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Time series are the primary data type used to record dynamic system measurements and generated in great volume by both physical sensors and online processes (virtual sensors). Time series analytics is therefore crucial to unlocking the wealth of information implicit in available data. With the recent advancements in graph neural networks (GNNs), there has been a surge in GNN-based approaches for time series analysis. These approaches can explicitly model inter-temporal and inter-variable relationships, which traditional and other deep neural network-based methods struggle to do. In this survey, we provide a comprehensive review of graph neural networks for time series analysis (GNN4TS), encompassing four fundamental dimensions: forecasting, classification, anomaly detection, and imputation. Our aim is to guide designers and practitioners to understand, build applications, and advance research of GNN4TS. At first, we provide a comprehensive task-oriented taxonomy of GNN4TS. Then, we present and discuss representative research works and introduce mainstream applications of GNN4TS. A comprehensive discussion of potential future research directions completes the survey. This survey, for the first time, brings together a vast array of knowledge on GNN-based time series research, highlighting foundations, practical applications, and opportunities of graph neural networks for time series analysis.

The increased complexity and intelligence of automation systems require the development of intelligent fault diagnosis (IFD) methodologies. By relying on the concept of a suspected space, this study develops explainable data-driven IFD approaches for nonlinear dynamic systems. More specifically, we parameterize nonlinear systems through a generalized kernel representation for system modeling and the associated fault diagnosis. An important result obtained is a unified form of kernel representations, applicable to both unsupervised and supervised learning. More importantly, through a rigorous theoretical analysis, we discover the existence of a bridge (i.e., a bijective mapping) between some supervised and unsupervised learning-based entities. Notably, the designed IFD approaches achieve the same performance with the use of this bridge. In order to have a better understanding of the results obtained, both unsupervised and supervised neural networks are chosen as the learning tools to identify the generalized kernel representations and design the IFD schemes; an invertible neural network is then employed to build the bridge between them. This article is a perspective article, whose contribution lies in proposing and formalizing the fundamental concepts for explainable intelligent learning methods, contributing to system modeling and data-driven IFD designs for nonlinear dynamic systems.

Many recent works in the field of graph machine learning have introduced pooling operators to reduce the size of graphs. In this article, we present an operational framework to unify this vast and diverse literature by describing pooling operators as the combination of three functions: selection, reduction, and connection (SRC). We then introduce a taxonomy of pooling operators, based on some of their key characteristics and implementation differences under the SRC framework. Finally, we propose three criteria to evaluate the performance of pooling operators and use them to investigate the behavior of different operators on a variety of tasks.

Reservoir computing is a popular approach to design recurrent neural networks, due to its training simplicity and approximation performance. The recurrent part of these networks is not trained (e.g., via gradient descent), making them appealing for analytical studies by a large community of researchers with backgrounds spanning from dynamical systems to neuroscience. However, even in the simple linear case, the working principle of these networks is not fully understood and their design is usually driven by heuristics. A novel analysis of the dynamics of such networks is proposed, which allows the investigator to express the state evolution using the controllability matrix. Such a matrix encodes salient characteristics of the network dynamics; in particular, its rank represents an input-independent measure of the memory capacity of the network. Using the proposed approach, it is possible to compare different reservoir architectures and explain why a cyclic topology achieves favorable results as verified by practitioners.

Popular graph neural networks implement convolution operations on graphs based on polynomial spectral filters. In this paper, we propose a novel graph convolutional layer inspired by the auto-regressive moving average (ARMA) filter that, compared to polynomial ones, provides a more flexible frequency response, is more robust to noise, and better captures the global graph structure. We propose a graph neural network implementation of the ARMA filter with a recursive and distributed formulation, obtaining a convolutional layer that is efficient to train, localized in the node space, and can be transferred to new graphs at test time. We perform a spectral analysis to study the filtering effect of the proposed ARMA layer and report experiments on four downstream tasks: semi-supervised node classification, graph signal classification, graph classification, and graph regression. Results show that the proposed ARMA layer brings significant improvements over graph neural networks based on polynomial filters.

In recent years, the artificial intelligence community has seen a continuous interest in research aimed at investigating dynamical aspects of both training procedures and machine learning models. Of particular interest among recurrent neural networks, we have the Reservoir Computing (RC) paradigm characterized by conceptual simplicity and a fast training scheme. Yet, the guiding principles under which RC operates are only partially understood. In this work, we analyze the role played by Generalized Synchronization (GS) when training a RC to solve a generic task. In particular, we show how GS allows the reservoir to correctly encode the system generating the input signal into its dynamics. We also discuss necessary and sufficient conditions for the learning to be feasible in this approach. Moreover, we explore the role that ergodicity plays in this process, showing how its presence allows the learning outcome to apply to multiple input trajectories. Finally, we show that satisfaction of the GS can be measured by means of the mutual false nearest neighbors index, which makes effective to practitioners theoretical derivations.

