Real-world GPS Research Articles

GPS TRAJECTORY CLUSTERING FOR SPATIO – TEMPORAL BEHAVIOR ANALYSIS: THE APPLICATION OF HEATMAP TECHNIQUES AND SPATIO- TEMPORAL DUAL GRAPH NEURAL NETWORK

The introduction of GPS technology has led to the creation of vast amounts of spatio-temporal data, which captures the movement patterns of different things. Efficient allocation of resources to ensure user satisfaction is a crucial factor in shaping the future of urban planning and development. It is required to comprehend the factors that can contribute to the creation of methods for studying user behaviours using a substantial number of persons within a brief timeframe. It is essential to employ appropriate clustering approaches to analyze this data in order to comprehend spatio-temporal behaviours.Heatmaps offer a graphical display of changes in density across both location and Time, making them a user-friendly tool for initial data analysis and identifying areas of high activity. The Spatio-Temporal Dynamic Graph Neural Network (ST-DGNN) utilizes graph neural networks to represent the intricate connections present in spatio-temporal data, encompassing both spatial interdependencies and temporal changes. Our methodology improves the accuracy and interpretability of trajectory clustering by integrating different methods. The suggested method has been shown to identify relevant clusters effectively and reveal noteworthy spatio-temporal characteristics through experimental analysis on real-world GPS datasets. The research utilizes a dataset comprising 182 users for analysis. Numerous measures are taken to boost the clustering accuracy of the applied techniques, including addressing missing values and outliers. Additionally, this thesis introduces a framework for time estimation based on graph-based deep learning, termed Spatio-Temporal Dual Graph Neural II Networks (STDGNN). The method entails constructing node-level and edge-level graphs that depict the adjacency connections between intersections and road segments. The results showed a number of cluster changes in each period of time dependent on move users and period; for example, the (2592) cluster of period one hour.

Towards effective, robust and utility-preserving watermarking of GPS trajectories

Personal GPS trajectory is essential for businesses and emerging data markets due to its relevance in various data-driven methods, including traffic forecasting, accident prediction, and profiling driving behavior. Watermarking is a method that facilitates verification of data ownership and authenticity by embedding provenance information into the data. Whereas watermarking is commonly adopted in the image and audio domains, only a few initial watermarking methods exist for GPS trajectory data. GPS trajectory watermarking is particularly challenging due to the spatio-temporal data properties and easiness of data modification. As a result, existing watermarking methods often embed only minimal provenance information, lack robustness, and can fail to preserve data utility for downstream applications. In this work, we propose W-Trace - a novel, effective, robust, and utility-preserving GPS trajectory watermarking method. W-Trace transforms a GPS trajectory into a complex domain and applies the Fourier transformation to decompose the trajectory into the frequency representation. W-Trace embeds watermarks in the frequency representation and verifies them in a spatiotemporally-aware procedure. We demonstrate the effectiveness, robustness, and utility of the proposed W-Trace approach in realistic settings using real-world GPS trajectory datasets. In contrast to the baselines, the proposed W-Trace approach is robust to a wide range of trajectory modifications while preserving the GPS trajectory characteristics required for the downstream applications.

Vector-Indistinguishability: Location Dependency Based Privacy Protection for Successive Location Data

With the wide use of GPS enabled devices and Location-Based Services, location privacy has become an increasingly worrying challenge to our community. Existing approaches provide solid bases for addressing this challenge. However, they mainly focus on independent location perturbation or whole trajectory perturbation with little attention to location dependency based perturbation between two successive locations. This may result in that perturbed successive locations lose mutual distance and direction dependency, which in turn can lead to significant data utility loss. To address this problem, we propose a new location dependency based privacy notion named as vector-indistinguishability (vector-ind). Vector-ind defines a vector to represent the dependency relationship between two successive locations. Correspondingly, it consists of distance-indistinguishability for distance dependency and direction-indistinguishability for direction dependency. Noise generation for applying Differential Privacy is based on the distance and direction, hence can reflect the location dependency to ensure data utility after perturbation. We also present four mechanisms to achieve vector-ind notion. Finally, we evaluate the empirical privacy and utility of vector-ind in real-world GPS data to demonstrate how our proposed mechanisms for vector-ind can protect location privacy with high data utility in successive location data.

