As a crucial aspect of data mining, high average utility sequential pattern mining (SPM) aims to discover low frequency and high average utility patterns (subsequences) in sequence data. Most existing high average utility SPM methods overlook the repetitive occurrences of patterns in each sequence, resulting in some important patterns being ignored. To address this issue, we focus on the problem of mining high average utility nonoverlapping patterns (HUPs) from sequential database, and propose an HUP-Miner algorithm. To reduce the need for repeated scanning of the original database, we use a position dictionary to record the occurrence information of each item. To reduce the number of candidate patterns generated, we adopt a pattern join strategy and explore four pruning strategies. To efficiently calculate the average utility of a pattern, we propose an SPC algorithm that utilizes the occurrence positions of sub-patterns. When compared with 12 competitive algorithms, the experimental results on 14 databases show that HUP-Miner gives superior results. Furthermore, we use information gain as the utility for each item, and find that the HUPs discovered in this way can generate better performance via a clustering analysis. All of the algorithms and databases used here are available from https://github.com/wuc567/Pattern-Mining/tree/master/HUP-Miner .

Sequential pattern mining (SPM) with gap constraints (or repetitive SPM or tandem repeat discovery in bioinformatics) can find frequent repetitive subsequences satisfying gap constraints, which are called positive sequential patterns with gap constraints (PSPGs). However, classical SPM with gap constraints cannot find the frequent missing items in the PSPGs. To tackle this issue, this article explores negative sequential patterns with gap constraints (NSPGs). We propose an efficient NSPG-Miner algorithm that can mine both frequent PSPGs and NSPGs simultaneously. To effectively reduce candidate patterns, we propose a pattern join strategy with negative patterns which can generate both positive and negative candidate patterns at the same time. To calculate the support (frequency of occurrence) of a pattern in each sequence, we explore a NegPair algorithm that employs a key-value pair array structure to deal with the gap constraints and the negative items simultaneously and can avoid redundant rescanning of the original sequence, thus improving the efficiency of the algorithm. To report the performance of NSPG-Miner, 11 competitive algorithms and 11 datasets are employed. The experimental results not only validate the effectiveness of the strategies adopted by NSPG-Miner but also verify that NSPG-Miner can discover more valuable information than the state-of-the-art algorithms. Algorithms and datasets can be downloaded from https://github.com/wuc567/Pattern-Mining/tree/master/NSPG-Miner .

Sequential pattern mining (SPM) is an important branch of knowledge discovery that aims to mine frequent sub-sequences (patterns) in a sequential database. Various SPM methods have been investigated, and most of them are classical SPM methods, since these methods only consider whether or not a given pattern occurs within a sequence. Classical SPM can only find the common features of sequences, but it ignores the number of occurrences of the pattern in each sequence, i.e., the degree of interest of specific users. To solve this problem, this paper addresses the issue of repetitive nonoverlapping sequential pattern (RNP) mining and proposes the RNP-Miner algorithm. To reduce the number of candidate patterns, RNP-Miner adopts an itemset pattern join strategy. To improve the efficiency of support calculation, RNP-Miner utilizes the candidate support calculation algorithm based on the position dictionary. To validate the performance of RNP-Miner, 10 competitive algorithms and 20 sequence databases were selected. The experimental results verify that RNP-Miner outperforms the other algorithms, and using RNPs can achieve a better clustering performance than raw data and classical frequent patterns. All the algorithms were developed using the PyCharm environment and can be downloaded fromhttps://github.com/wuc567/Pattern-Mining/tree/master/RNP-Miner.

Order-preserving pattern (OPP) mining is a type of sequential pattern mining method in which a group of ranks of time series is used to represent an OPP. This approach can discover frequent trends in time series. Existing OPP mining algorithms consider data points at different time to be equally important; however, newer data usually have a more significant impact, while older data have a weaker impact. We therefore introduce the forgetting mechanism into OPP mining to reduce the importance of older data. This paper explores the mining of OPPs with forgetting mechanism (OPF) and proposes an algorithm called OPF-Miner that can discover frequent OPFs. OPF-Miner performs two tasks, candidate pattern generation and support calculation. In candidate pattern generation, OPF-Miner employs a maximal support priority strategy and a group pattern fusion strategy to avoid redundant pattern fusions. For support calculation, we propose an algorithm called support calculation with forgetting mechanism, which uses prefix and suffix pattern pruning strategies to avoid redundant support calculations. The experiments are conducted on nine datasets and 12 alternative algorithms. The results verify that OPF-Miner is superior to other competitive algorithms. More importantly, OPF-Miner yields good clustering performance for time series, since the forgetting mechanism is employed.

