Temporal Encoding Research Articles

Multi-layer encoder–decoder time-domain single channel speech separation

With the emergence of more advanced separation networks, significant progress has been made in time-domain speech separation methods. These methods typically use a temporal encoder–decoder structure to encode speech feature sequences, thereby accomplishing the separation task. However, due to the limitation of traditional encoder–decoder structure, the separation performance decreases sharply when the encoded sequence is short, and when encoded sequence is sufficiently long, the separation performance improves, but which leads to an increase in computational complexity and training cost. Therefore, this paper compresses and reconstructs the speech feature sequence through a multi-layer convolution structure, and proposes a multi-layer encoder–decoder time-domain speech separation model (MLED). In this model, our encoder–decoder structure can compress speech sequence to a short length while ensuring the separation performance does not decrease. And combined with our multi-scale temporal attention (MSTA) separation network, MLED achieves efficient and precise separation of short encoded sequences. Therefore, compared to previous advanced time-domain separation methods, our experiments show that MLED achieves competitive separation performance with smaller model size, lower computational complexity, and training cost.

Artifact removal by template subtraction enables recordings of the frequency following response in cochlear-implant users

Electrically evoked frequency-following responses (eFFRs) provide insight in the phase-locking ability of brainstem of cochlear-implant (CI) users. eFFRs can potentially be used to gain insight in the individual differences in the biological limitation on temporal encoding of the electrically stimulated auditory pathway, which can be inherent to the electrical stimulation itself and/or the degenerative processes associated with hearing loss. One of the major challenge of measuring eFFRs in CI users is the process of isolating the stimulation artifact from the neural response, as both the response and the artifact overlap in time and have similar frequency characteristics. Here we introduce a new artifact removal method based on template subtraction that successfully removes the stimulation artifacts from the recordings when CI users are stimulated with pulse trains from 128 to 300 pulses per second in a monopolar configuration. Our results show that, although artifact removal was successful in all CI users, the phase-locking ability of the brainstem to the different pulse rates, as assessed with the eFFR differed substantially across participants. These results show that the eFFR can be measured, free from artifacts, in CI users and that they can be used to gain insight in individual differences in temporal processing of the electrically stimulated auditory pathway.

Two-Level Spatio-Temporal Feature Fused Two-Stream Network for Micro-Expression Recognition.

Micro-expressions, which are spontaneous and difficult to suppress, reveal a person's true emotions. They are characterized by short duration and low intensity, making the task of micro-expression recognition challenging in the field of emotion computing. In recent years, deep learning-based feature extraction and fusion techniques have been widely used for micro-expression recognition, particularly methods based on Vision Transformer that have gained popularity. However, the Vision Transformer-based architecture used in micro-expression recognition involves a significant amount of invalid computation. Additionally, in the traditional two-stream architecture, although separate streams are combined through late fusion, only the output features from the deepest level of the network are utilized for classification, thus limiting the network's ability to capture subtle details due to the lack of fine-grained information. To address these issues, we propose a new two-level spatio-temporal feature fused with a two-stream architecture. This architecture includes a spatial encoder (modified ResNet) for learning texture features of the face, a temporal encoder (Swin Transformer) for learning facial muscle motor features, a feature fusion algorithm for integrating multi-level spatio-temporal features, a classification head, and a weighted average operator for temporal aggregation. The two-stream architecture has the advantage of extracting richer features compared to the single-stream architecture, leading to improved performance. The shifted window scheme of Swin Transformer restricts self-attention computation to non-overlapping local windows and allows cross-window connections, significantly improving the performance and reducing the computation compared to Vision Transformer. Moreover, the modified ResNet is computationally less intensive. Our proposed feature fusion algorithm leverages the similarity in output feature shapes at each stage of the two streams, enabling the effective fusion of multi-level spatio-temporal features. This algorithm results in an improvement of approximately 4% in both the F1 score and the UAR. Comprehensive evaluations conducted on three widely used spontaneous micro-expression datasets (SMIC-HS, CASME II, and SAMM) consistently demonstrate the superiority of our approach over comparative methods. Notably, our approach achieves a UAR exceeding 0.905 on CASME II, making it one of the few frameworks in the published micro-expression recognition literature to achieve such high performance.