Sphere2Vec: A general-purpose location representation learning over a spherical surface for large-scale geospatial predictions

Generating learning-friendly representations for points in space is a fundamental and long-standing problem in machine learning. Recently, multi-scale encoding schemes (such as Space2Vec and NeRF) were proposed to directly encode any point in 2D or 3D Euclidean space as a high-dimensional vector, and has been successfully applied to various (geo)spatial prediction and generative tasks. However, all current 2D and 3D location encoders are designed to model point distances in Euclidean space. So when applied to large-scale real-world GPS coordinate datasets (e.g., species or satellite images taken all over the world), which require distance metric learning on the spherical surface, both types of models can fail due to the map projection distortion problem (2D) and the spherical-to-Euclidean distance approximation error (3D). To solve these problems, we propose a multi-scale location encoder called Sphere2Vec which can preserve spherical distances when encoding point coordinates on a spherical surface. We developed a unified view of distance-reserving encoding on spheres based on the Double Fourier Sphere (DFS). We also provide theoretical proof that the Sphere2Vec encoding preserves the spherical surface distance between any two points, while existing encoding schemes such as Space2Vec and NeRF do not. Experiments on 20 synthetic datasets show that Sphere2Vec can outperform all baseline models including the state-of-the-art (SOTA) 2D location encoder (i.e., Space2Vec) and 3D encoder NeRF on all these datasets with up to 30.8% error rate reduction. We then apply Sphere2Vec to three geo-aware image classification tasks - fine-grained species recognition, Flickr image recognition, and remote sensing image classification. Results on 7 real-world datasets show the superiority of Sphere2Vec over multiple 2D and 3D location encoders on all three tasks. Further analysis shows that Sphere2Vec outperforms other location encoder models, especially in the polar regions and data-sparse areas because of its nature for spherical surface distance preservation. Code and data of this work are available at https://gengchenmai.github.io/sphere2vec-website/.

Predicting electric vehicle charging demand using a heterogeneous spatio-temporal graph convolutional network

Short-term Electric Vehicle (EV) charging demand prediction is an essential task in the fields of smart grid and intelligent transportation systems, as understanding the spatiotemporal distribution of charging demand over the next few hours could help operators of charging stations and the grid to take measures (e.g., dynamic pricing) in response to varying charging demand. This study proposed a heterogeneous spatial–temporal graph convolutional network to predict the EV charging demand at different spatial and temporal resolutions. Specifically, we first learned the spatial correlations between charging regions by constructing heterogeneous graphs, i.e., a geographic graph and a demand graph. Then, we used graph convolutional layers and gated recurrent units to extract spatio-temporal features in the observations. Further, we designed a region-specific prediction module that grouped regions based on graph embedding and point of interest (POI) data for prediction. We used a large real-world GPS dataset which contained over 76,000 private EVs in Beijing for model training and validation. The results showed that, compared with recently popular spatio-temporal prediction methods, the proposed model had superior prediction accuracy and steady performance at different scales of regions. In addition, we conducted ablation studies and hyperparameter sensitivity tests. The results suggested that incorporating the demand graph and geographic graph could help improve model performance.

