On anti-monotone frequency measures for extracting sequential patterns from a single very-long data sequence

Abstract

Abstruct-In this paper, we propose a novel frequency measure, called the total frequuicy, for counting multiple occurrences of a sequential pattern in a very-long single data sequence. The total frequency satisfies the anti-monotonicity property, and makes it possible to count up pattern occurrences without duplication. Moreover the total frequency has a good property for implementation based on the dynamic programming strategy. We also show a preliminary resuit of our experiment for evaluating ' the total frequency.

Efficient mining of frequent episodes from complex sequences

“…{B, D} { [3,3], [6,6], [9,9], [12,12], [16,16]} (a) Encoding table of the frequent itemsets for Figure 1 …”

“…, p k , f > is defined as the set of intervals [ts i , te j ] such that te j − ts i < maxwin, and te j > te i for some j (1 ≤ j ≤ m). [4,4], [7,7], [8,8], [11,11], [14,14]}, < B > .boundlist = { [3,3], [6,6], [9,9], [12,12], [16,16]},and < C > .boundlist = { [1,1], [4,4], [8,8], [11,11], [14,14], [15,15] …”

“…For example, if we want to extend #3 = {C} with boundlist { [1,1], [4,4], [8,8], [11,11], [14,14], [15,15]}, we need to count the occurrences of IDs in the following bounds not exceeding maxwin = 4, i.e. [2,4], [5,7], [9,11], [12,14], [15,16] and [16,16].…”

“…With local frequent items, we reduce a lot of unnecessary joins of the existing frequent itemset with any [4,4], [7,7], [8,8], [11,11], [14,14]} #2 {B} { [3,3], [6,6], [9,9], [12,12], [16,16] [4,4], [8,8], [11,11], [14,14], [15,15]} #4 {D} { [3,3], [5,5], [6,6], [9,9], [12,12], [13,13], [16,16] [4,4], [7,7], [8,8], [11,11], [14,14] …”

“…Therefore, we need a measure that facilitates the calculating of such episode rules to replace the number of sliding windows or minimal occurrences. The problem has also been discussed in [16], but no algorithms are proposed.…”