Developing an AI-empowered head-only ultra-high-performance gradient MRI system for high spatiotemporal neuroimaging

Recent advances in neuroscience requires high-resolution MRI to decipher the structural and functional details of the brain. Developing a high-performance gradient system is an ongoing effort in the field to facilitate high spatial and temporal encoding. Here, we proposed a head-only gradient system NeuroFrontier, dedicated for neuroimaging with an ultra-high gradient strength of 650 mT/m and 600 T/m/s. The proposed system features in 1) ultra-high power of 7MW achieved by running two gradient power amplifiers using a novel paralleling method; 2) a force/torque balanced gradient coil design with a two-step mechanical structure that allows high-efficiency and flexible optimization of the peripheral nerve stimulation; 3) a high-density integrated RF system that is miniaturized and customized for the head-only system; 4) an AI-empowered compressed sensing technique that enables ultra-fast acquisition of high-resolution images and AI-based acceleration in q-t space for diffusion MRI (dMRI); and 5) a prospective head motion correction technique that effectively corrects motion artifacts in real-time with 3D optical tracking. We demonstrated the potential advantages of the proposed system in imaging resolution, speed, and signal-to-noise ratio for 3D structural MRI (sMRI), functional MRI (fMRI) and dMRI in neuroscience applications of submillimeter layer-specific fMRI and dMRI. We also illustrated the unique strength of this system for dMRI-based microstructural mapping, e.g., enhanced lesion contrast at short diffusion-times or high b-values, and improved estimation accuracy for cellular microstructures using diffusion-time-dependent dMRI or for neurite microstructures using q-space approaches.

Dynamic multi-granularity spatial-temporal graph attention network for traffic forecasting

Traffic forecasting, as the cornerstone of the development of intelligent transportation systems, plays a crucial role in facilitating accurate control and management of urban traffic. By treating sensors as nodes in a road network, recent research on modeling complex spatial-temporal graph structures has achieved notable advancements in traffic forecasting. However, limited by the increasing number of sensors and recorded data points, most of the recent studies on spatial-temporal graph neural network (STGNN) research concentrate on aggregating short-term (e.g. recent one-hour) traffic history to predict future data. Furthermore, almost all previous STGNNs neglect to incorporate the cyclical patterns that appear in the traffic historical data. For example, the cyclical patterns of traffic on the same day or hour of each week can help improve the accuracy of future traffic predictions. In this paper, we propose a novel Dynamic Multi-Granularity Spatial-Temporal Graph Attention Network (DmgSTGAT) framework for traffic forecasting, which leverages multi-granularity spatial-temporal correlations across different time-scales and variables to efficiently consider cyclical patterns in traffic data. We also design effective temporal encoding and transformer encoding layers to produce meaningful multi-granularity sensor-level, day-level, hour-level, and point-level representations. The multi-granularity spatial-temporal graph attention network can use the produced representations to extract useful but sparsely distributed patterns accurately, which also avoids the influence of extra noise from the long-term history. Experimental results on four real-world traffic datasets show that DmgSTGAT can achieve state-of-the-art performance with the help of multi-granularity cyclical patterns compared with various recent baselines.

ERNetCL: A novel emotion recognition network in textual conversation based on curriculum learning strategy

Emotion recognition in conversation (ERC) has emerged as a research hotspot in domains such as conversational robots and question-answer systems. How to efficiently and adequately retrieve contextual emotional cues has been one of the key challenges in the ERC task. Existing efforts do not fully model the context and employ complex network structures, resulting in limited performance gains. In this paper, we propose a novel emotion recognition network based on curriculum learning strategy (ERNetCL). The proposed ERNetCL primarily consists of temporal encoder (TE), spatial encoder (SE), and curriculum learning (CL) loss. We utilize TE and SE to combine the strengths of previous methods in a simplistic manner to efficiently capture temporal and spatial contextual information in the conversation. To ease the harmful influence resulting from emotion shift and simulate the way humans learn curriculum from easy to hard, we apply the idea of CL to the ERC task to progressively optimize the network parameters. At the beginning of training, we assign lower learning weights to difficult samples. As the epoch increases, the learning weights for these samples are gradually raised. Extensive experiments on four datasets exhibit that our proposed method is effective and dramatically beats other baseline models.

