Module 5: Disk-based Index Structures
Lecture 24:
Analysis of High Dimensional Data
Analysis of high dimensional data
Assumptions
Uniformly distributed data
In a
-dimensional hypercube
Distance is Euclidean
Dimensions are independent
Most data lies near the boundary
When within
of outer boundary, volume of inside hypercube is
Example: For
, inside volume is
Even for small size of answer set, the range on each dimension should be large
For selectivity of
points, query range on each dimension should be
Example: For
, query range is
-dimensional hypercube 
of outer boundary, volume of inside hypercube is 
, inside volume is 
points, query range on each dimension should be 
, query range is 