Recently, order-preserving pattern (OPP) mining, a new sequential pattern mining method, has been proposed to mine frequent relative orders in a time series. Although frequent relative orders can be used as features to classify a time series, the mined patterns do not reflect the differences between two classes of time series well. To effectively discover the differences between time series, this paper addresses the top-kcontrast OPP (COPP) mining and proposes a COPP-Miner algorithm to discover the top-kcontrast patterns as features for time series classification, avoiding the problem of improper parameter setting. COPP-Miner is composed of three parts: extreme point extraction to reduce the length of the original time series, forward mining, and reverse mining to discover COPPs. Forward mining contains three steps: group pattern fusion strategy to generate candidate patterns, the support rate calculation method to efficiently calculate the support of a pattern, and two pruning strategies to further prune candidate patterns. Reverse mining uses one pruning strategy to prune candidate patterns and consists of applying the same process as forward mining. Experimental results validate the efficiency of the proposed algorithm and show that top-kCOPPs can be used as features to obtain a better classification performance.

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.

Negative sequential pattern mining (SPM) is an important SPM research topic. Unlike positive SPM, negative SPM can discover events that should have occurred but have not occurred, and it can be used for financial risk management and fraud detection. However, existing methods generally ignore the repetitions of the pattern and do not consider gap constraints, which can lead to mining results containing a large number of patterns that users are not interested in. To solve this problem, this article discovers frequent one-off negative sequential patterns (ONPs). This problem has the following two characteristics. First, the support is calculated under the one-off condition, which means that any character in the sequence can only be used once at most. Second, the gap constraint can be given by the user. To efficiently mine patterns, this article proposes the ONP-Miner algorithm, which employs depth-first and backtracking strategies to calculate the support. Therefore, ONP-Miner can effectively avoid creating redundant nodes and parent-child relationships. Moreover, to effectively reduce the number of candidate patterns, ONP-Miner uses pattern join and pruning strategies to generate and further prune the candidate patterns, respectively. Experimental results show that ONP-Miner not only improves the mining efficiency but also has better mining performance than the state-of-the-art algorithms. More importantly, ONP mining can find more interesting patterns in traffic volume data to predict future traffic.

The aim of sequential pattern mining (SPM) is to discover potentially useful information from a given sequence. Although various SPM methods have been investigated, most of these focus on mining all of the patterns. However, users sometimes want to mine patterns with the same specific prefix pattern, called co-occurrence pattern. Since sequential rule mining can make better use of the results of SPM, and obtain better recommendation performance, this paper addresses the issue of maximal co-occurrence nonoverlapping sequential rule (MCoR) mining and proposes the MCoR-Miner algorithm. To improve the efficiency of support calculation, MCoR-Miner employs depth-first search and backtracking strategies equipped with an indexing mechanism to avoid the use of sequential searching. To obviate useless support calculations for some sequences, MCoR-Miner adopts a filtering strategy to prune the sequences without the prefix pattern. To reduce the number of candidate patterns, MCoR-Miner applies the frequent item and binomial enumeration tree strategies. To avoid searching for the maximal rules through brute force, MCoR-Miner uses a screening strategy. To validate the performance of MCoR-Miner, eleven competitive algorithms were conducted on eight sequences. Our experimental results showed that MCoR-Miner outperformed other competitive algorithms, and yielded better recommendation performance than frequent co-occurrence pattern mining. All algorithms and datasets can be downloaded fromhttps://github.com/wuc567/Pattern-Mining/tree/master/MCoR-Miner.