Rotation invariant GPS trajectory mining

Mining of GPS trajectories of moving vehicles and devices can provide valuable insights into urban systems, planning and operational applications. Understanding object motion often requires that the spatial-temporal matching of trajectories be invariant to shifting, scaling and rotation. To this end, Procrustes analysis enables to transform one data set of a trajectory to represent another set of data as closely as possible. We propose a novel shift-scale-rotation invariant Procrustes distance metric based on the Kabsch algorithm, which calculates the optimal rotation matrix by minimizing the root-mean squared deviation between two paired sets of points of trajectories or trajectory segments. We present two novel runtime efficient algorithms which are based on our proposed distance metric: 1) the sliding-shifting-scaling-Kabsch-rotation (S3KR) algorithm for detecting recurring short query patterns in longer motion trajectories and 2) a novel time series subsequence clustering algorithm to group GPS trajectory data and to discover prototypical patterns. We demonstrate the potential of our proposed sliding Procrustes analysis algorithms by applying it on real-world GPS trajectories collected in urban and rural areas from different transport modes, as well as on nautical GPS trajectories. We also demonstrate that our methods outperform the state of the art in accuracy and runtime on synthetic and real world data.

Driving Maneuver Anomaly Detection Based on Deep Auto-Encoder and Geographical Partitioning

This paper presents GeoDMA , which processes the GPS data from multiple vehicles to detect anomalous driving maneuvers, such as rapid acceleration, sudden braking, and rapid swerving. First, an unsupervised deep auto-encoder is designed to learn a set of unique features from the normal historical GPS data of all drivers. We consider the temporal dependency of the driving data for individual drivers and the spatial correlation among different drivers. Second, to incorporate the peer dependency of drivers in local regions, we develop a geographical partitioning algorithm to partition a city into several sub-regions to do the driving anomaly detection. Specifically, we extend the vehicle-vehicle dependency to road-road dependency and formulate the geographical partitioning problem into an optimization problem. The objective of the optimization problem is to maximize the dependency of roads within each sub-region and minimize the dependency of roads between any two different sub-regions. Finally, we train a specific driving anomaly detection model for each sub-region and perform in-situ updating of these models by incremental training. We implement GeoDMA in Pytorch and evaluate its performance using a large real-world GPS trajectories. The experiment results demonstrate that GeoDMA achieves up to 8.5% higher detection accuracy than the baseline methods.

Capitalize Your Data: Optimal Selling Mechanisms for IoT Data Exchange

More and more IoT data is being traded online in cloud-based data marketplaces due to the fast-growing market demand. Within the current data selling mechanisms, data consumers have difficulties in making purchasing decisions due to uncertain IoT data quality and inflexible pricing interface. To resolve these issues, potential solutions could be to launch data demonstrations and release free sampling data to reduce the uncertainty about data quality, and to charge based on the volume of data actually used to enable flexible pricing. However, there is still no clear understanding of economic benefits of these mechanisms. In this paper, we design the optimal data selling mechanisms for IoT data exchange, and derive the following two results. First, whether to deploy a data demonstration and how much free sampling data to release depend on the extent of data consumers' inaccuracy perceptions for data quality, which varies over a wide range in IoT applications. We found that the data vendor has no incentive to conduct these strategies if data consumers extremely overestimate data quality. Second, although flexible data pricing mechanisms provide convenience for real-time and streaming IoT data exchange, it brings less economic benefits to the data vendor compared with the fixed pricing scheme, which sells the whole data set with a fixed price. We evaluate the optimal selling mechanisms on a real-world Taxi GPS data set, and evaluation results verify the insights derived from our theoretical analysis.

Graph-based representation for identifying individual travel activities with spatiotemporal trajectories and POI data

