • Ex. Angle-based outliers: Kriegel, Schubert, and Zimek [KSZ08]
  • For each point o, examine the angle ∆xoy for every pair of points x, y.
    • Point in the center (e.g., a), the angles formed differ widely
    • An outlier (e.g., c), angle variable is substantially smaller

  • Use the variance of angles for a point to determine outlier
  • Combine angles and distance to model outliers
    • Use the distance-weighted angle variance as the outlier score
    • Angle-based outlier factor (ABOF):

\[ ABOF(o)=VAR_{x,y\epsilon D,x\neq o,y\neq o}\frac{<\vec{ox},\vec{oy} > }{dist(o,x)^2dist(o,y)^2} \]

    • Efficient approximation computation method is developed
    • It can be generalized to handle arbitrary types of data
  • Develop new models for high-dimensional outliers directly
  • Avoid proximity measures and adopt new heuristics that do not deteriorate in high-dimensional data

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