Partial Periodic Pattern Mining (3PM) is a key knowledge discovery technique with many applications. It involves discovering all patterns that have exhibited partial periodic behavior in a temporal database. Unfortunately, the widespread adoption of this technique has been hindered by the following two limitations: ( i ) the rare item problem , which involves either missing the patterns containing rare items or producing too many patterns, most of which may be uninteresting to the user, and ( ii ) computationally expensive mining process as its mining algorithms were inefficient in reducing the enormous search space. This paper makes the following efforts to address the above-mentioned two limitations. First, we introduce a new null-invariant measure, periodic-confidence , to determine the periodic interestingness of a pattern in a database. Second, an alternative model of a partial periodic pattern has been defined based on the proposed measure. Third, an efficient depth-first search algorithm based on the renowned pattern-growth technique has been introduced to discover all partial periodic patterns in a database. Fourth, the proposed algorithm employs a novel lossless pruning technique called “irregularity pruning” to reduce the search space and computational cost-efficiently. Experiments on several datasets demonstrate that our model can effectively tackle the rare item problem and our algorithm is efficient. Finally, we discuss the usefulness of patterns with case studies performed on air pollution and traffic congestion databases.

“Rare item problem” is a fundamental problem in pattern mining. It represents the inability of a pattern mining model to discover the knowledge about frequent and rare items in a database. In the literature, researchers advocated the usage of null-invariant measures as they disclose genuine correlations without being influenced by the object co-absence in the database. Since the existing null-invariant measures consider only an item’s frequency and disregard its temporal occurrence information, they are inadequate to address the rare item problem faced by the partial periodic pattern model. This paper proposes a novel null-invariant measure, called relative periodic-support, to find the patterns containing both frequent and rare items in non-uniform temporal databases. We also introduce an efficient pattern-growth algorithm to find all desired patterns in a database. Experimental results demonstrate that our algorithm is efficient.

Periodic pattern mining is an emerging technique for knowledge discovery. Most previous approaches have aimed to find only those patterns that exhibit full (or perfect) periodic behavior in databases. Consequently, the existing approaches miss interesting patterns that exhibit partial periodic behavior in a database. With this motivation, this paper proposes a novel model for finding partial periodic patterns that may exist in temporal databases. An efficient pattern-growth algorithm, called Partial Periodic Pattern-growth (3P-growth), is also presented, which can effectively find all desired patterns within a database. Substantial experiments on both real-world and synthetic databases showed that our algorithm is not only efficient in terms of memory and runtime, but is also highly scalable. Finally, the effectiveness of our patterns is demonstrated using two case studies. In the first case study, our model was employed to identify the highly polluted areas in Japan. In the second case study, our model was employed to identify the road segments on which people regularly face traffic congestion.

Partial Periodic itemsets are an important class of regularities that exist in a temporal database. A Partial Periodic itemset is something persistent and predictable that appears in the data. Past studies on Partial Periodic itemsets have been primarily focused on centralized databases and are not scalable for Big Data environments. One cannot ignore the advantage of scalability by using more resources. This is because we deal with large databases in a real-time environment and using more resources can increase the performance. To address the issue we have proposed a parallel algorithm by including the step of distributing transactional identifiers among the machines and mining the identical itemsets independently over the different machines. Experiments on Apache Spark’s distributed environment show that the proposed approach speeds up with the increase in a number of machines.

Periodic-frequent pattern mining is a challenging problem of great importance in many applications. Most previous works focused on finding these patterns in binary temporal databases and did not take into account the quantities of items within the data. This paper proposes a novel model of fuzzy periodic-frequent pattern (FPFP) that may exist in a quantitative temporal database (QTD). Finding FPFPs in QTD is a non-trivial and challenging task due to its huge search space. A novel pruning technique, called improved maximum scalar cardinality, has been introduced to effectively reduce the search space and the computational cost of finding the desired itemsets. This technique facilitates the mining of FPFPs in real-world very large databases practicable. An efficient algorithm has also been presented to find all FPFPs in a QTD. Experimental results demonstrate that the proposed algorithm is efficient. We also present a case study in which we apply our model to find useful information in air pollution database.

. Periodic-frequent pattern mining is an important model in data mining. The popular adoption and successful industrial application of this model has been hindered by the following two limitations: ( i ) The periodic-frequent pattern model implicitly assumes that all transactions within the data occur at a uniform time interval. This assumption limits the model’s applicability as the transactions in many real-world databases occur at irregular time intervals. ( ii ) Finding periodic-frequent patterns in very large databases is a memory intensive process because its mining algorithm has to maintain a list structure to record all timestamps at which an itemset has appeared in the whole data. This paper makes an effort to address these two limitations. A flexible model of periodic-frequent pattern in temporal databases has been described to address the former issue. In order to address the latter issue, a novel concept known as period summary has been introduced to effectively capture the temporal occurrence information of an itemset in a database. A new tree structure, called Periodic Summary-tree (PS-tree), has be introduced to record the temporal occurrence information of an itemset in a temporal database. A pattern-growth algorithm has also been described to find all periodic-frequent patterns from PS-tree. Experimental results demonstrate that the proposed algorithm is efficient.

Finding partial periodic patterns in very large databases is a challenging problem of great importance in many real-world applications. Most previous work focused on finding these patterns in temporal (or transactional) databases and did not recognize the spatial characteristics of items. In this paper, we propose a more flexible model of partial periodic spatial pattern that may be present in spatiotemporal database. Three constraints, maximum inter-arrival time(maxIAT), minimum period-support(minPS) and maximum distance(maxDist), have been employed to determine the interestingness of a pattern in a spatiotemporal database. The maxIAT controls the maximum duration in which a pattern must reappear to consider its occurrence as periodic within the data. The minPS controls the minimum number of periodic occurrences of a pattern within the data. The maxDist controls the maximum distance between the items in a pattern. All patterns satisfying these three constraints are returned. An efficient algorithm, called SpatioTemporal-Equivalence CLAss Transformation (ST-ECLAT), has also been described to discover all partial periodic spatial patterns in a spatiotemporal database. This algorithm employs a novel smart depth-first search technique to discover desired patterns effectively. Experimental results demonstrate that the proposed algorithm is efficient. We also present a case study in which we apply our model to find useful information in the air pollution database.

Finding (partial) periodic patterns in time series data is a challenging problem of great importance in many applications. Due to computational reasons, most previous studies in this area have focused on the efficient discovery of periodic patterns in regular time series data. Unfortunately, these studies have limited applicability because real-world data naturally exists as an irregular time series. This paper proposes a more flexible model of periodic pattern that may be present in irregular time series. Two measures, period and period-support, were employed to determine the interestingness of a pattern in a series. The former measure captures the inter-arrival times of a pattern in a series, while the latter captures the number of periodic occurrences of a pattern in a series. A novel tree structure, called Periodic Pattern tree (PP-tree), has been introduced to record the irregular occurrences of items within the series. A pattern-growth algorithm has also been presented to find all periodic patterns from PP-tree. Experimental results demonstrate that the proposed model can find useful information, and the algorithm is efficient.