Multivariate time series classification (MTSC) has broad applications in numerous domains. Existing MTSC methods typically focus on either temporal dynamics or variable interactions of the data, often overlooking cross-scale couplings among different variables. To bridge this gap, we propose Scale-Variable Graph Learning (SVGL), a novel framework that effectively captures data-inherent scale-variable interactions for MTSC. SVGL begins with spectral analysis to adaptively identify key periodic scales for each variable. A period-aware reservoir computing network is then incorporated to fit the variable at these scales, encoding the sequential and periodic dynamics into multi-scale dynamic representations. Subsequently, we construct a scale-variable graph to model interactions of the encoded temporal dynamics, where nodes represent scale-variable pairs and edges denote their correlations. After sparsely initializing the graph via nearest neighbors, a parallel graph learning architecture is integrated in SVGL, combining global graph convolutional and sample-specific graph attention to aggregate effective features for classification. Extensive experiments on 30 UEA datasets demonstrate that SVGL outperforms state-of-the-art baselines in accuracy and maintains low training overhead.

Fault Diagnosis (FD) on sequential data suffers from irregular sampling (with missing values), limited training data, and varying underlying environments. In response, this paper proposes FD by adjoint learning in continuous-time model space. Model-Space Learning employs well-fitted models that capture data's dynamics (i.e., changing information) as more stable and concise representations of the original data. The Continuous-Time Reservoir Computing Network (CT-Res) is first introduced, which embeds Ordinary Differential Equation (ODE) within the reservoir-based hidden layer to govern continuous-time hidden-state evolution, naturally handling irregular sampling without relying on fixed time steps and effectively capturing intrinsic data dynamics. By fitting each sequence via CT-Res and representing it with the fitted model, the original sequences are mapped from the data space into the continuous-time model space. We further develop an adjoint learning strategy by incorporating a discrete-time "adjoint Echo State Network (ESN)" that shares structure and parameters with CT-Res, thus enabling efficient training by bypassing the computationally intensive ODE solver, with joint optimization of fitting accuracy and class discrimination in the model space. Experiments on multiple FD benchmarks highlight the effectiveness and efficiency of our study, particularly with missing values and scarce training data.

Anomaly detection in sequential signals is gaining prominence, especially with limited training data and timeliness requirements. Fully extracting the data-inside changing information, we propose a novel Wavelet-Enhanced Reservoir Computing framework (WE-Res). Our framework uses Discrete Wavelet Transform (DWT) to decompose signals for multi-level detail and trend extraction recursively. Each level is fitted using an Echo State Network (ESN) respectively, extracting its inside dynamic features into fitted models. Integrating these dynamic features creates a "multi-level dynamic feature" that enhances signal representation, aiding in distinguishing between normal and anomalous patterns. We further introduce a dual-objective optimization to refine ESNs’ reservoirs, increasing the fitting accuracy and improving category discrimination among the captured features. Validation on real-world data confirms our method’s effectiveness, especially in data-limited scenarios and less training time compared to recent baselines.

Fault Diagnosis (FD) in time-varying systems faces challenges like limited training data, varying environments, and timeliness. Building upon the framework of model-space learning (MSL), we introduce co-objective learning in Dynamic-Integration network (DynInt) model space as a solution for FD. MSL involves utilizing well-fitted models that capture the dynamics within the data as more stable and parsimonious representations of the original data. DynInt integrates pooling and reservoir computing to adequately capture the data-inherent multi-scale dynamics. Representing the signal with the fitted DynInt model transforms the original signal from data space into the DynInt model space. A co-objective optimization is further introduced on DynInt, improving the fitting accuracy and category discrimination. Validation on real-world data confirms our method’s effectiveness, especially in data-limited scenarios.

Analyzing inherent temporal dynamics is a critical pathway for time series classification, where Reservoir Computing (RC) exhibits effectiveness and high efficiency. However, typical RC considers recursive updates from adjacent states, struggling with long-term dependencies. In response, this paper proposes a Spectral-Aware Reservoir Computing framework (SARC), incorporating spectral insights to enhance long-term dependency modeling. Prominent frequencies are initially extracted to reveal explicit or implicit cyclical patterns. For each prominent frequency, SARC further integrates a Frequency-informed Reservoir Network (FreqRes) to adequately capture both sequential and cyclical dynamics, thereby deriving effective dynamic features. Synthesizing these features across various frequencies, SARC offers a multi-scale analysis of temporal dynamics and improves the modeling of long-term dependencies. Experiments on public datasets demonstrate that SARC achieves state-of-the-art results, while maintaining high efficiency compared to existing methods.

Ground Penetrating Radar (GPR) provides detailed subterranean insights. Nevertheless, underground diagnosis via GPR is hindered by the fact that training data typically contain only normal samples, along with the complexity of GPR data’s wave-collection characteristics. This paper proposes subsurface anomaly detection within the Cubic Correlation Reservoir Network (CuCoRes) model space. CuCoRes incorporates three reservoirs with spatial correlation adjustment in each direction to adequately and accurately capture multi-directional dynamics (i.e., changing information) within GPR data. Fitting GPR data with CuCoRes and representing data with fitted models, the original GPR data is mapped into a category-discriminative CuCoRes model space, where anomalies could be efficiently identified and categorized based on model dissimilarities. Our approach leverages only limited normal GPR data, easily accessible, to support subsequent anomaly detection and categorization, enhancing its applicability in practical scenarios. Experiments on real-world data demonstrate its effectiveness, outperforming state-of-the-art.

