Discovering High-Order Periodic Patterns

Abstract

Abstract. Discovery of periodic patterns in time series data has become an active research area with many applications. These patterns can be hierarchical in nature, where a higher-level pattern may consist of repetitions of lower-level patterns. Unfortunately, the presence of noise may prevent these higher-level patterns from being recognized in the sense that two portions (of a data sequence) that support the same (high-level) pattern may have different layouts of occurrences of basic symbols. There may not exist any common representation in terms of raw symbol combinations; and hence such (high-level) pattern may not be expressed by any previous model (defined on raw symbols or symbol combinations) and would not be properly recognized by any existing method. In this paper, we propose a novel model, namely meta-pattern, to capture these high-level patterns. As a more flexible model, the number of potential meta-patterns could be very large. A substantial difficulty lies in how to identify the proper pattern candidates. However, the well-known Apriori property is not able to provide sufficient pruning power. A new property, namely component location property, is identified and used to conduct the candidate generation so that an efficient computation-based mining algorithm can be developed. Last, but not least, we apply our algorithm to some real and synthetic sequences and some interesting patterns are discovered.

Stop Chasing Trends: Discovering High Order Models in Evolving Data

“…However, as in the examples we mentioned above, concept changes may occur at any time, instead of exhibiting simple patterns such as periodicity [14]. The second component of the high-order model is the concept change patterns, which are also learned from the historical data, that is, we analyze how individual concepts interact with each other by collecting the statistics of concept changes.…”

“…The block size should be small enough (e.g., [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] such that data within a block represents a same concept with high probability. Then we group adjacent blocks into data chunks, each representing an concept occurrence, and the boundary between two chunks represents a concept change.…”

New and efficient knowledge discovery of partial periodic patterns with multiple minimum supports

“…Ma and Hellerstein (2001) and Yang et al (2004) proposed their algorithms to discover periodic patterns with noise, respectively. Cao et al (2004) introduced a method to discover partial periodic patterns in discrete data sequences.…”

Sequence Data Mining

“…• Several papers considered various extensions to partial periodicity. Reference [128] studied how to mine high-level partial periodic patterns, where a higher level pattern may consist of repetitions of lower level patterns. The paper overcame difficulties caused by the presence of noise for the discovery of high-level patterns.…”