Individual daily travel activities (e.g., work, eating) are identified with various machine learning models (e.g., Bayesian Network, Random Forest) for understanding people’s frequent travel purposes. However, labor-intensive engineering work is often required to extract effective features. Additionally, features and models are mostly calibrated for individual trajectories with regular daily travel routines and patterns, and therefore suffer from poor generalizability when applied to new trajectories with more irregular patterns. Meanwhile, most existing models cannot extract features to explicitly represent regular travel activity sequences. Therefore, this paper proposes a graph-based representation of spatiotemporal trajectories and point-of-interest (POI) data for travel activity type identification, defined as Gstp2Vec. Specifically, a weighted directed graph is constructed by connecting regular activity areas (i.e., zones) detected via clustering individual daily travel trajectories as graph nodes, with edges denoting trips between pairs of zones. Statistics of trajectories (e.g., visit frequency, activity duration) and POI distributions (e.g., percentage of restaurants) at each activity zone are encoded as node features. Next, trip frequency, average trip duration, and average trip distance are encoded as edge weights. Then a series of feedforward neural networks are trained to generate low-dimensional embeddings for activity nodes through sampling and aggregating spatiotemporal and POI features from their multihop neighborhoods. Activity type labels collected via travel surveys are used as ground truth for backpropagation. The experiment results with real-world GPS trajectories show that Gstp2Vec significantly reduces feature engineering efforts by automatically learning feature embeddings from raw trajectories with minimal prepossessing efforts. It not only enhances model generalizability to receive higher identification accuracy on test individual trajectories with diverse travel patterns, but also obtains better efficiency and robustness. In particular, our identification of the most common daily travel activities (e.g., Dwelling and Work) for people with diverse travel patterns outperforms state-of-the-art classification models.

Estimating fundamental diagram for multi-modal signalized urban links with limited probe data

Being one of the most classic concepts in the traffic flow theory, the fundamental diagram (FD) describes the relationship between average flow and average density of link-level traffic flow dynamics. Inductive loop detectors or closed-circuit television are commonly used for FD estimations and they are known to have cost-effective and accuracy issues. Thanks to the GPS-enabled smartphones and GPS-equipped probe vehicles, high temporal and spatial resolution traffic data are available which enable traffic condition inference over time and space continuously. Several existing studies have explored FD estimation algorithms on freeways where flow is generally uninterrupted and uni-modal, based on GPS trajectory data. These developments motivate this study, where the objective is to extend the application to multi-modal and interrupted environment, i.e., urban signalized areas. In this paper, an estimation method is developed to capture the FD of multi-modal traffic streams on signalized urban links. The proposed algorithm is empirically tested using real-world GPS datasets collected on a signalized arterial road in Shenzhen City. Promising results show that the proposed algorithm is capable to estimate the FD under such condition. Furthermore, impacts of multi-modal traffic and signal operations on the FD estimation are analyzed and discussed.

Discovering urban functional zones from biased and sparse points of interests and sparse human activities

With rapid development of socio-economics, the task of discovering functional zones becomes critical to better understand the interactions between social activities and spatial locations. In this paper, we propose a framework to discover the real functional zones from the biased and extremely sparse Point of Interests (POIs). To cope with the bias and sparsity of POIs, the unbiased inner influences between spatial locations and human activities are introduced to learn a balanced and dense latent region representation. In addition, a spatial location based clustering method is also included to enrich the spatial information for latent region representation and enhance the region functionality consistency for the fine-grained region segmentation. Moreover, to properly annotate the various and fine-grained region functionalities, we estimate the functionality of the regions and rank them by the differences between the normalized POI distributions to reduce the inconsistency caused by the fine-grained segmentation. Thus, our whole framework is able to properly address the biased categories in sparse POI data and explore the true functional zones with a fine-grained level. To validate the proposed framework, a case study is evaluated by using very large real-world users GPS and POIs data from city of Raleigh. The results demonstrate that the proposed framework can better identify functional zones than the benchmarks, and, therefore, enhance understanding of urban structures with a finer granularity under practical conditions.

