variablegram

A variablegram is a unit of sequence data that generalizes the idea of an n-gram by allowing the length of the unit to vary within a predefined range. Unlike fixed-length n-grams, which are limited to a single window size, a variablegram can capture motifs that occur at different scales, from short collocations to longer phrases. The concept is used in fields such as natural language processing, text mining, and bioinformatics to model patterns that do not conform to a single fixed length.

Construction typically involves selecting a minimum length m and maximum length M, then enumerating all substrings of the sequence whose length lies in [m, M]. To manage the combinatorial growth, researchers apply constraints such as frequency thresholds, approximate matching, or data structures like suffix trees and rolling hash indexes. Some approaches treat variablegrams as nodes in variable-length pattern lattices or as features in machine learning models, with weighting schemes reflecting their informativeness.

Relation to related concepts: variablegrams extend n-grams and relate to variable-length motifs, substrings, and k-grams with adaptable length. Applications include language modeling, where variablegrams can improve coverage of multi-word expressions; information retrieval, where they support phrase-based indexing; and genomics or musicology, where motifs vary in length. Limitations include computational cost, sparsity for long ranges, and the need for careful normalization across sequences. The term variablegram has appeared in discussions on flexible pattern discovery, but there is no universally formal standard, and definitions may vary by domain.