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This paper introduces an algorithm for the detection of change-points and the identification of the corresponding subsequences in transient multivariate time-series data (MTSD). The analysis of such data has become more and more important due to the increase of availability in many industrial fields. Labeling, sorting or filtering highly transient measurement data for training condition based maintenance (CbM) models is cumbersome and error-prone. For some applications it can be sufficient to filter measurements by simple thresholds or finding change-points based on changes in mean value and variation. But a robust diagnosis of a component within a component group for example, which has a complex non-linear correlation between multiple sensor values, a simple approach would not be feasible. No meaningful and coherent measurement data which could be used for training a CbM model would emerge. Therefore, we introduce an algorithm which uses a recurrent neural network (RNN) based Autoencoder (AE) which is iteratively trained on incoming data. The scoring function uses the reconstruction error and latent space information. A model of the identified subsequence is saved and used for recognition of repeating subsequences as well as fast offline clustering. For evaluation, we propose a new similarity measure based on the curvature for a more intuitive time-series subsequence clustering metric. A comparison with seven other state-of-the-art algorithms and eight datasets shows the capability and the increased performance of our algorithm to cluster MTSD online and offline in conjunction with mechatronic systems., 26 pages, 11 figures, for associated python code repositories see https://github.com/Jokonu/mt3scm and https://github.com/Jokonu/abimca; Minor spelling and grammar corrections, fixed wrong bibtex entry for SOStream, some improvements and corrections in formulas of section 4

Let G be a finite group. For a positive integer d, let s d N ( G ) denote the smallest integer l such that every sequence S over G of length | S | ≥ l has a nonempty product-one subsequence T with | T | ≡ 0 (mod d). In this paper, we mainly study this invariant for dihedral groups D 2 n and metacyclic groups C p ⋉ s C q .

Subsequence clustering is an important issue in time series data mining. Observing that most time series consist of various patterns with different unknown lengths, we propose an optimization framework to adaptively estimate the lengths and representations for different patterns. Our framework minimizes the inner subsequence cluster errors with respect to subsequence clusters and segmentation under time series cover constraint where the subsequence cluster lengths can be variable. To optimize our framework, we first generate abundant initial subsequence clusters with different lengths. Then, three cluster operations, i.e., cluster splitting, combination and removing, are used to iteratively refine the cluster lengths and representations by respectively splitting clusters consisting of different patterns, joining neighboring clusters belonging to the same pattern and removing clusters to the predefined cluster number. During each cluster refinement, we employ an efficient algorithm to alternatively optimize subsequence clusters and segmentation based on dynamic programming. Our method can automatically and efficiently extract the unknown variable-length subsequence clusters in the time series. Comparative results with the state-of-the-art are conducted on various synthetic and real time series, and quantitative and qualitative performances demonstrate the effectiveness of our method.

We introduce a new graph-theoretic paradigm called a graph signature that describes persistent patterns in a sequence of graphs. This framework is motivated by the need to detect subgraphs of significance in temporal networks, e.g., social and biological networks that evolve over time. Because the subgraphs of interest may not all “look alike” in the snapshots of the temporal network, the framework deems a subgraph to be persistent if it satisfies one of several preselected properties in each snapshot of a consecutive subsequence. The persistency requirement is parameterized by the length of this subsequence. This discrete mathematical framework can be viewed more broadly as a way to generalize classical graph properties and invariants associated with a single graph to a sequence of graphs. In this introductory article, we formulate the graph signature identification problem as a mixed-integer program and propose an algorithmic framework based on dynamic programming. This methodology is applicable to any collection of mixed-integer representable graph properties. We also demonstrate how this framework can be tailored to exploit property-specific decomposition and scale reduction techniques through three different computational case-studies. Our experiments show that the dynamic programming algorithm solves this problem across most instances in our test bed to optimality. Moreover, for the instances in our test bed, the optimal signature sizes are comparable to those of their static counterparts, suggesting that our new framework can identify subgraphs of significance in complex dynamic networks.

In the research of control chart pattern recognition (CCPR), most previous methods used a classifier to label abnormal CCPs. However, long-term control chart data often contains a large number of small abnormal patterns, with characteristics unlike those seen from a global view of the entire chart. There is also a high probability that local abnormal patterns are worthy of analysis. This article presents a novel multiscale control chart pattern recognition scheme, MS-CCPR, which does not focus on the classification of data from a single chart. Rather, the proposed scheme uses a proposed histogram-based data representation in conjunction with time series subsequence matching to identify abnormal patterns on various scales from a long series of control charts. Experimental results demonstrate the efficacy of the proposed framework in the efficient detection of chart patterns at various scales, outperforming the state-of-the-art time series subsequence matching algorithms.

