Pattern in continuous sequence data

Question

Suppose I have a list of events. For example A, D, T, H, U, A, B, F, H, ....

What I need is to find frequent patterns that occur in the complete sequence. In this problem we cannot use traditional algorithms like a priori or fp growth because they require separate item sets. And, I cannot break this stream into smaller sets.

Any idea which algorithm would work for me?

---

EDIT

For example, for the sequence A, D, T, H, U, A, D, T, H, T, H, U, A, H, T, H and with min_support = 2.

The frequent patterns will be

Of length 1 --> [A, D, T, H, U]
Of length 2 --> [AD, DT, TH, HU, UA, HT]
Of length 3 --> [ADT, DTH, THU, HUA]
Of length 4 --> [ADTH, THUA]
No sequences of length 5 and further

Answer 1

You can try aho-corasick algorithm with a wildcard and/or just with all substrings. Aho-corasick is basically a finite state machine it needs a dictionary but then it find multiple pattern in the search string very fast. You can build a finite state machine with a trie and a breadth-first search. Here is nice example with animation:http://blog.ivank.net/aho-corasick-algorithm-in-as3.html. So you need basically 2 steps: build the finite state machine and search the string.