Application of a Novel Fuzzy Pattern Mining Algorithm for Sequence Data

For many Markov chains that arise in applications (health, finance, etc.), state spaces are huge, and existing matrix methods may not be practical or even not possible to implement. In the literature, the expected waiting time for Markov chain (with a smaller number of states) generated patterns are obtained by finding an appropriate pattern matrix and solving a set of linear equations. In this paper, a fuzzy transition probability (TP) matrix is introduced, and a data-driven fuzzy pattern mining algorithm is proposed for sequence data of any length. The proposed algorithm, which avoids the inversion of the pattern matrix, is applicable to Markov chains with huge state spaces. The proposed algorithm studies two examples involving DNA sequence data with 3954 base pairs and patterns generated by the log-returns of the stocks/cryptocurrencies. Expected weighting times are compared with the traditional matrix approach. Incorporating stochastic variation in the TP estimates through fuzzy matrices, the new approach provides an alternative path to produce
$\alpha$
-cuts for TP matrices. The main contribution of this paper is to fit an appropriate MC model to a given sequence data and use the proposed fuzzy pattern mining algorithm to obtain resilient probabilistic forecasts and expected waiting time to reach patterns of interest.