This article develops a novel sliding-mode surface (SMS)-based approximate optimal control scheme for a large class of nonlinear systems affected by unknown mismatched perturbations. The observer-based perturbation estimation procedure is employed to establish the online updated value function. The solution to the Hamilton-Jacobi-Bellman equation is approximated by an SMS-based critic neural network whose weights error dynamics is designed to be asymptotically stable by nested update laws. The sliding-mode control strategy is combined with the approximate optimal control design procedure to obtain a faster control action. The stability is proved based on the Lyapunov's direct method. The simulation results show the effectiveness of the developed control scheme.

The lethal novel coronavirus disease 2019 (COVID-19) pandemic is affecting the health of the global population severely, and a huge number of people may have to be screened in the future. There is a need for effective and reliable systems that perform automatic detection and mass screening of COVID-19 as a quick alternative diagnostic option to control its spread. A robust deep learning-based system is proposed to detect the COVID-19 using chest X-ray images. Infected patient's chest X-ray images reveal numerous opacities (denser, confluent, and more profuse) in comparison to healthy lungs images which are used by a deep learning algorithm to generate a model to facilitate an accurate diagnostics for multi-class classification (COVID vs. normal vs. bacterial pneumonia vs. viral pneumonia) and binary classification (COVID-19 vs. non-COVID). COVID-19 positive images have been used for training and model performance assessment from several hospitals of India and also from countries like Australia, Belgium, Canada, China, Egypt, Germany, Iran, Israel, Italy, Korea, Spain, Taiwan, USA, and Vietnam. The data were divided into training, validation and test sets. The average test accuracy of 97.11 ± 2.71% was achieved for multi-class (COVID vs. normal vs. pneumonia) and 99.81% for binary classification (COVID-19 vs. non-COVID). The proposed model performs rapid disease detection in 0.137 s per image in a system equipped with a GPU and can reduce the workload of radiologists by classifying thousands of images on a single click to generate a probabilistic report in real-time., (© 2021 Nalecz Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Sciences. Published by Elsevier B.V. All rights reserved.)

The space of graphs is often characterized by a nontrivial geometry, which complicates learning and inference in practical applications. A common approach is to use embedding techniques to represent graphs as points in a conventional Euclidean space, but non-Euclidean spaces have often been shown to be better suited for embedding graphs. Among these, constant-curvature Riemannian manifolds (CCMs) offer embedding spaces suitable for studying the statistical properties of a graph distribution, as they provide ways to easily compute metric geodesic distances. In this paper, we focus on the problem of detecting changes in stationarity in a stream of attributed graphs. To this end, we introduce a novel change detection framework based on neural networks and CCMs, which takes into account the non-Euclidean nature of graphs. Our contribution in this paper is twofold. First, via a novel approach based on adversarial learning, we compute graph embeddings by training an autoencoder to represent graphs on CCMs. Second, we introduce two novel change detection tests operating on CCMs. We perform experiments on synthetic data, as well as two real-world application scenarios: the detection of epileptic seizures using functional connectivity brain networks and the detection of hostility between two subjects, using human skeletal graphs. Results show that the proposed methods are able to detect even small changes in a graph-generating process, consistently outperforming approaches based on Euclidean embeddings.

Among the various architectures of Recurrent Neural Networks, Echo State Networks (ESNs) emerged due to their simplified and inexpensive training procedure. These networks are known to be sensitive to the setting of hyper-parameters, which critically affect their behavior. Results show that their performance is usually maximized in a narrow region of hyper-parameter space called edge of criticality. Finding such a region requires searching in hyper-parameter space in a sensible way: hyper-parameter configurations marginally outside such a region might yield networks exhibiting fully developed chaos, hence producing unreliable computations. The performance gain due to optimizing hyper-parameters can be studied by considering the memory-nonlinearity trade-off, i.e., the fact that increasing the nonlinear behavior of the network degrades its ability to remember past inputs, and vice-versa. In this paper, we propose a model of ESNs that eliminates critical dependence on hyper-parameters, resulting in networks that provably cannot enter a chaotic regime and, at the same time, denotes nonlinear behavior in phase space characterized by a large memory of past inputs, comparable to the one of linear networks. Our contribution is supported by experiments corroborating our theoretical findings, showing that the proposed model displays dynamics that are rich-enough to approximate many common nonlinear systems used for benchmarking.

Graph representations offer powerful and intuitive ways to describe data in a multitude of application domains. Here, we consider stochastic processes generating graphs and propose a methodology for detecting changes in stationarity of such processes. The methodology is general and considers a process generating attributed graphs with a variable number of vertices/edges, without the need to assume a one-to-one correspondence between vertices at different time steps. The methodology acts by embedding every graph of the stream into a vector domain, where a conventional multivariate change detection procedure can be easily applied. We ground the soundness of our proposal by proving several theoretical results. In addition, we provide a specific implementation of the methodology and evaluate its effectiveness on several detection problems involving attributed graphs representing biological molecules and drawings. Experimental results are contrasted with respect to suitable baseline methods, demonstrating the effectiveness of our approach.