This article addresses novel real-valued consensus problems in the presence of malicious adversaries that can move within the network and induce faulty behaviors in the attacked agents. By adopting several mobile adversary models from the computer science literature, we develop protocols which can mitigate the influence of such malicious agents. The algorithms follow the class of mean subsequence reduced (MSR) algorithms, under which agents ignore the suspicious values received from neighbors during their state updates. Different from the static adversary models, even after the adversaries move away, the infected agents may remain faulty in their values, whose effects must be taken into account. We develop conditions on the network structures for both the complete and non-complete directed graph cases, under which the proposed algorithms are guaranteed to attain resilient consensus. The tolerance bound for network conditions becomes more strict as the adversaries are allowed to have more power. Extensive simulations are carried out over random graphs to verify the effectiveness of our approach when the information of the adversarial agents in terms of their models and numbers is unknown to the agents.

Recent years have witnessed an enormous growth in the number of wireless IoT devices and thereby Internet of Things (IoT) is classified as one of the novel cutting edge technologies that has redesigned the traditional industry into a smart industry, given its applicability for a wide range of applications in providing data-driven decision-making. Meanwhile, the data with missing values is still emerging as one of the longstanding challenges in an IoT architecture due to the common-mode failures, potentially leading to both bias and loss of precision. In spite of the fact that numerous techniques have been developed for imputing missing values, the major issue in terms of imputation precision or computational complexity for large missing subsequences is still a matter under debate. To address this issue, this paper proposes a newly developed algorithm called MP-BMDI that ensures high imputation performance for supporting big data analyses in IoT-based applications, where the absence of large missing subsequences is fully required to offer unbiased results. In our approach, we initially seek a finite number of subsequences that are mostly similar to the subsequence before the missing values, then adjust the height of these following subsequences to optimal locations. Once the most proper subsequence for replacing is chosen among them based on the pattern score function PSF(r) introduced in this paper, the missing gap is completely filled by the corresponding subsequence. Numerical results are here presented to validate the merits of the proposed algorithm compared to the alternative benchmark approaches by leveraging sensor data collected from real-time environmental monitoring and deliver significant insights on the effectiveness of the proposed algorithm from various perspectives.

Unsupervised subsequence outlier detection on multivariate time series (MTS) is a valuable problem in practice that can observably save the cost of labeling and provide interpretability in real applications. For the task, most of the classic methods are under two strong assumptions: (i) stationary MTS. it may have difficulty coping with the phenomenon of time drift. (ii) Attribute-level IIDness (independent and identically distributed), it may ignore the relationship between attribute when measuring the similarity between multivariate subsequences. The above assumptions limit the availability of existing methods in real scenarios. To address this issue, this paper introduces a novel coupled generalized local outlier detection model for MTS, which extends the traditional generalized local outlier detection model to cope with subsequence outlier detection tasks by incorporating a novel Non-IID similarity metric. Specifically, the proposed method mainly includes three aspects: (i) represents the MTS relationship in symbolic space which provides a lower complexity and satisfactory sensitivity. (ii) Proposes a Non-IID coupled similarity metric (TSDis) which considers the intrinsic intra-attribute and inter-attribute coupling between segments. (iii) Extends the traditional generalized local outlier detection model to handle subsequence outlier detection tasks by embedding Non-IID coupled similarity metric. Experimental results show the proposed method can utilize the potential characteristics of MTS effectively and stably. Meanwhile, it detects outliers more accurately than baseline approaches on 12 time-series datasets.

The objective of the present paper is to provide a detailed account of a local min-orthogonal method for finding multiple coexisting solutions to cooperative p-Laplacian systems. A local L-⊥ selection mapping on a product space of two Banach spaces is introduced in order to develop a local characterization of the coexisting solutions. Using this local characterization we propose a numerical algorithm for finding multiple coexisting solutions to the system and provide a subsequence convergence result of the algorithm. We also discuss the discretization of the problem using the finite element method and the associated convergence results of the numerical solutions. Finally, we provide the numerical results to demonstrate the efficiency of the proposed method and also to confirm its related theoretical results.

