NetDPO: (delta, gamma)-approximate pattern matching with gap constraints under one-off condition

OPP-Miner: Order-Preserving Sequential Pattern Mining for Time Series

Traditional sequential pattern mining methods were designed for symbolic sequence. As a collection of measurements in chronological order, a time series needs to be discretized into symbolic sequences, and then users can apply sequential pattern mining methods to discover interesting patterns in time series. The discretization will not only cause the loss of some important information, which partially destroys the continuity of time series, but also ignore the order relations between time-series values. Inspired by order-preserving matching, this article explores a new method called order-preserving sequential pattern (OPP) mining, which does not need to discretize time series into symbolic sequences and represents patterns based on the order relations of time series. An inherent advantage of such representation is that the trend of a time series can be represented by the relative order of the values underneath time series. We propose an OPP-Miner algorithm to mine frequent patterns in time series with the same relative order. OPP-Miner employs the filtration and verification strategies to calculate the support and uses the pattern fusion strategy to generate candidate patterns. To compress the result set, we also study to find the maximal OPPs. Experimental results validate that OPP-Miner is not only efficient but can also discover similar subsequences in time series. In addition, case studies show that our algorithms have high utility in analyzing the COVID-19 epidemic by identifying critical trends and improve the clustering performance. The algorithms and data can be downloaded from https://github.com/wuc567/Pattern-Mining/tree/master/OPP-Miner.

NetNDP: Nonoverlapping (delta, gamma)-approximate pattern matching

Pattern matching can be used to calculate the support of patterns, and is a key issue in sequential pattern mining (or sequence pattern mining). Nonoverlapping pattern matching means that two occurrences cannot use the same character in the sequence at the same position. Approximate pattern matching allows for some data noise, and is more general than exact pattern matching. At present, nonoverlapping approximate pattern matching is based on Hamming distance, which cannot be used to measure the local approximation between the subsequence and pattern, resulting in large deviations in matching results. To tackle this issue, we present a Nonoverlapping Delta and gamma approximate Pattern matching (NDP) scheme that employs the (δ,γ)-distance to give an approximate pattern matching, where the local and the global distances do not exceed δ and γ, respectively. We first transform the NDP problem into a local approximate Nettree and then construct an efficient algorithm, called the local approximate Nettree for NDP (NetNDP). We propose a new approach called the Minimal Root Distance which allows us to determine whether or not a node has root paths that satisfy the global constraint and to prune invalid nodes and parent-child relationships. NetNDP finds the rightmost absolute leaf of the max root, searches for the rightmost occurrence from the rightmost absolute leaf, and deletes this occurrence. We iterate the above steps until there are no new occurrences. Numerous experiments are used to verify the performance of the proposed algorithm.