SafeMove: monitoring seniors with mild cognitive impairments using deep learning and location prediction

Due to society aging, age-related issues such as mild cognitive impairments (MCI) and dementia are attracting the attention of health professionals, scientists and governments. Seniors suffering from such impairments notice a slight deterioration in their cognitive abilities, which may lead to memory loss and behavioural disorders. In consequence, such seniors refrain from doing their everyday outdoor activities. Technology, e.g. smartphones, wearables and artificial intelligence, can provide seniors and their relatives with a variety of monitoring tools. In a nutshell, locations are analysed and, under specific situations, alarms are raised so that caregivers urgently informed. In this context, the discovery and prediction of trajectories and behaviours play a key role in deploying effective monitoring solutions. In this paper, we present a real-time smartphone-based monitoring system, called SafeMove, to discover and predict elderly people behaviours by analyzing outdoor trajectories. This is achieved by firstly analysing the elder’s mobility data previously collected using the proposed model called SpaceTime-Convolutional Neural Network (ST-CNN) in order to predict the most popular locations he/she might visit in the next time. Based on the predicted locations, the elder can be monitored in bounded region. Time and space-related variables, such as the distance traversed, the direction of the movements and the time spent, are analyzed in our abnormal behaviour detection (ABD) model that takes advantage of recurrent neural networks (RNNs). The effectiveness and the efficiency of our system for predicting the next location and detection the abnormal behaviors are evaluated using different datasets comprising real-world GPS trajectories.

Impacts of Regional Speed Control Strategy Based on Macroscopic Fundamental Diagram on Energy Consumption and Traffic Emissions: A Case Study of Beijing.

Numerous studies shown that particulate matter in the ambient environment has a significant impact on the health of the respiratory system. To understand the interrelationships between urban built environment, transportation operations and health, this study proposes an innovative approach that uses real-world GPS datasets to calculate energy consumption and emissions from transportation. The experiment used the traffic operation state in the Fourth Ring Road of Beijing as the research object and tested the impact of using the Regional speed optimization (RSO) strategy based on Macroscopic Fundamental Diagram (MFD) on energy consumption and emissions during peak hours. The impact of traffic emission on the health of roadside pedestrians is also considered. Changes in PM2.5 concentrations around four different built-up areas were calculated and compared. The computational experiments indicate that the PM2.5 pollutants exhausted by the traffic on the Ring Road during peak hours can reach up to 250 μg/m3, while the traffic emission on general roads near residential areas is only 50 μg/m3. Adopting Regional speed optimization can reduce the energy consumption of the road network by up to 18.8%. For roadside runners, the PM2.5 inhalation caused by night running in commercial and recreational areas is about 1.3-2.6 times that of night running in residential areas. Compared with morning or night running, the risk of respiratory disease caused by PM2.5 inhalation was about 10.3% higher than commuter running behavior. The research results provide a useful reference for energy conservation and emission reduction control strategies for different road types in cities and help existing cities to establish a traveler health evaluation system caused by traffic operation.

Potential of Using Medium Electric Vehicle Fleet in a Commercial Enterprise Transport in Germany on the Basis of Real-World GPS Data

The intensive electrification of the automotive sector means that the energy system must be able to adapt to the current market situation. The increase in energy demand is a major factor associated with electric vehicles. The study analyzed the operation of a grid-connected facility operating a vehicle fleet providing transport services in the region Halle/Saale, Germany. Measurement data were used in the analysis, including global positioning system data of the vehicles and technical data, including average fuel consumption on a given route section, daily load demand of the industrial facility, and energy generation from photovoltaics. This paper shows the impact of using a battery electric vehicles (BEVs) fleet in the load distribution for the industrial facility considered. The NEDC energy consumption profile for the Nissan e-NV200 were used in this study. Furthermore, the paper presented simulation results allowing one to determine the usage potential, energy demand, and consumption of EVs using real data, reliably representing the processes related to EV daily use. The measurement data were captured using available specialized equipment: Dako-Key (GPS data), PV power generation (Siemens 7KM PAC4200), and load (Janitza UMG 604-Pro) in September, 2018. On this basis, it is possible to identify the effects and variations in load on the power grid during the replacement of combustion vehicle fleets used currently by EVs for the provision of transport services. Three models were presented, making it possible to calculate changes in energy demand for each scenario. In the first model, EVs were charged exclusively from the distribution network. In the second, the energy generation from a renewable source was considered and the possibility of compensating the energy demand of the vehicles from this source was demonstrated. In the third model, the daily load profile and the period of maximum load in the electricity grid were considered. The results are presented in graphical and tabular form. Finally, the potential of using an EV fleet to increase the functionality of a modern industry object was determined and discussed. Based on data for the adopted scenarios, electrification of transport can increase demand for energy by 40.9% for individual enterprises. The electrification of the automotive sector will increase the instantaneous energy demand of businesses, forcing the integration of renewable energy sources during designing new invests.