It is a widely accepted fact that the computational capability of recurrent neural networks (RNNs) is maximized on the so-called "edge of criticality." Once the network operates in this configuration, it performs efficiently on a specific application both in terms of: 1) low prediction error and 2) high short-term memory capacity. Since the behavior of recurrent networks is strongly influenced by the particular input signal driving the dynamics, a universal, application-independent method for determining the edge of criticality is still missing. In this paper, we aim at addressing this issue by proposing a theoretically motivated, unsupervised method based on Fisher information for determining the edge of criticality in RNNs. It is proved that Fisher information is maximized for (finite-size) systems operating in such critical regions. However, Fisher information is notoriously difficult to compute and requires the analytic form of the probability density function ruling the system behavior. This paper takes advantage of a recently developed nonparametric estimator of the Fisher information matrix and provides a method to determine the critical region of echo state networks (ESNs), a particular class of recurrent networks. The considered control parameters, which indirectly affect the ESN performance, are explored to identify those configurations lying on the edge of criticality and, as such, maximizing Fisher information and computational performance. Experimental results on benchmarks and real-world data demonstrate the effectiveness of the proposed method.

In this paper, we elaborate over the well-known interpretability issue in echo-state networks (ESNs). The idea is to investigate the dynamics of reservoir neurons with time-series analysis techniques developed in complex systems research. Notably, we analyze time series of neuron activations with recurrence plots (RPs) and recurrence quantification analysis (RQA), which permit to visualize and characterize high-dimensional dynamical systems. We show that this approach is useful in a number of ways. First, the 2-D representation offered by RPs provides a visualization of the high-dimensional reservoir dynamics. Our results suggest that, if the network is stable, reservoir and input generate similar line patterns in the respective RPs. Conversely, as the ESN becomes unstable, the patterns in the RP of the reservoir change. As a second result, we show that an RQA measure, called , is highly correlated with the well-established maximal local Lyapunov exponent. This suggests that complexity measures based on RP diagonal lines distribution can quantify network stability. Finally, our analysis shows that all RQA measures fluctuate on the proximity of the so-called edge of stability, where an ESN typically achieves maximum computational capability. We leverage on this property to determine the edge of stability and show that our criterion is more accurate than two well-known counterparts, both based on the Jacobian matrix of the reservoir. Therefore, we claim that RPs and RQA-based analyses are valuable tools to design an ESN, given a specific problem.

The ability to detect online changes in stationarity or time variance in a data stream is a hot research topic with striking implications. In this paper, we propose a novel probability density function-free change detection test, which is based on the least squares density-difference estimation method and operates online on multidimensional inputs. The test does not require any assumption about the underlying data distribution, and is able to operate immediately after having been configured by adopting a reservoir sampling mechanism. Thresholds requested to detect a change are automatically derived once a false positive rate is set by the application designer. Comprehensive experiments validate the effectiveness in detection of the proposed method both in terms of detection promptness and accuracy.

One-class classifiers offer valuable tools to assess the presence of outliers in data. In this paper, we propose a design methodology for one-class classifiers based on entropic spanning graphs. Our approach also takes into account the possibility to process nonnumeric data by means of an embedding procedure. The spanning graph is learned on the embedded input data, and the outcoming partition of vertices defines the classifier. The final partition is derived by exploiting a criterion based on mutual information minimization. Here, we compute the mutual information by using a convenient formulation provided in terms of the -Jensen difference. Once training is completed, in order to associate a confidence level with the classifier decision, a graph-based fuzzy model is constructed. The fuzzification process is based only on topological information of the vertices of the entropic spanning graph. As such, the proposed one-class classifier is suitable also for data characterized by complex geometric structures. We provide experiments on well-known benchmarks containing both feature vectors and labeled graphs. In addition, we apply the method to the protein solubility recognition problem by considering several representations for the input samples. Experimental results demonstrate the effectiveness and versatility of the proposed method with respect to other state-of-the-art approaches.

Evolutionary multiobjective optimization in dynamic environments is a challenging task, as it requires the optimization algorithm converging to a time-variant Pareto optimal front. This paper proposes a dynamic multiobjective optimization algorithm which utilizes an inverse model set to guide the search toward promising decision regions. In order to reduce the number of fitness evalutions for change detection purpose, a two-stage change detection test is proposed which uses the inverse model set to check potential changes in the objective function landscape. Both static and dynamic multiobjective benchmark optimization problems have been considered to evaluate the performance of the proposed algorithm. Experimental results show that the improvement in optimization performance is achievable when the proposed inverse model set is adopted.

