In this blog post, I will list the key algorithms for **periodic itemset mining** (according to me) with comments about their contributions. Of course, **this list is subjective**. I did not list all the papers of all authors but I have listed the key papers that I have read and found interesting, as they introduced some innovative ideas. I did not list papers that were mostly incremental in their contributions. I also did not list papers that had very few references unless I found them interesting.

Algorithm | Author / Date | Key idea |

PF-Growth | Tanbeer 2009 | – First algorithm for periodic itemset mining in transactionsUses the maxPer constraint to select periodic patterns.– Based on FP-Growth |

MTKPP | Amphawan 2009 | – First algorithm for top-k periodic itemset mining– Uses the maxPer constraint to select periodic patterns. – Based on Eclat |

ITL-tree | Amphawan 2010 | – Performs an approximate calculation of the periods of patterns– Based on FP-Growth |

MIS-PF-tree | Kiran 2009 | – Mining periodic patterns with a maxPer threshold for each item– Based on FP-Growth |

Lahiri 2010 | – Proposed to study periodic patterns as subgraphs in a sequence of graphs. | |

PFP | Rashid 2012 | – Find periodic itemsets using the variance of periods.– The periodic patterns are called regular periodic patterns.– Based on FP-Growth |

PFPM | Fournier-Viger 2016 | – Generalize the problem of periodic itemset mining to provide more flexibility using three measures: the average periodicity, minimum periodicity and maximum periodicity– It is shown that average periodicity is inversely related to the support measure. – Based on Eclat |

PHM | Fournier-Viger 2015 | – An extension of the PFPM algorithm to mine high utility itemsets (itemsets that are periodic but also important such as yield a high profit)– Based on PFPM, Eclat and FHM |

MPFPS | Fournier-Viger 2019 (ppt) | – Find periodic patterns in multiple sequences– Introduce a measure called “ sequence periodic ratio“– Based on PFPM and Eclat |

MRCPPS | Fournier-Viger 2019 | – Find periodic patterns in multiple sequences that are rare and correlated.– Use the sequence periodic ratio, bond measure and maximum periodicity to select patterns– Based on PFPM and Eclat |

PPFP | Nofong 2016 | – Find periodic itemsets using the standard deviation of periods as measure to select patterns.– Apply a statistical test to select periodic patterns that are significant.– Vertical algorithm based on Eclat and inspired by OPUS-Miner for the statistical test |

PPFP+, PFP+… | Nofong 2018 | – Find periodic itemsets using the standard deviation and variance of periods as measure to select patterns. – The measures are integrated in existing algorithms such as PPFP and PFP |

PHUSPM | Dinh 2018 | – Proposed to find periodic sequential patterns (subsequences that are periodic) |

SPP-Growth | Fournier-Viger 2019 (ppt) | – Find the stable periodic patterns using a novel measure called lability.– The goal is to find patterns that are generally stable rather than enforcing a very strict maxPer constraint as many algorithms do.– Based on FPGrowth |

TSPIN | Fournier-Viger 2020 | – Algorithm for mining the top-k stable periodic patterns.– Based on SPP-Growth |

LPP-Growth LPP-Miner | Fournier-Viger 2020 (ppt) | – Find locally periodic patterns (periodic in some time intervals rather than the whole database). That is, unlike most algorithms, it is not assumed that a pattern must be always periodic.– LPP-Growth is based on FPGrowth – LPP-Miner is based on PFPM, which is inspired by Eclat and Apriori-TID |

**Implementations**

Several algorithms above are implemented in the SPMF data mining software in Java as open-source code.

**Some survey papers**

I have also written two chapters recently that give some overview of some topics on periodic pattern mining. You may read them if you want to have a quick and easy-to-understand overview of some topics in **periodic pattern mining.**

- Fournier-Viger, P., Wu. Y., Dinh, D.-T., Song, W., Lin, J.C.W. (2021).
**Discovering Periodic High Utility Itemsets in a Discrete Sequence**. In the book “Periodic Pattern Mining: Theory, Algorithms and Application”, Springer, to appear. - Fournier-Viger, P., Chi, T. T., Wu, Y., Qu, J.-F., Lin, J. C.W., Li, Z. (2021).
**Finding Periodic Patterns in Multiple Discrete Sequences**. In the book “Periodic Pattern Mining: Theory, Algorithms and Application”, Springer, to appear.

**Conclusion**

In this blog post, I have listed some key references in periodic pattern mining. Of course, I did not list all the references of all authors. I mainly listed the key papers that I have read and found interesting. This is obviously subjective.

**Philippe Fournier-Viger** is a full professor working in China and founder of the **SPMF** open source data mining software.