Due to the dynamic changes and complex time-delay characteristics of signal transmission between brain regions, this information can help identify early signs in individuals with Alzheimer's Disease (AD). Conventional Functional Connectivity Networks (FCN) may overlook interaction delays, leading to inaccurate representations of activity between brain regions. Recognizing the varying delays between patients and healthy individuals, we constructed a dynamic FCN using a Sliding Window based on Derivative Regularity Correlation (SWDRC) and a Functional Delay Network (FDN). These methods aim to improve the detection and analysis of brain networks through the Correlation-based Derivative Regularity (CDR) algorithm. The key advancement of this study is the CDR algorithm, which enables nonlinear time series alignment, unlike traditional correlation methods. This improvement allows for the analysis of asynchronous and nonlinear features in brain activity. Using CDR, SWDRC identifies local and asynchronous characteristics via a sliding window, while FDN quantifies measurable delays between brain regions in both healthy subjects and patients. Our methods show strong potential for revealing the mechanisms underlying neurodegenerative conditions. In classification experiments, combining complementary features from SWDRC and FDN achieved higher accuracy, effectively extracting disease-related patterns. FDN analysis of ADNI data indicates an increasing network delay from Healthy Control to Mild Cognitive Impairment to AD. Our code and models are available at https://github.com/hxpotato/SWDRC.

In many fields, time series prediction is gaining more and more attention, e.g., air pollution, geological hazards, and network traffic prediction. Water quality prediction uses historical data to predict future water quality. However, it is difficult to learn a representation map from a time series that captures the trends and fluctuations to effectively remove noise from the time series data and investigate complex nonlinear relationships. To solve these problems, this work proposes a time series prediction model, called DPSGT for short, which integrates Dual Patch Savitsky–Golay filtering and Transformer. First, DPSGT adopts the SG filtering to decompose the time series data and reduce the noise interference to improve long–term prediction capabilities. Second, to tackle the limitation of temporal representation capability, DPSGT adopts dual patches to ravel temporal series into local and global patches, which can tackle local semantic information and enlarge the receptive field. Third, it utilizes a transformer mechanism to address the nonlinear problem of the water quality time series and improve the accuracy of the prediction. Two real-world datasets are utilized to evaluate the proposed DPSGT, and experiments prove that DPSGT improves root mean-square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and R2 by 6%, 5%, 8%, and 7%, respectively, compared with other benchmark models.

In many fields, spatiotemporal prediction is gaining more and more attention,e.g., air pollution, weather forecasting, and traffic forecasting. Water quality prediction is a spatiotemporal prediction task. However, there are several challenges in water quality prediction: 1) Water quality time series has a complex nonlinear relationship, making it difficult to predict; 2) Water quality sensors are distributed on the river networks and have a strong spatial dependence on water quality prediction; and 3) Poor long-term forecast accuracy. To solve these problems, this work proposes a spatiotemporal prediction model called a Fusion Spatio-temporal Graph Convolution Neural network (FSGCN). First, This work uses a temporal attention mechanism to solve the nonlinear problem of water quality time series. Second, It adopts a graph convolution to extract spatial dependencies of river networks, and the fusion of spatiotemporal can more easily capture spatiotemporal features. Third, it adopts a temporal convolution residual mechanism, improving long-term series prediction accuracy. This work adopts two real-world datasets to evaluate the proposed FSGCN, and experiments demonstrate that FSGCN outperforms several state-of-the-art methods in terms of prediction accuracy.Note to Practitioners—This work considers the critical problem of spatiotemporal water quality prediction. Accurate water quality prediction can effectively prevent environmental pollution. Traditional water quality prediction only focuses on time series features without considering spatial features. In this work, a novel spatiotemporal prediction approach is proposed that combines spatial-temporal graph fusion construction networks for water quality time series prediction in a real-time manner. This work shows that this approach can achieve longer forecasting sequences and more accurate results than traditional forecasting methods. As a practical consequence of this research, spatiotemporal graph fusion convolution networks for water quality prediction can effectively integrate multi-dimensional data and improve the accuracy of long-term water quality prediction. This approach can also be applied to other fields, including intelligent transportation, smart manufacturing, finance, the Internet of Things, and urban computing.

In many fields, time series prediction is gaining more and more attention, e.g., air pollution, geological hazards, and network traffic prediction. Water quality prediction is based on historical data to predict future water quality. However, it is difficult to learn a representation map from a time series that captures the trends and fluctuations to effectively remove noise from time series data and capture complex nonlinear relationships. To solve these problems, this work proposes a time series prediction model, called PSGT for short, which integrates Patch Savitsky-Golay filtering and Transformer. First, this work adopts a Patching method to embed sub-time series data and obtains the trends and semantic information of the time series. Second, it uses the Savitsky-Golay filtering to effectively remove the noise data in the patch and improve the prediction accuracy. Third, it uses a Transformer mechanism to address the nonlinear problem of water quality time series and improve long-term prediction capability. Two real-world datasets are utilized to evaluate the proposed PSGT, and experiments prove that PSGT performs better than other benchmark models by at least 6%.

Accurate prediction of water quality indicators can effectively prevent sudden water pollution events, and control pollution diffusion. Neural networks, e.g., long short-term memory (LSTM) and encoder-decoder network, have been widely used to predict time series data. However, as the water quality data increases, it becomes unstable and highly nonlinear. Accurate prediction of water quality becomes a big challenge. This work proposes a hybrid prediction method called VBAED to predict the water quality time series. VBAED combines Variational mode decomposition (VMD), Bidirectional input Attention mechanism, an Encoder with bidirectional LSTM (BiLSTM), and a Decoder with temporal attention mechanism and LSTM. Specifically, VBAED first adopts VMD to decompose the ground truth time series, and the decomposed results are used as the input along with other features. Then, a bidirectional input attention mechanism is adopted to add weights to input features from both directions. VBAED adopts BiLSTM as an encoder to extract hidden features from input features. Finally, the predicted result is obtained by an LSTM decoder with a temporal attention mechanism. Real-life data-based experiments demonstrate that VBAED obtains the best prediction results compared with other widely used methods.

Spatio-temporal prediction has a wide range of applications in many fields, e.g., air pollution, weather forecasting, and traffic forecasting. Water quality prediction is also one of spatio-temporal prediction tasks. However, it faces the following challenges: 1) Water quality in river networks has complex spatial dependencies; 2) There are complex nonlinear relations in water quality time series; and 3) It is difficult to realize long-term forecasting. To address these challenges, this work proposes a spatio-temporal prediction model called a Graph Attention-based Spatio-Temporal (GAST) neural network. GAST investigates spatial and temporal dependencies of water quality time series. First, we introduce a temporal attention mechanism to capture time series dependencies, which can effectively handle nonlinear relationships in time series. Second, we adopt a spatial attention mechanism to extract spatial dependencies of river networks and fuse temporal features of spatial nodes. Third, we adopt a temporal convolution residual mechanism based on the spatio-temporal fusion, which improves the accuracy of long-term series prediction. This work adopts two real-world datasets to evaluate the proposed GAST and experiments demonstrate that GAST outperforms several state-of-the-art methods in terms of prediction accuracy.