Two-pathway spatiotemporal representation learning for extreme water temperature prediction

Accurate predictions of extreme water temperatures are criticalto understanding the variability of the marine environment and reducing marine disasters maximized by global warming. In this study, we propose a two-pathway framework with separated spatial and temporal encoders for accurate prediction of water temperature, especially extremely high water temperature, through effective spatiotemporal representation learning. The spatial and temporal encoder networks based on the Transformer’s self-attention mechanism performs the task of predicting the water temperature time series at the 16 coastal locations around the Korean Peninsula for the seven consecutive days ahead at daily intervals with various combinations of patch embedding methods, positional embedding for spatial features. Comparative experiments with conventional deep convolutional and recurrent networks are also conducted for comparison. By comparing and assessing these results, the proposed two-pathway framework can improve the predictability of extremely high coastal water temperature by better capturing spatiotemporal interrelationships and long-range dependencies from open ocean and regional sea, and further determines the optimal architectural details of self-attention-based spatial and temporal encoders. Furthermore, to examine the explainability of the proposed model and its consistency with domain knowledge, spatial and temporal attention maps are visualized and analyzed that represents weights for spatiotemporal input sequences that are more relevant to predict for future predictions.

Cardiac Bioengineering Analysis of Electrophysiological Signals Driven by Deep Learning

Advanced methods are needed for fast and reliable detection of cardiovascular illnesses, which continue to be a primary source of morbidity and death globally. Using deep learning, this research presents a new method, dubbed DeepLearnCardia, for analyzing electrophysiological data in cardiac bioengineering. To improve the analysis of cardiac electrophysiological data and provide a complete solution for arrhythmia prediction, the proposed technique combines wavelet transformations, attention processes, and multimodal fusion. Data preprocessing, feature extraction using wavelets, temporal encoding using Long Short-Term Memory (LSTM) networks, an attention mechanism, multimodal fusion, and spatial analysis with Convolutional Neural Networks (CNNs) are all components of this technique. In order to train the model, we use an adaptive optimizer and binary cross entropy as the loss function. Key performance metrics such as accuracy, sensitivity, specificity, precision, F1 score, and area under the ROC curve (AUC-ROC) are used to compare the proposed method's performance to that of six established methods: Signal Pro Analyzer, Electro Cardio Suite, Bio Signal Master, Cardio Wave Analyzer, EKG Precision Pro, and Heart Stat Analyzer. The results suggest that the proposed technique is superior to the state-of-the-art in cardiac signal analysis across all criteria. The suggested technique not only requires less resources, but also trains and infers more quickly and uses less of them.

Temporal encoding in deep reinforcement learning agents

Neuroscientists have observed both cells in the brain that fire at specific points in time, known as “time cells”, and cells whose activity steadily increases or decreases over time, known as “ramping cells”. It is speculated that time and ramping cells support temporal computations in the brain and carry mnemonic information. However, due to the limitations in animal experiments, it is difficult to determine how these cells really contribute to behavior. Here, we show that time cells and ramping cells naturally emerge in the recurrent neural networks of deep reinforcement learning models performing simulated interval timing and working memory tasks, which have learned to estimate expected rewards in the future. We show that these cells do indeed carry information about time and items stored in working memory, but they contribute to behavior in large part by providing a dynamic representation on which policy can be computed. Moreover, the information that they do carry depends on both the task demands and the variables provided to the models. Our results suggest that time cells and ramping cells could contribute to temporal and mnemonic calculations, but the way in which they do so may be complex and unintuitive to human observers.

DERGCN: Dynamic-Evolving graph convolutional networks for human trajectory prediction

Pedestrian trajectory prediction is an increasingly important research area in applied autonomous driving and social robotics. Effectively modeling the intricate interactions between pedestrians is paramount for improving trajectory prediction accuracy. However, when using Graph Neural Networks(GNNs) to model these interactions, fixed interactions tend to remain, preventing the graph model from making adaptive adjustments and thus resulting in significant discrepancies between the predicted and true trajectories. In this study, we propose a Dynamic-Evolving Relative Graph Convolutional Network(DERGCN) to predict the future trajectories of pedestrians. The network model captures the dynamically evolving pedestrian interactions and incorporates an evolving mechanism to simulate them. In addition, with a relative temporal encoding strategy employed to improve the dynamics of the graph further, our policy network yielded an improved predictive performance when tested on two challenging datasets.

