Example of sequential patterns. Example: (a) an expression matrix, E ∈ ℜ|G|×|S| where |G| = 11 and |S| = 7, (b) a sequence database, D, and (c) the set of sequential patterns, P, identified by each of the three cases. The search parameters are set to u = 5, l = 2, w
= 4, and w
= 2. is the summary set eliminating trivial patterns which are enclosed by other patterns. Compared with Case 1, Case 3 searches long sequential patterns. All the patterns found from Case 1 have the length of 2 or 3 (|p
| = 2 or |p
| = 3), whereas 27 out of the 43 patterns found from Case 3 have longer length than 3 (|p
| ≥ 3). Note that the longer patterns are more likely to have biological implication than the shorter ones which can be found by chance. Compared with Case 2, Case 3 shows the effect of backward lookup. By allowing trivial switch between consecutive elements in a sequence, one can still identify sequential patterns despite innate noise in data, e.g., experimental noises in a microarray matrix.