Periodic high-utility sequential patterns (PHUSPs) mining is one of the research hotspots in data mining, which aims to discover patterns that not only have high utility but also regularly appear in sequence datasets. Traditional PHUSP mining mainly focuses on mining patterns from a single sequence, which often results in some interesting patterns being discarded due to strict constraints, and most of the discovered patterns are unstable and difficult to use for decision-making. In response to this issue, a novel algorithm called TKSPUS (top-k stable periodic high-utility sequential pattern mining) is proposed to discover stable top-k periodic high-utility sequential patterns that co-occur in multi-sequences. TKSPUS extends the traditional periodic high-utility sequential patterns mining, and designs two new metrics, namely utility stability coefficient (usc) and periodic stability coefficient (sr), to determine the periodic stability and utility stability of patterns in multi-sequences respectively. Additionally, the TKSPUS algorithm adopts the projection mechanism to mine stable periodic high-utility patterns over multi-sequence, while a new data structure called pusc and two corresponding pruning strategies are also introduced to boost the mining process. Experiments show that compared with the other four related algorithms, the TKSPUS algorithm has better performance in memory consumption and execution time, and the stability of the mining results is improved by 47% on average compared with the traditional periodic high-utility patterns mining algorithm.

Prototypes help to explain the predictions of deep classification models for time series. However, most models learn prototypes by randomly initializing an uncertain number of low-discriminative prototypes, which may lead to unstable models and unreliable results. To address these issues, we propose a new class D iscriminative P rototype L earning Net work (DPL-Net), which learns an appropriate number of class-discriminative prototypes, thus improving classification performance. Specifically, the proposed P rototype I nitialization M echanism (PIM) introduces a new proximity metric based on the silhouette coefficient and statistical metrics. It facilitates the automatic determination of the class-discriminative prototypes for each class. Then, the encoder layer encodes the prototypes derived from PIM and the input series using one-dimensional convolutional neural networks (1D-CNN). Finally, the prototype classification layer optimizes the prototypes according to the regularization terms, while simultaneously classifying the input sequence based on its similarity to the updated prototypes. The comparison experiments are conducted on 26 UCR datasets compared with 10 baselines. The results show that our proposed approach achieves the best accuracy on 11 datasets. Specifically, our method outperforms PIP, CSSL, and LSS by an average of 16.33%, 9.77% and 5.96% on 22, 14 and 16 datasets, respectively. The interpretability experimental results and the application analysis on spectral data indicate that the learned prototypes can provide reasonable explanations for the classification results of the model.

The extensive growth of data quantity has posed many challenges to data analysis and retrieval. Noise and redundancy are typical representatives of the above-mentioned challenges, which may reduce the reliability of analysis and retrieval results and increase storage and computing overhead. To solve the above problems, a two-stage data pre-processing framework for noise identification and data reduction, called ARIS, is proposed in this article. The first stage identifies and removes noises by the following steps: First, the influence space (IS) is introduced to elaborate data distribution. Second, a ranking factor (RF) is defined to describe the possibility that the points are regarded as noises, then, the definition of noise is given based on RF. Third, a clean dataset (CD) is obtained by removing noise from the original dataset. The second stage learns representative data and realizes data reduction. In this process, CD is divided into multiple small regions by IS. Then the reduced dataset is formed by collecting the representations of each region. The performance of ARIS is verified by experiments on artificial and real datasets. Experimental results show that ARIS effectively weakens the impact of noise and reduces the amount of data and significantly improves the accuracy of data analysis within a reasonable time cost range.

In this paper, a novel trajectory clustering algorithm - TAD - is proposed to extract trajectory Stays based on spatial-temporal density analysis of data. Two new metrics - NMAST (Neighbourhood Move Ability and Stay Time) density function and NT (Noise Tolerance) factor - are defined in this algorithm. Firstly, NMAST integrates the characteristics of Neighbourhood Move Ability (NMA, extended from the concept of Move Ability MA), Stay Time (ST), and evaluation factor Eμ to measure the spatial-temporal density of data. Secondly, NT utilizes the features of noise to dynamically evaluate and reduce the influence of noise. The experimental results on Geolife dataset shows that the distributions hidden in data are extracted more realistically, especially for various complex or special trajectories with long-duration gaps. Furthermore, our analytical method of trajectory data is particularly applied in the spectra of LAMOST survey to analyse the variation characteristics of sky-background. The results show a regular distribution on observational date which is relatively concentrated in the month of 1, 10, 11, 12 in each year. The laws discovered in this work would provide a reasonable support for the designation of observational plans, and the new trajectory analysis method would also provide the services for the astronomical data analysis and then for the further studies of formation and evolution of the universe.