The dual role of time perception in trauma-exposed individuals: A conceptual review.

This comprehensive review seeks to integrate knowledge on the dual role of time as a reactive and a constructive measure with literature on the distinctive encoding of traumatic memories. First, we discuss the dual role of time. Later, we show how encoding traumatic events may lead to chronic alteration in time perception. Finally, we review the potential of temporal metacognitive awareness as a therapeutic avenue to rectify chronic time dilation following trauma, ultimately mitigating posttraumatic symptoms. A systematic search of electronic databases was conducted using four main terms: time perception, temporal encoding of traumatic memories, temporal metacognitive awareness, and temporal learning tasks as clinical interventions. The review proposes that the interplay between the dual roles of time-reactive and constructive-alongside the elemental encoding of traumatic events can give rise to a self-perpetuating cycle. Within this cycle, overgeneralized fear could lead to neutral stimuli triggering and fortifying time dilation, thus contributing to the maintenance of posttraumatic stress disorder (PTSD) symptoms. Furthermore, we propose that cultivating temporal metacognitive awareness could potentially yield a positive impact on time dilation by embracing a more adaptable learning approach-one that places less emphasis on external signals and does not necessitate direct engagement with traumatic content. Strengthened temporal awareness might serve to mitigate chronic time dilation, potentially leading to a reduction in PTSD symptoms. The review emphasizes the need for further research to examine whether enhancing temporal metacognitive awareness for time duration may offer an innovative and effective avenue for alleviating PTSD symptoms in trauma-exposed individuals. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

A Spatio-Temporal Encoding Neural Network for Semantic Segmentation of Satellite Image Time Series

Remote sensing image semantic segmentation plays a crucial role in various fields, such as environmental monitoring, urban planning, and agricultural land classification. However, most current research primarily focuses on utilizing the spatial and spectral information of single-temporal remote sensing images, neglecting the valuable temporal information present in historical image sequences. In fact, historical images often contain valuable phenological variations in land features, which exhibit diverse patterns and can significantly benefit from semantic segmentation tasks. This paper introduces a semantic segmentation framework for satellite image time series (SITS) based on dilated convolution and a Transformer encoder. The framework includes spatial encoding and temporal encoding. Spatial encoding, utilizing dilated convolutions exclusively, mitigates the loss of spatial accuracy and the need for up-sampling, while allowing for the extraction of rich multi-scale features through a combination of different dilation rates and dense connections. Temporal encoding leverages a Transformer encoder to extract temporal features for each pixel in the image. To better capture the annual periodic patterns of phenological phenomena in land features, position encoding is calculated based on the image’s acquisition date within the year. To assess the performance of this framework, comparative and ablation experiments were conducted using the PASTIS dataset. The experiments indicate that this framework achieves highly competitive performance with relatively low optimization parameters, resulting in an improvement of 8 percentage points in the mean Intersection over Union (mIoU).

A Shape-constrained Transfer Temporal Transformer Network for remaining useful life prediction of rotating machines

Predicting remaining useful life (RUL) of rotating machines can promote predictive maintenance and improve the mechanical system reliability. This paper proposes a Shape-constrained Transfer Temporal Transformer Network (SC3TN) for RUL prediction across different rotating machines. The disentangled representation learning is utilized to extract invariant features across different domains. Health indexes are constructed with invariant features considering shape constraints and all previous health states. The operating time is encoded by a Temporal Encoding in predicting process. The SC3TN is tested on two tasks, namely RUL prediction across different working conditions and different equipment. Compared to state-of-the-art methods, SC3TN reduces the mean absolute error by 4.94% and 5.47% and improves the score by 8.5% and 20.83% on two tasks. The experiments show that the proposed method can achieve more accurate RUL prediction than existing methods, which demonstrates the potential of the proposed method for predicting RUL without collecting degradation data in advance.

