Discovering Unbounded Episodes in Sequential Data

Abstract

Abstract. One basic goal in the analysis of time-series data is to find frequent interesting episodes, i.e, collections of events occurring frequently together in the input sequence. Most widely-known work decide the interestingness of an episode from a fixed user-specified window width or interval, that bounds the length of the subsequent sequential association rules. We present in this paper, a more intuitive definition that allows, in turn, interesting episodes to grow during the mining without any user-specified help. A convenient algorithm to efficiently discover the proposed unbounded episodes is also implemented. Experimental results confirm that our approach results useful and advantageous.

MARBLES: Mining Association Rules Buried in Long Event Sequences

“…Further interestingness measures for episodes, either statistically motivated or aimed at removing bias towards smaller episodes, were made by Garriga [5], Gwadera et al [10,11], Calders et al [4], and Tatti [17]. All these methods, however, were limited to finding interesting episodes, and stopped short of discovering association rules between them.…”

“…First of all, the confidence of rule G ⇒ H would depend on our choice of disjoint minimal windows -if we chose the first minimal window of H, s [1,5], we would find two occurrences of G outside it and the confidence of the rule would be 1 3 , whereas if we chose the second minimal window of H, s [4,10], we would find just one occurrence of G outside it, and the confidence would be 2 3 . More importantly, whichever choice we made, we would not be able to get the correct result, showing that every occurrence of G is contained within an occurrence of H. Now that we have seen that we cannot define the confidence of an association rule using either the disjoint-window frequencies, or the containment of the disjoint occurrences, of the two episodes, we are ready to present a definition that corresponds exactly to our intuition.…”

“…Consider sequence s = axybca and episodes X = b → c and Y = {a, b → c}. Sequence s contains one minimal window of X, namely s [4,5]. This occurrence of X can be extended in search of an occurrence of Y .…”

“…This occurrence of X can be extended in search of an occurrence of Y . There are two candidate minimal windows of Y that can be considered, s [1,5] and s [4,6]. If we choose the former, the extensibility of s [4,5] into Y would equal 2 5 , and if we use the latter, this value would rise up to 2 3 .…”

“…There are two candidate minimal windows of Y that can be considered, s [1,5] and s [4,6]. If we choose the former, the extensibility of s [4,5] into Y would equal 2 5 , and if we use the latter, this value would rise up to 2 3 . Since we are interested in how far we need to look in order to extend an occurrence of X into an occurrence of Y , we clearly need to look for the smallest minimal window of Y that satisfies the conditions.…”