We present hierarchical change-detection tests (HCDTs), as effective online algorithms for detecting changes in datastreams. HCDTs are characterized by a hierarchical architecture composed of a detection layer and a validation layer. The detection layer steadily analyzes the input datastream by means of an online, sequential CDT, which operates as a low-complexity trigger that promptly detects possible changes in the process generating the data. The validation layer is activated when the detection one reveals a change, and performs an offline, more sophisticated analysis on recently acquired data to reduce false alarms. Our experiments show that, when the process generating the datastream is unknown, as it is mostly the case in the real world, HCDTs achieve a far more advantageous tradeoff between false-positive rate and detection delay than their single-layered, more traditional counterpart. Moreover, the successful interplay between the two layers permits HCDTs to automatically reconfigure after having detected and validated a change. Thus, HCDTs are able to reveal further departures from the postchange state of the data-generating process.

This paper introduces a novel cognitive fault diagnosis system (FDS) for distributed sensor networks that takes advantage of spatial and temporal relationships among sensors. The proposed FDS relies on a suitable functional graph representation of the network and a two-layer hierarchical architecture designed to promptly detect and isolate faults. The lower processing layer exploits a novel change detection test (CDT) based on hidden Markov models (HMMs) configured to detect variations in the relationships between couples of sensors. HMMs work in the parameter space of linear time-invariant dynamic systems, approximating, over time, the relationship between two sensors; changes in the approximating model are detected by inspecting the HMM likelihood. Information provided by the CDT layer is then passed to the cognitive one, which, by exploiting the graph representation of the network, aggregates information to discriminate among faults, changes in the environment, and false positives induced by the model bias of the HMMs.

Just-in-time (JIT) classifiers operate in evolving environments by classifying instances and reacting to concept drift. In stationary conditions, a JIT classifier improves its accuracy over time by exploiting additional supervised information coming from the field. In nonstationary conditions, however, the classifier reacts as soon as concept drift is detected; the current classification setup is discarded and a suitable one activated to keep the accuracy high. We present a novel generation of JIT classifiers able to deal with recurrent concept drift by means of a practical formalization of the concept representation and the definition of a set of operators working on such representations. The concept-drift detection activity, which is crucial in promptly reacting to changes exactly when needed, is advanced by considering change-detection tests monitoring both inputs and classes distributions.

Classification systems meant to operate in nonstationary environments are requested to adapt when the process generating the observed data changes. A straightforward form of adaptation implementing the instance selection approach suggests releasing the obsolete data onto which the classifier is configured by replacing it with novel samples before retraining. In this direction, we propose an adaptive classifier based on the intersection of confidence intervals rule for detecting a possible change in the process generating the data as well as identifying the new data to be used to configure the classifier. A key point of the research is that no assumptions are made about the distribution of the process generating the data. Experimental results show that the proposed adaptive classification system is particularly effective in situations where the process is subject to abrupt changes., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

Aging effects, environmental changes, thermal drifts, and soft and hard faults affect physical systems by changing their nature and behavior over time. To cope with a process evolution adaptive solutions must be envisaged to track its dynamics; in this direction, adaptive classifiers are generally designed by assuming the stationary hypothesis for the process generating the data with very few results addressing nonstationary environments. This paper proposes a methodology based on k-nearest neighbor (NN) classifiers for designing adaptive classification systems able to react to changing conditions just-in-time (JIT), i.e., exactly when it is needed. k-NN classifiers have been selected for their computational-free training phase, the possibility to easily estimate the model complexity k and keep under control the computational complexity of the classifier through suitable data reduction mechanisms. A JIT classifier requires a temporal detection of a (possible) process deviation (aspect tackled in a companion paper) followed by an adaptive management of the knowledge base (KB) of the classifier to cope with the process change. The novelty of the proposed approach resides in the general framework supporting the real-time update of the KB of the classification system in response to novel information coming from the process both in stationary conditions (accuracy improvement) and in nonstationary ones (process tracking) and in providing a suitable estimate of k. It is shown that the classification system grants consistency once the change targets the process generating the data in a new stationary state, as it is the case in many real applications.

Temporal and spatial locality of the inputs, i.e., the property allowing a classifier to receive the same samples over time--or samples belonging to a neighborhood--with high probability, can be translated into the design of embedded classifiers. The outcome is a computational complexity and power aware design particularly suitable for implementation. A classifier based on the gated-parallel family has been found particularly suitable for exploiting locality properties: Subclassifiers are generally small, independent each other, and controlled by a master-enabling module granting that only a subclassifier is active at a time, the others being switched off. By exploiting locality properties we obtain classifiers with accuracy comparable with the ones designed without integrating locality but gaining a significant reduction in computational complexity and power consumption.