Neural Network-Based Solar Irradiance Forecast for Edge Computing Devices

Aiming at effectively improving photovoltaic (PV) park operation and the stability of the electricity grid, the current paper addresses the design and development of a novel system achieving the short-term irradiance forecasting for the PV park area, which is the key factor for controlling the variations in the PV power production. First, it introduces the Xception long short-term memory (XceptionLSTM) cell tailored for recurrent neural networks (RNN). Second, it presents the novel irradiance forecasting model that consists of a sequence-to-sequence image regression NNs in the form of a spatio-temporal encoder–decoder including Xception layers in the spatial encoder, the novel XceptionLSTM in the temporal encoder and decoder and a multilayer perceptron in the spatial decoder. The proposed model achieves a forecast skill of 16.57% for a horizon of 5 min when compared to the persistence model. Moreover, the proposed model is designed for execution on edge computing devices and the real-time application of the inference on the Raspberry Pi 4 Model B 8 GB and the Raspberry Pi Zero 2W validates the results.

A novel algorithm for full-coverage daily aerosol optical depth retrievals using machine learning-based reconstruction technique

The ubiquitous missing values in the satellite-derived aerosol optical depth (AOD) products have always been a challenge for spatial and temporal analysis. To address this concern, we propose a novel data-driven model to attain the full-coverage daily AOD dataset with 0.01° spatial resolution in the Guangdong-Hong Kong-Macao Greater Bay Area (hereafter GBA) from 2010 to 2021. Firstly, the missing values of top-of-atmosphere (TOA) reflectance and surface reflectance of Moderate Resolution Imaging Spectroradiometer (MODIS) caused by cloud contamination, were reconstructed using the Data Interpolating Empirical Orthogonal Functions (DINEOF). Subsequently, a new model was developed for the estimation of AOD which integrates the geographical and temporal encodings into the Light Gradient Boosting Machine (LightGBM) with the inputs of reconstructed TOA/surface reflectance and other influencing variables like meteorological and geographical factors. Results showed that the derived gap-free AOD dataset outperforms the MODIS Multi-Angle Implementation of Atmospheric Correction (MAIAC) AOD product and agrees well with the ground-based observations, achieving an index of agreement (IOA) of 0.88, R of 0.84, root mean square error (RMSE) of 0.19 and mean absolute error (MAE) of 0.14. Moreover, the derived AOD dataset presents consistent temporal patterns with in-situ measurements, but with more spatial details than other gapless AOD datasets, i.e., Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2). Overall, this study has developed a promising meteorological framework for the estimation of full-coverage AOD, which can also be applied over other regions. The derived long-term full-coverage daily AOD dataset can also be used for other applications related to climate change, air quality and ecosystem assessment.

Super-resolution non-line-of-sight imaging based on temporal encoding.

Non-line-of-sight (NLOS) imaging techniques have the ability to reconstruct objects beyond line-of-sight view, which would be useful in a variety of applications. In transient NLOS techniques, a fundamental problem is that the time resolution of imaging depends on the single-photon timing resolution (SPTR) of a detector. In this paper, a temporal super-resolution method named temporal encoding non-line-of-sight (TE-NLOS) is proposed. Specifically, by exploiting the spatial-temporal correlation among transient images, high-resolution transient images can be reconstructed through modulator encoding. We have demonstrated that the proposed method is capable of reconstructing transient images with a time resolution of 20 picoseconds from a detector with a limited SPTR of approximately nanoseconds. In systems with low time jitter, this method exhibits superior accuracy in reconstructing objects compared to direct detection, and it also demonstrates robustness against miscoding. Utilizing high-frequency modulation, our framework can reconstruct accurate objects with coarse-SPTR detectors, which provides an enlightening reference for solving the problem of hardware defects.

MAGSleepNet: Adaptively multi-scale temporal focused sleep staging model for multi-age groups

Deep learning-based automatic sleep staging methods have been widely applied for sleep scoring and sleep diagnosis. However, most methods consider only a single temporal scale when dealing with sleep signals. Furthermore, these methods are limited to target only a single-age group or single dataset. In this paper, we propose a multi-scale temporally focused sleep staging model, MAGSleepNet, which can be used for multi-age groups simultaneously. MAGSleepNet consists of (1) a group age classification (GAC) module that can offer a preliminary screening on epidemic estimation of multiple age, (2) a dimensional expansion module (DEM) that can expand the dimension of the input signals, (3) a sequential multi-scale convolutional neural network (SMCNN) that extracts multi-scale features and short-time temporal information, and (4) sequence temporal encoder (STE) that extracts sequential temporal information. In addition, two auxiliary tasks are used to complement the short-time temporal information and to reassign the probabilities of different age groups to enhance the model robustness, respectively. The MAGSleepNet is evaluated in adult, child and infant, tested on MASS, CHAT, and CHFU datasets with accruacy of 86.7%, 80.1% and 66.5%, outperforming the state-of-the-art methods. Based on the excellent performance of the proposed method, it is expected to pave the way for automatic sleep staging methods with strong generalizability for multiple age groups.

