Choosing the number of motifs (k) automatically for a multi-dimensional pan matrix profile (using mstump)

[thohenadl]

Data. T is a multi-dimensional time series of shape (d, n), with d ≈ 20 and n ≈ 3,000–10,000. It is derived from a discrete event log: each index is one event, mapped to a fixed embedding vector. T is therefore piecewise constant per index (step-like), not a sampled signal. Each dimension is z-normalized globally.

Motifs. Motifs are repeated event sequences of variable subsequence length, m ≈ 10–100. There are several motif types per series, each with roughly 5–15 occurrences, which can sit back to back. Occurrences are often exact copies (distance ≈ 0) or near-copies with a few inserted, deleted or swapped events. The rest of T is non-repeating background.

Approach. A pan matrix profile computed by brute force: mstump for every m from min_m = 10 to max_m = 100, using the full-dimensional profile (all d dimensions). Exact repeats make every sub-window of a motif score 0, so raw distances can't rank across m. Instead, each P value is standardized against the profile of its own m. Motifs are then selected greedily from the best standardized value. Each one is expanded into a motif set at its own m (mmotifs-style, max_distance = max(mean − 2·std, min) of the distance profile, exclusion zone m/4), and overlapping occurrences are suppressed.

Problem. The loop stops after a fixed number of motifs (k, i.e. max_motifs), and the right k isn't known in advance. The current stand-in is the ground-truth number of occurrences, which isn't available in practice.

Question. What automated criterion should decide when to stop extracting motifs? Candidates we're considering:

• a threshold on the standardized P value (e.g. stop once it rises above −2);
• MDL (as mmotifs uses to pick k dimensions, but applied to the number of motifs);
• the largest gap in the sorted candidate scores (Knee-Elbow method).

Is there an established, ideally parameter-free, rule for this across window sizes? The Pan-Matrix-Profil paper puts this as an open / known problem.

Happy to clarify any open points. Summarized my problem with support of AI to align with Stumpy Library Terms.

-- Additional: Some Pseudo code --
T: (d, n) multi-dimensional time series
S = {}
for m in range(10, 101):
P, I = stumpy.mstump(T, m)
S[m] = zscore(P[-1]) # full-dim profile, standardized per m

motifs = []
for score, m, idx in sorted((S[m][i], m, i) for m in S for i in range(len(S[m]))):
if STOP(score, motifs): # ??? today: len(motifs) >= k
break
if not overlaps(idx, m, motifs):
motifs += motif_set(T, idx, m) # matches at m, max_distance = mean - 2*std

How to define STOP without knowing k?