src.dackar.RCA.log_pattern_recognition.rca_pattern_search.metrics

Similarity metrics for the RCA pattern search pipeline.

Three metrics answer complementary questions about two incident fingerprints:

jaccard — did the same event types occur? (set, order-agnostic) nlcs — did they occur in a similar order? (sequence-aware) emd_similarity — did they repeat with similar intensity? (frequency-based)

All functions return a value in [0, 1] where 1 is identical.

Functions

jaccard(a, b)	Set-based similarity between two event sets.
_lcs_length(a, b)	Standard O(m·n) DP for LCS length.
nlcs(a, b)	Normalised Longest Common Subsequence similarity.
emd_similarity(a, b[, normalization_factor])	Frequency-based similarity between two event count vectors.
combined_score(j, n, e, alpha, beta_w, gamma)	Weighted combination of the three metric scores.

Module Contents

src.dackar.RCA.log_pattern_recognition.rca_pattern_search.metrics.jaccard(a, b)

Set-based similarity between two event sets.

J(A, B) = |A ∩ B| / |A ∪ B|

Returns 0.0 when both sets are empty (undefined ratio treated as no similarity rather than perfect similarity, which is the safer default for retrieval purposes).

Parameters:

• a (frozenset[str])

• b (frozenset[str])

Return type:

float

src.dackar.RCA.log_pattern_recognition.rca_pattern_search.metrics._lcs_length(a, b)

Standard O(m·n) DP for LCS length.

Parameters:

• a (list[str])

• b (list[str])

Return type:

int

src.dackar.RCA.log_pattern_recognition.rca_pattern_search.metrics.nlcs(a, b)

Normalised Longest Common Subsequence similarity.

NLCS(A, B) = |LCS(A, B)| / max(|A|, |B|)

Operates on deduplicated ordered sequences so high-frequency events do not dominate the ordering signal.

Returns 0.0 when both sequences are empty.

Parameters:

• a (list[str])

• b (list[str])

Return type:

float

src.dackar.RCA.log_pattern_recognition.rca_pattern_search.metrics.emd_similarity(a, b, normalization_factor=None)

Frequency-based similarity between two event count vectors.

Captures the repetition signal that Jaccard and NLCS deliberately discard.

Implementation uses the Total Variation (TV) distance between the two probability distributions derived by normalising the count vectors. For categorical distributions with unit ground distance between any two distinct types, TV distance equals the (unit-ground) Earth Mover’s Distance:

TV(P, Q) = 0.5 · Σ_t |P(t) − Q(t)| where P(t) = a[t] / Σa

This is always in [0, 1], so:

emd_similarity = 1 − TV(P, Q)

Alternative (raw-count) normalisation:

If normalization_factor is provided the raw L1 distance between the unnormalised count vectors is used instead:

raw_emd = Σ_t |a.get(t, 0) − b.get(t, 0)| emd_similarity = max(0.0, 1 − raw_emd / normalization_factor)

Suitable when an empirically derived or vocabulary-size-based upper bound is available (see spec open point on normalisation).

Edge cases:

Both empty → 1.0 (identical — neither has any events) One empty → 0.0 (maximally dissimilar)

Parameters:

• a (dict[str, int])

• b (dict[str, int])

• normalization_factor (float | None)

Return type:

float

src.dackar.RCA.log_pattern_recognition.rca_pattern_search.metrics.combined_score(j, n, e, alpha, beta_w, gamma)

Weighted combination of the three metric scores.

Score = alpha · J + beta_w · NLCS + gamma · EMD

Inputs are assumed to be valid (alpha + beta_w + gamma ≈ 1). No re-normalisation is applied here; the caller (PatternSearcher) is responsible for passing a coherent weight triple via SearchConfig.

Parameters:

• j (float)

• n (float)

• e (float)

• alpha (float)

• beta_w (float)

• gamma (float)

Return type:

float