RNA-binding proteins (RBPs) have a significant role in various regulatory tasks. However, the mechanism by which RBPs identify the subsequence target RNAs is still not clear. In recent years, several machine and deep learning-based computational models have been proposed for understanding the binding preferences of RBPs. These methods required integrating multiple features with raw RNA sequences such as secondary structure and their performances can be further improved. In this paper, we propose an efficient and simple convolution neural network, RBPCNN, that relies on the combination of the raw RNA sequence and evolutionary information. We show that conservation scores (evolutionary information) for the RNA sequences can significantly improve the overall performance of the proposed predictor. In addition, the automatic extraction of the binding sequence motifs can enhance our understanding of the binding specificities of RBPs. The experimental results show that RBPCNN outperforms significantly the current state-of-the-art methods. More specifically, the average area under the receiver operator curve was improved by 2.67 percent and the mean average precision was improved by 8.03 percent. The datasets and results can be downloaded from https://home.jbnu.ac.kr/NSCL/RBPCNN.htm.

Knowledge of protein functions plays an important role in biology and medicine. With the rapid development of high-throughput technologies, a huge number of proteins have been discovered. However, there are a great number of proteins without functional annotations. A protein usually has multiple functions and some functions or biological processes require interactions of a plurality of proteins. Additionally, Gene Ontology provides a useful classification for protein functions and contains more than 40,000 terms. We propose a deep learning framework called DeepGOA to predict protein functions with protein sequences and protein-protein interaction (PPI) networks. For protein sequences, we extract two types of information: sequence semantic information and subsequence-based features. We use the word2vec technique to numerically represent protein sequences, and utilize a Bi-directional Long and Short Time Memory (Bi-LSTM) and multi-scale convolutional neural network (multi-scale CNN) to obtain the global and local semantic features of protein sequences, respectively. Additionally, we use the InterPro tool to scan protein sequences for extracting subsequence-based information, such as domains and motifs. Then, the information is plugged into a neural network to generate high-quality features. For the PPI network, the Deepwalk algorithm is applied to generate its embedding information of PPI. Then the two types of features are concatenated together to predict protein functions. To evaluate the performance of DeepGOA, several different evaluation methods and metrics are utilized. The experimental results show that DeepGOA outperforms DeepGO and BLAST.

In this paper, a color image encryption algorithm based on Fisher-Yates scrambling and DNA subsequence operation (elongation operation, truncation operation, deletion operation, insertion arithmetic) is proposed. Firstly, the three-dimensional color image is transformed into two-dimensional gray image, and the chaotic sequence generated by Chen system and Fisher-Yates scrambling method is used to scramble the plaintext images of R, G and B channels. Secondly, the three channel images of the scrambled plaintext image are transformed into three DNA sequence matrixes by using the DNA coding rules, and then the three DNA sequence matrixes are manipulated by using DNA subsequence operation and DNA addition, subtraction and XOR operation to destroy the scrambled plaintext information. Finally, the color encrypted image is obtained by using the DNA decoding rule. Experimental results and security analysis demonstrate that our encryption algorithm has good performance and may resist against various typical attacks.

In this paper, the combined gradient methods are designed to solve multiobjective optimization problems. According to the special structure of the problem, we only use the gradient information of each objective function and combine each gradient by combining parameters to obtain the search direction of the problem. The Hessian matrix of each objective function is avoided in the methods. Under the assumption that the gradient of objective function is linearly independent, we prove that the methods can always produce a subsequence that converges to the local Pareto point of the problem, and analysis its worst-case iteration complexity. The numerical results are reported for showing the effectiveness of the algorithm.

The aim of the present article is to introduce the concepts of $$s_{p}-$$ convergent sequence in generalized intuitionistic fuzzy metric spaces, i.e., $${\mathscr {L}}$$ -fuzzy metric spaces and analyze relations of convergence, $$s_{p}-$$ convergence, $$s_{\infty }-$$ convergence and $$st-$$ convergence in $${\mathscr {L}}$$ -fuzzy metric spaces. Further, we examine $$s_{p}-$$ convergence, $$s_{\infty }-$$ convergence and $$st-$$ convergence using the subsequence of convergent sequence for above-stated spaces. We finally define $$s_{p}-$$ closed sets, $$s_{\infty }-$$ closed sets and $$st-$$ closed sets in intuitionistic fuzzy metric spaces and investigate relations of them.

We consider positive classical solutions of $$ \left\{ \begin{array}{rcl} -{\Delta} u + \lambda a(x) \cdot \nabla u &=& u^{p} \qquad\text{in} {\Omega}, \\ u&=& 0 \qquad \quad \text{on} {\partial {\Omega}}, \end{array}\right. $$ where p > 1, a is a smooth divergence free vector field and λ > 0 is a large parameter. Under certain assumptions on a(x) and (or) assumptions on the existence of first integrals of a(x) we show there is a subsequence of smooth positive solutions which converge to a nonzero first integral of a(x) as $ \lambda \rightarrow \infty $ .

