Spatial Data Mining: Spatial outlier detection Spatial outlier A data point that is extreme relative to it neighbors Given A spatial graph G={V,E} A neighbor relationship (K neighbors) An attribute function f: V -> R An aggregation function f aggr : R k -> R Confidence level threshold  Find O = {v i | v i  V, v i is a spatial outlier} Objective Correctness: The attribute values of v i is extreme, compared with its neighbors Computational efficiency Constraints Attribute value is normally distributed Computation cost dominated by I/O op.

Spatial Data Mining: Spatial outlier detection Spatial Outlier Detection Test 1. Choice of Spatial Statistic S(x) = [f(x)–E y  N(x) (f(y))] Theorem: S(x) is normally distributed if f(x) is normally distributed 2. Test for Outlier Detection | (S(x) -  s ) /  s | >  Hypothesis I/O cost determined by clustering efficiency f(x)S(x) Spatial outlier and its neighbors

Spatial Data Mining: Spatial outlier detection Results 1. CCAM achieves higher clustering efficiency (CE) 2. CCAM has lower I/O cost 3. Higher CE leads to lower I/O cost 4. Page size improves CE for all methods Z-order CCAM I/O costCE value Cell-Tree