A New Interval Algebra for Temporal Data Modeling and Analysis

Temporal data is pervasive. Temporal data include not only time-stamped raw data but also time intervals for events with a non-zero duration. Most temporal database systems adopt Allen's temporal relations as a base for querying time periods. On the other hand, discovering temporal knowledge from temporal data has been an active research topic in data mining community. One major research issue in this field is an interval pattern representation scheme which can adequately capture the temporal relations among interval events. The most common method to define the temporal patterns is using Allen's temporal relations. However, all the Allen's relations are binary relation and may suffer several problems when describing relationships among more than three event intervals. Complex relations may lead to generating a larger number of candidate sequences and a heavy workload for counting the support of a candidate sequence. In this paper, we study temporal data modeling and analysis from the algebraic perspectives. We propose a new interval algebra by introducing notions of real interval, null interval as well as a set of operations on intervals. To verify the power of the proposed interval algebra, we identify a $\delta$-intersecting aggregation problem and developed efficient algorithm based the algebra. We describe the detailed algorithms and report the experimental results.