Epilepsy, a chronic and recurrent brain disorder, profoundly impacts individuals' lives. The timely issuance of warnings during epileptic seizures is currently a significant concern for many. To achieve accurate prediction of epileptic seizures, we conducted an analysis of Local Field Potential (LFP) signals both before and after seizures. Our approach involved several steps: initially, we employed wavelet transform (WT) to extract key features from the LFP signals. Subsequently, we utilized probability density estimation and clustering algorithms to sample these signals effectively. Following this, we constructed a Multi-Layer Long-Short-Term Memory (mLSTM) strategy to capture the sequential features of the sampled LFP signals and classify them according to their seizure status. Ultimately, we predicted the LFP signals associated with epilepsy and validated the efficacy of our method. The experimental results demonstrated that, under the WT-mLSTM model, the LFP signals sampled through clustering achieved an average accuracy of 95.93 % in predicting epilepsy, with a sensitivity for seizure prediction reaching 99.87 %. Compared to other prediction models (CNN, Bi-LSTM), our proposed method is more accurate in obtaining epileptic seizure signals. Evidently, the combination of density sampling and the WT-mLSTM strategy enables timely prediction of LFP signals related to epilepsy.

Repetitive Negative Sequential Patterns (RNSPs) can provide critical insights into the importance of sequences. However, most current RNSP mining methods require users to set an appropriate support threshold to obtain the expected number of patterns, which is a very difficult task for the users without prior experience . To address this issue, we propose a new algorithm, TK-RNSP, to mine the Top- K RNSPs with the highest support, without the need to set a support threshold. In detail, we achieve a significant breakthrough by proposing a series of definitions that enable RNSP mining to satisfy anti-monotonicity. Then, we propose a bitmap-based Depth-First Backtracking Search (DFBS) strategy to decrease the heavy computational burden by increasing the speed of support calculation. Finally, we propose the algorithm TK-RNSP in an one-stage process, which can effectively reduce the generation of unnecessary patterns and improve computational efficiency comparing to those two-stage process algorithms. To the best of our knowledge, TK-RNSP is the first algorithm to mine Top- K RNSPs. Extensive experiments on eight datasets show that TK-RNSP has better flexibility and efficiency to mine Top- K RNSPs.

The sequence analysis handles sequential discrete events and behaviors, which can be represented by temporal point processes (TPPs). However, TPP models only occurring events and behaviors. This article explores an efficient method for the negative sequential pattern (NSP) mining to leverage TPP in modeling both frequently occurring and nonoccurring events and behaviors. NSP mining is good at the challenging modeling of nonoccurrences of events and behaviors and their combinations with occurring events, with existing methods built on incorporating various constraints into NSP representations, e.g., simplifying NSP formulations and reducing computational costs. Such constraints restrict the flexibility of NSPs, and nonoccurring behaviors (NOBs) cannot be comprehensively exposed. This article addresses this issue by loosening some inflexible constraints in NSP mining and solves a series of consequent challenges. First, we provide a new definition of negative containment with the set theory according to the loose constraints. Second, an efficient method quickly calculates the supports of negative sequences. Our method only uses the information about the corresponding positive sequential patterns (PSPs) and avoids additional database scans. Finally, a novel and efficient algorithm, NegI-NSP, is proposed to efficiently identify highly valuable NSPs. Theoretical analyses, comparisons, and experiments on four synthetic and two real-life data sets clearly show that NegI-NSP can efficiently discover more useful NOBs.

As an important tool for behavior informatics, negative sequential patterns (NSPs) (such as missing a medical treatment) are sometimes much more informative than positive sequential patterns (PSPs) (e.g., attending a medical treatment) in many applications. However, NSP mining is at an early stage and faces many challenging problems, including 1) how to mine an expected number of NSPs; 2) how to select useful NSPs; and 3) how to reduce high time consumption. To solve the first problem, we propose an algorithm Topk-NSP to mine the k most frequent negative patterns. In Topk-NSP, we first mine the top-k PSPs using the existing methods, and then we use an idea which is similar to top-k PSPs mining to mine the top-k NSPs from these PSPs. To solve the remaining two problems, we propose three optimization strategies for Topk-NSP. The first optimization strategy is that, in order to consider the influence of PSPs when selecting useful top-k NSPs, we introduce two weights, wPand wN, to express the user preference degree for NSPs and PSPs, respectively, and select useful NSPs by a weighted support wsup. The second optimization strategy is to merge wsup and an interestingness metric to select more useful NSPs. The third optimization strategy is to introduce a pruning strategy to reduce the high computational costs of Topk-NSP. Finally, we propose an optimization algorithm Topk-NSP+. To the best of our knowledge, Topk-NSP+is the first algorithm that can mine the top-k useful NSPs. The experimental results on four synthetic and two real-life data sets show that the Topk-NSP+is very efficient in mining the top-k NSPs in the sense of computational cost and scalability.

Negative sequential patterns (NSP) become increasingly important and most of the existing methods introduce so strict constraints that many meaningful patterns would be lost. In this paper, we loosen these constraints and solve a series of consequent problems. Firstly, negative containment is defined to determine whether a data sequence contains a negative sequence. Secondly, an efficient method to fast calculate the supports of negative sequences is proposed. Finally, a novel and efficient algorithm, NegI-NSP, is proposed to efficiently identify meaningful NSP. Experiments show that NegI-NSP can efficiently obtain more meaningful patterns by directly using existing PSP mining algorithms.