A Study on the Accuracy of Frequency Measures and Its Impact on Knowledge Discovery in Single Sequences

In knowledge discovery in single sequences, different results could be discovered from the same sequence when different frequency measures are adopted. It is natural to raise such questions as (1) do these frequency measures reflect actual frequencies accurately? (2) what impacts do frequency measures have on discovered knowledge? (3) are discovered results accurate and reliable? and (4) which measures are appropriate for reflecting frequencies accurately? In this paper, taking three major factors (anti-monotonicity, maximum-frequency and window-width restriction) into account, we identify inaccuracies inherent in seven existing frequency measures, and investigate their impacts on the soundness and completeness of two kinds of knowledge, frequent episodes and episode rules, discovered from single sequences. In order to obtain more accurate frequencies and knowledge, we provide three recommendations for defining appropriate frequency measures. Following the recommendations, we introduce a more appropriate frequency measure. Empirical evaluation reveals the inaccuracies and verifies our findings.