Matching and retrieving sequential patterns using regression

Sequential pattern mining can prove to be very useful for predicating future activities, interpreting recurring phenomena, extracting similarities in a series of events, etc. For example, in the NASDAQ market, the problem of finding stocks whose closing prices are always about β_0 higher than or β_1 times the stocks of a given company, reduces to linear pattern retrieval: given query X, find all sequences Y from the database S so that, Y=β_0+β_1X with confidence C. In this paper, we introduce a novel approach using the Simple Linear Regression (SLR) model to match and retrieve sequential patterns. We extend the one-dimensional R² model to ER² for multi-dimensional sequence matching. In addition, we present the SLR + FFT pruning technique to speed up data retrieval without incurring any false dismissal. Experimental results on both synthetic and real datasets show that the pruning ratio of SLR + FFT can be above 99%. Applying the retrieval technique to real stocks resulted in the discovery many interesting patterns, some of which are presented in the paper. Also, using ER² as the similarity measure for on-line signature recognition yielded high accuracy.