OPTICS: Reachability Plot & Varying-Density Clustering (2D)

OPTICS Parameters

Neighborhood radius ε 1.00

Min points (MinPts) 5

Cluster-extraction threshold 1.00

Live Readout

Clusters found

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Noise points

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Core points

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Max reachability

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Visited (queue order)

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How it works

OPTICS (Ordering Points To Identify the Clustering Structure) walks every point once, always jumping next to the reachable point that is closest, and records how far each jump had to reach:

core-distance(p) = distance to the MinPts-th nearest
                   neighbor of p within radius ε
                   (∞ if fewer than MinPts neighbors exist)

reachability-distance(p, o) = max( core-distance(p), dist(p, o) )

A priority queue (seed list, keyed by reachability-distance) always pops the closest unvisited candidate next. The top canvas animates that live traversal: the highlighted point is the current queue pop, and the bottom bar chart grows one bar at a time in that exact visiting order. Dense clusters appear as shallow valleys and sparse clusters as deeper (but still bounded) valleys, while tall spikes between valleys are noise.

ε (epsilon) — the neighborhood radius searched for neighbors; too small and sparse clusters never form core points.
MinPts — how many neighbors within ε are required for a point to anchor a cluster (be a core point).
Threshold — a horizontal cut on the reachability plot: any run of consecutive points whose reachability-distance stays at or below it is read off as one cluster (a valley); a bar that spikes above the line starts a new run. Point colors in the scatter view come directly from these extracted runs, not a fixed palette assignment.

Unlike DBSCAN, which needs one global ε that works for every cluster at once, OPTICS computes the ordering a single time and lets you re-cut the same reachability plot at any threshold afterwards — so clusters of very different densities (the tight, medium and sparse blobs below) can all be recovered from one pass, which a fixed-ε DBSCAN run cannot do.

Point cloud (top) · colored by extracted cluster valley Reachability plot (bottom) · bar height = reachability-distance