Nonoccurring behavior (NOB) studies have attracted the growing attention of scholars as a crucial part of behavioral science. As an effective method to discover both NOB and occurring behaviors (OB), negative sequential pattern (NSP) mining is successfully used in analyzing medical treatment and abnormal behavior patterns. At this time, NSP mining is still an active and challenging research domain. Most of the algorithms are inefficient in practice. Briefly, the key weaknesses of NSP mining are: 1) an inefficient positive sequential pattern (PSP) mining process, 2) a strict constraint of negative containment, and 3) the lack of an effective Negative Sequential Candidate (NSC) generation method. To address these weaknesses, we propose a highly efficient algorithm with improved techniques, named sc-NSP, to mine NSP efficiently. We first propose an improved PrefixSpan algorithm in the PSP mining process, which connects to a bitmap storage structure instead of the original structure. Second, sc-NSP loosens the frequency constraint and exploits the NSC generation method of positive and negative sequential patterns mining (PNSP) (a classic NSP mining method). Furthermore, a novel pruning strategy is designed to reduce the computational complexity of sc-NSP. Finally, sc-NSP obtains the support of NSC by using the most efficient bitwise-based calculation operation. Theoretical analyses show that sc-NSP performs particularly well on data sets with a large number of elements and items in sequence. Comparison and extensive experiments along with case studies on health data show that sc-NSP is 10 times more efficient than other state-of-the-art methods, and the number of NSPs obtained is 5 times greater than other methods.

Density Peaks (DP) Clustering organizes data into clusters by finding peaks in dense regions. This involves computing density ($\rho$$\rho$) and distance ($\delta$$\delta$) of every point. As such, though DP has been very effective in producing high quality clusters, their complexity is O($N^2$$N^2$) where $N$$N$ is the number of data points. In this paper, we propose a fast distributed density peaks clustering algorithm, FDDP, based on the z-value index. In FDDP, we first employ the z-value index to map multi-dimensional data points into one dimensional space, and then range-partition the data according to the z-value to balance the load across the processing nodes. We ensure minimal overlapping range to handle computations at the boundary points. We also propose FC, an efficient algorithm that employs a forward computing strategy to calculate $\rho$$\rho$ linearly. Additionally, we propose another algorithm, CB, which uses a caching and efficient searching strategy to compute $\delta$$\delta$. Moreover, FDDP is able to reduce the time complexity from $O(N^2)$$O\left(N^2\right)$ to $O(N\cdot log(N))$$O(N·log(N\left)\right)$. We provide a theoretical analysis of FDDP and evaluated FDDP empirically. Our experimental results show that FDDP outperforms the state-of-the-art algorithms significantly.

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.