Fault Diagnosis (FD) in time-varying data presents considerations such as limited training data, intra- and inter-dimensional correlations, and constraints of training time. In response, this paper introduces FD in the Reservoir-Embedded-Directional Network (REDNet) model space. Model-oriented methods utilize well-fitted networks or functions, denoted as "models" that capture data's changing information, as more stable and parsimonious representations of the data. Our approach employs REDNet for data fitting, wherein multiple reservoirs are organized along intrinsic correlation directions to establish intra- and inter-dimensional dependencies, thereby capturing multi-directional dynamics in high-dimensional data. Representing each data instance with an independently fitted REDNet model maps these instances into a class-separable REDNet model space, where FD could be performed on the models rather than the original data. Concentrating on the data-intrinsic dynamics, our method achieves rapid training speeds, and maintains robust performance even with minimal training data. Experiments on several datasets demonstrate its effectiveness.

Time series classification (TSC) is crucial in many applications, yet accurately modeling complex time series patterns remains challenging. Model-based TSC strives to aptly model time series by capturing their intrinsic temporal dynamics, deriving effective dynamic representations for classification. Despite significant progress in this domain, existing works are still constrained by a singular and overly simplistic modeling paradigm, which proves inadequate to handle the multiscale hierarchies inherent in time series. Additionally, the prevailing reliance on manual model configuration fails to address the diverse dynamic characteristics across varying data scenarios. In this paper, we amalgamate multiple recurrent reservoirs to devise a model-based Multiscale Temporal Dynamic Learning (MsDL) approach. These reservoirs are endowed with varied recurrent connection skips, ensuring a comprehensive capture of temporal dynamics across different timescales. We also present a multi-objective optimization algorithm, which adaptively configures the memory length of each reservoir, allowing for more accurate time series modeling. This optimization further encourages time series from the same class to look closer, while separating those from different classes, thereby enhancing the category-discriminability. Extensive experiments on public datasets demonstrate that MsDL outperforms the state-of-the-art methods. Additionally, ablation studies confirm that our multiscale design and optimization algorithm effectively enhance classification accuracy.

As wireless communication and Internet of Things (IoT) technologies advance, edge computing brings computing and storage capabilities closer to users, providing low-latency and high-quality services. However, the limited resources of edge servers and the diverse resource demands of heterogeneous tasks may result in high latency and poor energy efficiency. To address this challenge, we investigate a Docker-based resource management framework for edge servers, involving the allocation of heterogeneous tasks and the configuration of the Docker container clusters. Then, we formulate the problem as one of minimizing energy consumption and task latency, concerning task allocation and server resource management, subject to server resource constraints. To solve this problem, we propose an effective task assignment and resource management strategy, which is developed based on convex optimization theory, aiming to achieve an approximate optimal solution. Simulation results demonstrate that, compared to other algorithms, the proposed algorithm significantly reduces server operating power consumption and task response latency.

Urban development requires meticulous attention to subsurface conditions to ensure the reliable operation of roads and facilities. Ground Penetrating Radar (GPR) offers a non-destructive solution for subsurface anomaly detection. However, the invisible and variable subsurface environments, combined with limited labeled data, make the detection process challenging. While the “Learning in the Model Space (LMS)” shows efficacy by fitting the data to capture the inherent dynamics and representing the original data with fitted models for further process, it falls short in handling GPR B-scan data due to its unidirectional fitting, static model metric, and manual model adjustment. Addressing these challenges, this paper introduces learning in the Dual-Directional Dynamic-captured (D3) model space. We frame the collected GPR B-scan data and fit the GPR data in each frame both horizontally and vertically, encapsulating the dual-directional dynamics within this data frame into a concise D3 model. This D3 model then serves as a representation for this GPR data, mapping the original data from the data space to the D3 model space, and enabling learning on the models rather than the raw data. With the proposed parameterized model metric, our method offers adaptability to diverse data scenarios. We further introduce an optimization algorithm that fine-tunes the fitting process and establishes an optimal model metric, resulting in a “category-distinctive” D3 model space. This enables precise anomaly detection and classification within the D3 model space. Experiments on GPR data underline the superiority of our method in real-world applications.

