Discovering frequent event patterns with multiple granularities in time sequences

Abstract

An important usage of time sequences is to discover temporal patterns. The discovery process usually starts with a userspecified skeleton, called an event structure, which consists of a number of variables representing events and temporal constraints among these variables; the goal of the discovery is to find temporal patterns, i.e., instantiations of the variables in the structure that appear frequently in the time sequence. This paper introduces event structures that have temporal constraints with multiple granularities, defines the pattern-discovery problem with these structures, and studies effective algorithms to solve it. The basic components of the algorithms include timed automata with granularities (TAGs) and a number of heuristics. The TAGs are for testing whether a specific temporal pattern, called a candidate complex event type, appears frequently in a time sequence. Since there are often a huge number of candidate event types for a usual event structure, heuristics are presented aiming at reducing the number of candidate event types and reducing the time spent by the TAGs testing whether a candidate type does appear frequently in the sequence. These heuristics exploit the information provided by explicit and implicit temporal constraints with granularity in the given event structure. The paper also gives the results of an experiment to show the effectiveness of the heuristics on a real data set.

Processing count queries over event streams at multiple time granularities

“…Data analysis at multiple time granularities was already explored in the context of sequential pattern mining by Bettini et al [5]. However, the target of their work is completely different from ours in that, they try to find sequences with predefined beginning and ending timestamps, and they would like to find sequences that have these predefined timestamps at multiple time granularities.…”

“…We have used this data set to simulate event streams. For each stock in the data set, the price change percentages are calculated and partitioned into seven categories: (3,5], (5,1). Each category of price change for each stock is considered as a distinct event, yielding a total 439 · 7 = 3073 number of event types and 3073 · 517 = 1,588,741 distinct htime À tick, event statei eventtype pairs.…”

“…We used the data set gathered in [5] and available at http://cs.bilkent.edu.tr/~unala/stockdata. The data set is the closing prices of 439 stocks for 517 trading days between January 3, 1994 and January 11, 1996.…”

Discovering High-Order Periodic Patterns

“…Most previous work on mining sequence data fell into two categories: discovering sequential patterns (Agrawal and Srikant, 1995;Berndt and Clifford, 1996;Padmanabhan and Tuzhilin, 1996;Srikand and Agrawal, 1996;Mannila et al, 1997;Bettini et al, 1998;Chakrabarti et al, 1998;Das et al, 1998;Guralnik et al, 1998;Padmanabhan and Tuzhilin, 1998;Garofalakis et al, 1999;Spiliopoulou, 1999;Han et al, 2000;Zaki, 2000Zaki, , 2001 and mining periodic patterns (Han et al, 1998;Ozden et al, 1998;Han et al, 1999;Yang et al, 2000). The primary difference between them is that the models of sequential pattern Discovering High-Order Periodic Patterns 247 purely take into account the number of occurrences of the pattern, while the frameworks for periodic patterns focus on characterizing cyclic behaviors.…”

Discovery of temporal patterns from process instances

“…Finally, Bettini et al (1998) deals with the discovery of frequent-event patterns in a time sequence that consists of a set of time-stamped events. The discovery process starts with a user-specified event structure that consists of a set of variables representing events and temporal constraints between variables.…”