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Density-Based Outlier Detection

Local outliers: Outliers comparing to their local neighborhoods, instead of the global data distribution
In Fig., o1 and o2 are local outliers to C1, o3 is a global outlier, but o4 is not an outlier. However, proximity-based clustering cannot find o1 and o2 are outlier (e.g., comparing with O4).

Intuition (density-based outlier detection): The density around an outlier object is significantly different from the density around its neighbors
Method: Use the relative density of an object against its neighbors as the indicator of the degree of the object being outliers
k-distance of an object o, distk(o): distance between o and its k-th NN
k-distance neighborhood of o, Nk(o) = {o’| o’ in D, dist(o, o’) ≤ distk(o)}

Nk(o) could be bigger than k since multiple objects may have identical distance to o

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