Current Slide

• 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