The stock market plays a vital role in the economic and social organization of many countries. Since stock price time series are highly noisy, nonparametric, volatility, complexity, nonlinearity, dynamics, and chaos, the stock market prediction is an important issue for investors and professional analysts. In the financial field, stock market prediction is not only an important task but also an important research topic. For different problems, researchers have proposed many prediction methods. Many papers provide strong evidence that stock prices can be predicted from past price data. In this paper, we propose a hybrid prediction model for stock price based on long short-term memory (LSTM) and variational mode decomposition (VMD). We use the variational mode decomposition method to decompose the complex time series of stock prices into several relatively flat, regular, and stable subsequences. Then, we use each subsequence to train the long- and short-term memory neural network and predict each subsequence. Finally, we merge the predicted values of several subsequences to form the predicted results of the stock price complex original time series. To verify fully the method, we selected four experimental data for testing. Compared with the prediction results of various prediction methods, the prediction accuracy of our proposed model is higher. Especially in the R2 index, the experimental effect is very good. The proposed method achieves good results of more than 0.991 on each data set. Therefore, our proposed hybrid prediction model is accurate and effective in forecasting stock prices and has practical significance and reference value.

The rapid advances in sequencing technology have led to an explosion of sequence data. Sequence alignment is the central and fundamental problem in many sequence analysis procedure, while local alignment is often the kernel of these algorithms. Usually, Smith–Waterman algorithm is used to find the best subsequence match between given sequences. However, the high time complexity makes the algorithm time-consuming. A lot of approaches have been developed to accelerate and parallelize it, such as vector-level parallelization, thread-level parallelization, process-level parallelization, and heterogeneous acceleration, but the current researches seem unsystematic, which hinders the further research of parallelizing the algorithm. In this paper, we summarize the current research status of parallel local alignments and describe the data layout in these work. Based on the research status, we emphasize large-scale genomic comparisons. By surveying some typical alignment tools’ performance, we discuss some possible directions in the future. We hope our work will provide the developers of the alignment tool with technical principle support, and help researchers choose proper alignment tools. Graphic abstract

Discovering task subsequences from a continuous video stream facilitates a robot imitation of sequential tasks. In this research, we develop unsupervised learning of the task subsequences which does not require a human teacher to give the supervised label of the subsequence. Task-discriminative feature, in the form of sparsely activated cells called task capsules, is proposed for self-training to preserve spatio-semantic information of a visual input. The task capsules are sparsely and exclusively activated with respect to the spatio-semantic context of the task subsequence: a type and location of the object. Therefore, the generalized purpose in multiple videos is unsupervisedly discovered according to the spatio-semantic context, and the demonstration is segmented into the task subsequences in an object-centric way. In comparison with the existing studies on unsupervised task segmentation, our work has the following distinct contribution: 1) the task provided as a video stream can be segmented without any pre-defined knowledge, 2) the trained features preserve spatio-semantic information so that the segmentation is object-centric. Our experiment shows that the recognition of the task subsequence can be applied to robot imitation for a sequential pick-and-place task by providing the semantic and location information of the object to be manipulated.

In the field of intensive aquaculture, the deterioration of water quality is one of the main factors restricting the normal growth of aquatic products. Predicting water quality in real time constitutes the theoretical basis for the evaluation, planning and intelligent regulation of the aquaculture environment. Based on the design principles of decomposition, recombination and integration, this paper constructs a multiscale aquaculture water quality prediction model. First, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method is used to decompose the different water quality variables at different time scales step by step to generate a series of intrinsic mode function (IMF) components with the same characteristic scale. Then, the sample entropy of each IMF component is calculated, the components with similar sample entropies are combined, and the original data are recombined into several subsequences through the above operations. In this paper, a prediction model based on a long short-term memory (LSTM) neural network is constructed to predict each recombination subsequence, and the Adam optimization algorithm is used to continuously update the weight of neural network to train and optimize the prediction performance. Finally, the predicted value of each subsequence is superimposed to predict the original water quality data. The dissolved oxygen and pH data of an aquaculture base were collected for prediction experiments, the results of which show that the proposed model has a high prediction accuracy and strong generalization performance.

