subsequencelevel

Subsequencelevel is a term used in sequence analysis and data mining to quantify the prominence of a subsequence across a dataset. The exact definition varies by discipline, but a common formalization defines the subsequencelevel of a subsequence w with respect to a dataset D as the fraction of sequences s in D that contain w as a subsequence (the elements of w appear in order in s, but not necessarily contiguously).

Computation and variants: To compute, test whether w is a subsequence of each s in D; the proportion is the subsequencelevel. Efficient checking can use a simple linear scan, dynamic programming, or automata. For large D or many w, indexing schemes, suffix automata, or subsequence-aware miners speed up evaluation. Variants may weight occurrences, count multiple occurrences within a sequence, or limit subsequence length.

Applications and use cases: Subsequencelevel is used in motif discovery, pattern mining, and recommender systems where non-contiguous patterns matter. In bioinformatics, it supports detection of sequence motifs that tolerate gaps. In NLP, it can measure the prevalence of non-contiguous phrase patterns across documents.

Relation to related concepts: It contrasts with contiguous substring support and with broader notions of pattern frequency. Subsequencelevel can be extended by considering gap penalties, subsequence variants, or probabilistic models that assign scores rather than binary containment. Some literature use related terms like subsequence support or gapped subsequence metrics.

Example: Given dataset D = {ABC, ACD, BCDA}, the subsequence "AC" is contained in ABC and ACD but not in BCDA, yielding a subsequencelevel of 2/3.