## 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. *