Detecting and classifying subsurface anomalies in urban infrastructure management is crucial and challenging due to the complexity of underground conditions, with ground penetrating radar (GPR) providing essential noninvasive insights. Challenges in GPR data analysis include: acquiring accurately labeled datasets that cover various anomaly categories, and achieving precise localization of these underground anomalies from GPR data. Addressing these limitations, this article introduces the spatial-dynamic-combined (SpaDyn) framework to identify and classify anomalies in GPR B-scan data, which consists of two main components: Anomaly Region Spatial Localization and Dynamic Feature Extraction. Using both normal and unclassified anomalous data, we first construct an abnormal region extractor extended from the Faster-RCNN architecture to determine the spatial coordinates of potential anomalies. Each identified region is then fit using the bidirectional reservoir computing network (BiD-Res), designed with two reservoirs to capture dynamic features in both horizontal and vertical directions, essential for GPR data due to the continuity of subterranean media and electromagnetic waves. The fit readout model from BiD-Res serves as the dynamic feature representation of the original region, thus transforming the identified regions into a size-independent and category-discriminative “dynamic feature space.” These dynamic features are then clustered to help ascertain the specific type of each region. Experimental results on real-world datasets validated the effectiveness of SpaDyn, particularly in scenarios where specific information about anomaly categories is unavailable.

A new research idea may be inspired by the connections of keywords. Link prediction discovers potential nonexisting links in an existing graph and has been applied in many applications. This article explores a method of discovering new research ideas based on link prediction, which predicts the possible connections of different keywords by analyzing the topological structure of the keyword graph. The patterns of links between keywords may be diversified due to different domains and different habits of authors. Therefore, it is often difficult for a single learner to extract diverse patterns of different research domains. To address this issue, groups of learners are organized with negative correlation to encourage the diversity of sublearners. Moreover, a hierarchical negative correlation mechanism is proposed to extract subgraph features in different order subgraphs, which improves the diversity by explicitly supervising the negative correlation on each layer of sublearners. Experiments are conducted to illustrate the effectiveness of the proposed model to discover new research ideas. Under the premise of ensuring the performance of the model, the proposed method consumes less time and computational cost compared with other ensemble methods.

Ground Penetrating Radar (GPR) provides an effective means for underground anomaly detection, but is also accompanied by some practical issues such as the lack of prior knowledge, insufficient labeled data, and timeliness constraints. In this paper, we propose detecting underground anomalies by adequately capturing multi-directional changing information within GPR B-scan data, which extends the framework of Model-Space Learning (MSL). MSL aims to transform the data from the data space to the model space by representing the original data with fitted models that capture the changes within the data. In GPR data, due to the continuity of the underground medium and electromagnetic wave, there is not only effective changing information in each column of data along the vertical direction, but also in the horizontal detecting direction according to the subsurface environments and existing underground structures. To fully capture the changing information within GPR data, we fit the GPR data along multiple directions respectively, and synthesize the fitted models into a Comprehensive-Change-Captured model (C3 model) wherein multi-directional changing information within the original data is captured. Representing the original data with the C3 model transforms the data from the data space to the C3 model space. The distance metric between C3 models is then introduced, and learning methods could be efficiently implemented on the models. Experiments are conducted on GPR data collected along urban roads, with or without prior knowledge about the existing subsurface anomalies. The obtained results demonstrate the effectiveness of the proposed method.

Recent years have witnessed the proliferation of the Functional Causal Model (FCM) for causal learning due to its intuitive representation and accurate learning results. However, existing FCM-based algorithms suffer from the ubiquitous nonlinear relations in time-series data, mainly because these algorithms either assume linear relationships, or nonlinear relationships with additive noise, or do not introduce additional assumptions but can only identify nonlinear causality between two variables. This paper contributes in particular to a practical FCM-based causal learning approach, which can maintain effectiveness for real-world nonstationary data with general nonlinear relationships and unlimited variable scale.Specifically, the non-stationarity of time series data is first exploited with the nonlinear independent component analysis, to discover the underlying components or latent disturbances. Then, the conditional independence between variables and these components is studied to obtain a relation matrix, which guides the algorithm to recover the underlying causal graph. The correctness of the proposal is theoretically proved, and extensive experiments further verify its effectiveness. To the best of our knowledge, the proposal is the first so far that can fully identify causal relationships under general nonlinear conditions.

Depression and anxiety are critical public health issues affecting millions of people around the world. To identify individuals who are vulnerable to depression and anxiety, predictive models have been built that typically utilize data from one source. Unlike these traditional models, in this study, we leverage a rich heterogeneous dataset from the University of Notre Dame’s NetHealth study that collected individuals’ (student participants’) social interaction data via smartphones, health-related behavioral data via wearables (Fitbit), and trait data from surveys. To integrate the different types of information, we model the NetHealth data as a heterogeneous information network (HIN). Then, we redefine the problem of predicting individuals’ mental health conditions (depression or anxiety) in a novel manner, as applying to our HIN a popular paradigm of a recommender system (RS), which is typically used to predict the preference that a person would give to an item (e.g., a movie or book). In our case, the items are the individuals’ different mental health states. We evaluate four state-of-the-art RS approaches. Also, we model the prediction of individuals’ mental health as another problem type—that of node classification (NC) in our HIN, evaluating in the process four node features under logistic regression as a proof-of-concept classifier. We find that our RS and NC network methods produce more accurate predictions than a logistic regression model using the same NetHealth data in the traditional non-network fashion as well as a random-approach. Also, we find that the best of the considered RS approaches outperforms all considered NC approaches. This is the first study to integrate smartphone, wearable sensor, and survey data in a HIN manner and use RS or NC on the HIN to predict individuals’ mental health conditions.