Let G be an additive finite abelian group. For a sequence T over G and $$g\in G$$ , let $$\mathrm {v}_{g}(T)$$ denote the multiplicity of g in T. Let $$\mathcal {B}(G)$$ denote the set of all zero-sum sequences over G. For $$\Omega \subset \mathcal {B}(G)$$ , let $$\mathsf {d}_{\Omega }(G)$$ be the smallest integer t such that every sequence S over G of length $$|S|\ge t$$ has a subsequence in $$\Omega $$ . The invariant $$\mathsf {d}_{\Omega }(G)$$ was formulated recently in [3] to take a unified look at zero-sum invariants, it led to the first results there, and some open problems were formulated as well. In this paper, we make some further study on $$\mathsf {d}_{\Omega }(G)$$ . Let $${\mathsf {q}}'(G)$$ be the smallest integer t such that every sequence S over G of length $$|S|\ge t$$ has two nonempty zero-sum subsequences, say $$T_{1}$$ and $$T_{2}$$ , having different forms, i.e., $$\mathrm {v}_{g}(T_{1})\ne \mathrm {v}_{g}(T_{2})$$ for some $$g\in G$$ . Let $${\mathsf {q}}(G)$$ be the smallest integer t such that $$\begin{aligned} \bigcap _{{\mathsf {d}}_{\Omega }(G)=t}\Omega =\emptyset . \end{aligned}$$ The invariants $${\mathsf {q}}(G)$$ and $${\mathsf {q}}'(G)$$ were also introduced in [3]. We prove, among other results, that $${\mathsf {q}}(G)={\mathsf {q}}'(G)$$ in fact.

With the fast digitalization of our society, mining patterns from large time series data is increasingly becoming a critical problem for a wide range of big data applications. Motif and discord discovery algorithms, which offer effective solutions to identify repeatedly appearing and abnormal patterns, respectively, are fundamental building blocks for time series processing. Both approaches, however, can be time extremely consuming when handling large time series due to the subsequence-based computations of distance similarity metrics. In this article, we show that the highly involved subsequence-based computations can actually be decomposed into a few fine-grained computing patterns for efficient data parallel computing. By developing highly efficient GPU algorithms for such basic patterns and effectively composing such patterns, we are able to solve both motif and discord discovery problems under euclidean and DTW distance metrics in a unified GPU acceleration framework. Extensive experiments prove that the proposed framework outperforms pruned CPU algorithms by up to three orders of magnitude. Our work paves the foundation of building GPU acceleration frameworks for large-scale time series datasets.

Consider n nodes $$\{X_i\}_{1 \le i \le n}$$ independently and identically distributed (i.i.d.) across N cities located within the unit square S. Each city is modelled as an $$r_n \times r_n$$ square, and $$\mathrm{{MSTC}}_n$$ denotes the weighted length of the minimum spanning tree containing all the n nodes, where the edge length between nodes $$X_i$$ and $$X_j$$ is weighted by a factor that depends on the individual locations of $$X_i$$ and $$X_j.$$ We use approximation methods to obtain variance estimates for $$\mathrm{{MSTC}}_n$$ and prove that if the cities are well connected in a certain sense, then $$\mathrm{{MSTC}}_n$$ appropriately centred and scaled converges to zero in probability. Using the above proof techniques we also study $$\mathrm{{MST}}_n,$$ the length of the minimum weighted spanning tree for nodes distributed throughout the unit square S with location-dependent edge weights. In this case, the variance of $$\mathrm{{MST}}_n$$ grows at most as a power of the logarithm of n and we use a subsequence argument to get almost sure convergence of $$\mathrm{{MST}}_n,$$ appropriately centred and scaled.

A previously unstudied optimization problem induced by noise-proof recognition of a quasi-periodic sequence, namely, by the recognition of a sequence $$Y$$ of length $$N$$ generated by a sequence $$U$$ belonging to a given finite set $$W$$ (alphabet) of sequences is considered. Each sequence $$U$$ from $$W$$ generates an exponentially sized set $$\mathcal{X}(U)$$ consisting of all sequences of length $$N$$ containing (as subsequences) a varying number of admissible quasi-periodic (fluctuational) repeats of $$U$$ . Each quasi-periodic repeat is generated by admissible transformations of U, namely, by shifts and extensions. The recognition problem is to choose a sequence $$U$$ from $$W$$ and to approximate $$Y$$ by an element $$X$$ of the sequence set $$\mathcal{X}(U)$$ . The approximation criterion is the minimum of the sum of the squared distances between the elements of the sequences. We show that the considered problem is equivalent to the problem of summing the elements of two numerical sequences so as to minimize the sum of an unknown number $$M$$ of terms, each being the difference between the nonweighted autoconvolution of $$U$$ extended to a variable length (by multiple repeats of its elements) and a weighted convolution of this extended sequence with a subsequence of Y. It is proved that the considered optimization problem and the recognition problem are both solvable in polynomial time. An algorithm is constructed and its applicability for solving model application problems of noise-proof processing of ECG- and PPG-like quasi-periodic signals (electrocardiogram- and photoplethysmogram-like signals) is illustrated using numerical examples.

