What is the local outlier factor and when should I use it?

Question

AcadiFi · Accepted Answer

Local outlier factor (LOF) is a density-based anomaly detection algorithm that measures how isolated a point is relative to its neighbors' density. A point in a sparse neighborhood embedded in an otherwise dense region scores high, even if its global position looks ordinary. This contrasts with isolation forest, which focuses on global isolation.

For each point, LOF computes the k-nearest neighbors, calculates the reachability distance (max of distance to a neighbor and that neighbor's k-distance), averages these to get local reachability density, and compares the point's density to its neighbors'. A ratio near 1.0 indicates a normal point; significantly above 1.0 flags an outlier. LOF scores are interpretable: 2.0 means the point is half as dense as its neighbors.

For options trades at a desk like Maldyne Analytics, LOF with k equal to 20 might flag a block trade whose size is normal globally but abnormal for its specific cluster of similar underlyings, whereas isolation forest sees only global patterns and misses this contextual outlier.

LOF works well on data with clusters of varying density but scales O(n squared) naively, though KD-tree or ball-tree indices reduce this. Choice of k matters: too small and results are noisy, too large and local context is lost (try k between 10 and 50). For CFA candidates, the decision rule is: isolation forest for fast scalable global detection, LOF for contextual local detection, autoencoders for learned nonlinear detection, one-class SVM for small well-defined normal regions.

What is the local outlier factor and when should I use it?

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