Question
Given the following distance matrix, compute LOF (Local Outlier Factor) of all points, based on 2-distance neighborhood consideration (k=2). Show intermediate steps.
Solution
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k = 2 => Second nearest neighbor
Step-1: Find the 
is the distance between point O and its
nearest neighbor.
Step-2: Calculate 
is the set of all points within the
distance neighborhood of O.
Step-3: Calculate 
is the Local Reachability Density of O.
means the number of objects in
.
is the reachability distance from O to O’.
Step-4: Calculate 
LOF is the Local Outlier Factor.
Step-5: Find the Outlier
Sort the LOF in descending order:
The top 1 outlier is P1.