NTformer: Near Time Transformer for multi-step prediction of wellhead pressure in fracturing operations

Fracturing process technology is a major factor in the effectiveness of fracturing for increasing production. One of the most critical issues during the construction of fracturing is the control of pressure variation, as excessive pressure can lead to serious accidents such as fracturing fluid leakage and well-bore control loss. To prevent accidents and improve operational efficiency, it is necessary to predict the future multi-step fracturing pressure in advance. Since fracturing operations are a process based on continuous changes in time dimensions, and their feature information has a high correlation in time series, this article optimizes a Transformer network with a serialization structure for wellhead pressure prediction, called Near Time Transformer (NTformer), which can effectively forecast pressure values across multiple time steps without relying on intricate feature engineering or domain-specific knowledge. Firstly, data cleaning and temporal encoding are performed on the original data to reduce the complexity of features at different stages and solve the problem of data temporal misalignment. To better learn from features, a feature conversion mechanism is proposed that the data features after embedding are divided into domain feature and wave feature. Further, utilizing the attention concept to spatially correlate feature information, and using the Transformer structure to transform features to achieve forecasting of future multi-step pressure. Finally, the idea of regularization is used to limit the parameters of the model to avoid over-fitting. Experimental results show that the method has a high prediction accuracy and can satisfy the accuracy requirements of the field application, offering a new ancillary method for improving the efficiency of oil and gas well fracturing construction and preventing safety accidents.

A multi-modal vehicle trajectory prediction framework via conditional diffusion model: A coarse-to-fine approach

Accurate prediction of the future motion of surrounding vehicles is crucial for ensuring the safety of motion planning in autonomous vehicles. However, it is challenging to perform because of the complex interactions between vehicles. In this study, we propose a novel multi-modal vehicle trajectory prediction framework that utilizes a coarse-to-fine approach by first generating initial trajectory proposals with a conditional variational autoencoder (CVAE) and then refining them using the conditional diffusion model. We first address the problems of data sparsity and irregularity by converting the trajectory coordinates to the Frenet coordinate system. To enable the model to better distinguish between different features, we employ a temporal encoder to extract trajectory features and a long short-term memory (LSTM) network to extract lane features. The target lane evaluator is utilized to calculate the attention weights for each lane candidate, thereby generating more deterministic future trajectories. We then use the CVAE to generate initial multiple trajectory proposals based on the surrounding scene context and the trajectory features of the target vehicle. Finally, we formulate the trajectory refinement task as a reverse process of the conditional diffusion model, which effectively enhances the multi-modal trajectory proposals. Experiments conducted on Argoverse and nuScenes demonstrate that our method outperforms state-of-the-art methods in some evaluation metrics while achieving the optimal trade-off between predictive accuracy and efficiency. Field experiments conducted in urban environments further validate the effectiveness of the proposed approach.

Unsupervised Retrieval Based Multivariate Time Series Anomaly Detection and Diagnosis with Deep Binary Coding Models

Retrieval based multivariate time series anomaly detection and diagnosis refer to identifying abnormal status in certain time steps and pinpointing the root cause input variables, i.e., sensors, by comparing a current time series segment and its relevant ones that are retrieved from huge amount of historical data. Binary coding with a deep neural network can be applied to reduce the computational cost of the retrieval tasks. However, it is hard to pinpoint the root cause sensors that are responsible for the anomaly, once multivariate time series segments are transformed into binary codes. In this paper, we present an unsupervised retrieval based multivariate time series anomaly detection and diagnosis method with deep binary coding model, to secure both efficiency and explainability. Specifically, we first transform input multivariate time series segments into low dimensional features with a temporal encoder. Subsequently, two hash functions predict two binary codes with different lengths from each feature. The binary codes with two different lengths can contribute to accelerate both anomaly detection and anomaly diagnosis. Experiments performed on datasets from various domains including real optical network, demonstrate the effectiveness and efficiency of the proposed method.