Subsequence anomaly detection in long data series is a significant problem. While the demand for real-time analytics and decision making increases, anomaly detection methods have to operate over streams and handle drifts in data distribution. Nevertheless, existing approaches either require prior domain knowledge or become cumbersome and expensive to use in situations with recurrent anomalies of the same type. Moreover, subsequence anomaly detection methods usually require access to the entire dataset and are not able to learn and detect anomalies in streaming settings. To address these limitations, we propose SAND, a novel online system suitable for domain-agnostic anomaly detection. SAND relies on a novel steaming methodology to incrementally update a model that adapts to distribution drifts and omits obsolete data. We demonstrate our system over different streaming scenarios and compare SAND with other subsequence anomaly detection methods.

Subsequence anomaly detection in long sequences is an important problem with applications in a wide range of domains. However, the approaches that have been proposed so far in the literature have severe limitations: they either require prior domain knowledge that is used to design the anomaly discovery algorithms, or become cumbersome and expensive to use in situations with recurrent anomalies of the same type. In this work, we address these problems, and propose an unsupervised method suitable for domain agnostic subsequence anomaly detection. Our method, Series2Graph, is based on a graph representation of a novel low-dimensionality embedding of subsequences. Series2Graph needs neither labeled instances (like supervised techniques), nor anomaly-free data (like zero-positive learning techniques), and identifies anomalies of varying lengths. The experimental results, on the largest set of synthetic and real datasets used to date, demonstrate that the proposed approach correctly identifies single and recurrent anomalies without any prior knowledge of their characteristics, outperforming by a large margin several competing approaches in accuracy, while being up to orders of magnitude faster.

We explore the semantic-rich structured information derived from the knowledge graphs (KGs) associated with the user-item interactions and aim to reason out the motivations behind each successful purchase behavior. Existing works on KGs-based explainable recommendations focus purely on path reasoning based on current user-item interactions, which generally result in the incapability of conjecturing users’ subsequence preferences. Considering this, we attempt to model the KGs-based explainable recommendation in sequential settings. Specifically, we propose a novel architecture called Reinforced Sequential Learning with Gated Recurrent Unit (RSL-GRU), which is composed of a Reinforced Path Reasoning Network (RPRN) component and a GRU component. RSL-GRU takes users’ sequential behaviors and their associated KGs in chronological order as input and outputs potential top-N items for each user with appropriate reasoning paths from a global perspective. Our RPRN features a remarkable path reasoning capacity, which is regulated by a user-conditioned derivatively action pruning strategy, a soft reward strategy based on an improved multi-hop scoring function, and a policy-guided sequential path reasoning algorithm. Experimental results on four of Amazon’s large-scale datasets show that our method achieves excellent results compared with several state-of-the-art alternatives.

Realizing the accurate prediction of data flow is an important and challenging problem in industrial automation. However, due to the diversity of data types, it is difficult for traditional time series prediction models to have good prediction effects on different types of data. To improve the versatility and accuracy of the model, this paper proposes a novel hybrid time-series prediction model based on recursive empirical mode decomposition (REMD) and long short-term memory (LSTM). In REMD-LSTM, we first propose a new REMD to overcome the marginal effects and mode confusion problems in traditional decomposition methods. Then use REMD to decompose the data stream into multiple in intrinsic modal functions (IMF). After that, LSTM is used to predict each IMF subsequence separately and obtain the corresponding prediction results. Finally, the true prediction value of the input data is obtained by accumulating the prediction results of all IMF subsequences. The final experimental results show that the prediction accuracy of our proposed model is improved by more than 20% compared with the LSTM algorithm. In addition, the model has the highest prediction accuracy on all different types of data sets. This fully shows the model proposed in this paper has a greater advantage in prediction accuracy and versatility than the state-of-the-art models. The data used in the experiment can be downloaded from this website: https://github.com/Yang-Yun726/REMD-LSTM .