Discovering frequent trends in time series is a critical task in data mining. Recently, order-preserving matching was proposed to find all occurrences of a pattern in a time series, where the pattern is a relative order (regarded as a trend) and an occurrence is a sub-time series whose relative order coincides with the pattern. Inspired by the order-preserving matching, the existing order-preserving pattern (OPP) mining algorithm employs order-preserving matching to calculate the support, which leads to low efficiency. To address this deficiency, this paper proposes an algorithm called efficient frequent OPP miner (EFO-Miner) to find all frequent OPPs. EFO-Miner is composed of four parts: a pattern fusion strategy to generate candidate patterns, a matching process for the results of sub-patterns to calculate the support of super-patterns, a screening strategy to dynamically reduce the size of prefix and suffix arrays, and a pruning strategy to further dynamically prune candidate patterns. Moreover, this paper explores the order-preserving rule (OPR) mining and proposes an algorithm called OPR-Miner to discover strong rules from all frequent OPPs using EFO-Miner. Experimental results verify that OPR-Miner gives better performance than other competitive algorithms. More importantly, clustering and classification experiments further validate that OPR-Miner achieves good performance.

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.

For sequence classification, an important issue is to find discriminative features, where sequential pattern mining (SPM) is often used to find frequent patterns from sequences as features. To improve classification accuracy and pattern interpretability, contrast pattern mining emerges to discover patterns with high-contrast rates between different categories. To date, existing contrast SPM methods face many challenges, including excessive parameter selection and inefficient occurrences counting. To tackle these issues, this article proposes a top- k self-adaptive contrast SPM, which adaptively adjusts the gap constraints to find top- k self-adaptive contrast patterns (SCPs) from positive and negative sequences. One of the key tasks of the mining problem is to calculate the support (the number of occurrences) of a pattern in each sequence. To support efficient counting, we store all occurrences of a pattern in a special array in a Nettree, an extended tree structure with multiple roots and multiple parents. We employ the array to calculate the occurrences of all its superpatterns with one-way scanning to avoid redundant calculation. Meanwhile, because the contrast SPM problem does not satisfy the Apriori property, we propose Zero and Less strategies to prune candidate patterns and a Contrast-first mining strategy to select patterns with the highest contrast rate as the prefix subpattern and calculate the contrast rate of all its superpatterns. Experiments validate the efficiency of the proposed algorithm and show that contrast patterns significantly outperform frequent patterns for sequence classification. The algorithms and datasets can be downloaded from https://github.com/wuc567/Pattern-Mining/tree/master/SCP-Miner.

As a novel deep learning model, gcForest has been widely used in various applications. However, current multi-grained scanning of gcForest produces many redundant feature vectors, and this increases the time cost of the model. To screen out redundant feature vectors, we introduce a hashing screening mechanism for multi-grained scanning and propose a model called HW-Forest which adopts two strategies: hashing screening and window screening. HW-Forest employs perceptual hashing algorithm to calculate the similarity between feature vectors in hashing screening strategy, which is used to remove the redundant feature vectors produced by multi-grained scanning and can significantly decrease the time cost and memory consumption. Furthermore, we adopt a self-adaptive instance screening strategy called window screening to improve the performance of our approach, which can achieve higher accuracy without hyperparameter tuning on different datasets. Our experimental results show that HW-Forest has higher accuracy than other models, and the time cost is also reduced.

Nonoverlapping sequential pattern mining is an important type of sequential pattern mining (SPM) with gap constraints, which not only can reveal interesting patterns to users but also can effectively reduce the search space using the Apriori (anti-monotonicity) property. However, the existing algorithms do not focus on attributes of interest to users, meaning that existing methods may discover many frequent patterns that are redundant. To solve this problem, this article proposes a task called nonoverlapping three-way sequential pattern (NTP) mining, where attributes are categorized according to three levels of interest: strong, medium, and weak interest. NTP mining can effectively avoid mining redundant patterns since the NTPs are composed of strong and medium interest items. Moreover, NTPs can avoid serious deviations (the occurrence is significantly different from its pattern) since gap constraints cannot match with strong interest patterns. To mine NTPs, an effective algorithm is put forward, called NTP-Miner, which applies two main steps: support (frequency occurrence) calculation and candidate pattern generation. To calculate the support of an NTP, depth-first and backtracking strategies are adopted, which do not require creating a whole Nettree structure, meaning that many redundant nodes and parent–child relationships do not need to be created. Hence, time and space efficiency is improved. To generate candidate patterns while reducing their number, NTP-Miner employs a pattern join strategy and only mines patterns of strong and medium interest. Experimental results on stock market and protein datasets show that NTP-Miner not only is more efficient than other competitive approaches but can also help users find more valuable patterns. More importantly, NTP mining has achieved better performance than other competitive methods in clustering tasks. Algorithms and data are available at: https://github.com/wuc567/Pattern-Mining/tree/master/NTP-Miner .