An eco-score system incorporating driving behavior, vehicle characteristics, and traffic conditions

This study employs two eco-scoring methods to evaluate driving behavior based on real-world GPS data collected from drivers using an insurance mobile application in two provinces of Canada, Ontario and Quebec. Method 1 provides an eco-score based on greenhouse gas emissions (CO2eq) and energy consumption considering vehicle characteristics. For electric and hybrid vehicles, an equivalent fuel efficiency, which is defined as the amount of energy consumed by alternative fuel vehicles to that of traditional gas-powered cars, is calculated for each trip record and each alternative vehicle model. Method 2 improves the algorithm by considering on-road traffic conditions and scoring trips relative to other trips experiencing similar traffic conditions. Our results demonstrate that representativeness of the eco-score system is improved after incorporating traffic conditions as trips will less likely be penalized for stop-and-go driving in congested conditions or receive high eco-scores although they have relatively low average speed on uncongested highways.

Trustworthy and Cost-Effective Cell Selection for Sparse Mobile Crowdsensing Systems

Cell selection is a critical issue in sparse mobile crowdsensing (MCS) systems. However, the sensing cost heterogeneity among different cells (subareas) has long been ignored by existing works. Moreover, the data provided by participants are not always trustworthy, and some malicious participants may intend to launch data positioning attacks, which raises a new challenge for cell selection. In this paper, to address these issues, we propose a trustworthy and cost-effective cell selection (TCECS) framework that takes cell heterogeneity and malicious participants into consideration simultaneously. To this end, we first offer to utilize an iterative statistical spatial interpolation technique to identify trustworthy participants with the help of a small portion of dedicated sensors. Furthermore, we employ the regularized mutual coherence (RMC) in compressive sensing (CS) theory to characterize the contribution to inference accuracy of measurements submitted by different trustworthy participants. Finally, the cell selection strategy, which consumes the least sensing cost while satisfying a given sensing quality, is determined via an RMC-constrained optimization problem. Extensive experiments on a real-world taxi GPS dataset demonstrate that the proposed approach can mitigate the adverse effects of malicious participants and outperforms the baselines with less sensing cost for the same required sensing quality.

Discovering Traffic Anomaly Propagation in Urban Space Using Enhanced Traffic Change Peaks

Discovering traffic anomaly propagation enables a thorough understanding of traffic anomalies and dynamics. Existing methods, such as Outlier-Tree, are not accurate to find out the trend of abnormal traffic for two reasons. First, they discover the propagation pattern based on the detected traffic anomalies. The imperfection of the detection method itself may introduce false anomalies and miss the real anomaly. Second, they develop a propagation tree of anomalies by searching continuous spatial and temporal outlier neighborhoods rather than considering from a global perspective, and thus cannot form a complete propagation tree if a spatial or temporal gap exists. In this paper, we propose a novel discovering traffic anomaly propagation method using the mesh data and enhanced traffic change peaks (en-TCP) to visualize the change of traffic anomalies (e.g., an area where vehicles are gathering or evacuating) and thus accurately capture traffic anomaly propagation. Inspired by image processing techniques, the GPS trajectory dataset in each time bin can be converted to one grid traffic image and be stored in the grid density matrix, in which the grid cell corresponds to the pixel and the density of grid cells corresponds to the Gray level ([Formula: see text]) of pixels. An enhanced adaptive filter is developed to generate traffic change graph sequences from grid traffic images in consecutive periods, and clustering en-TCP in a continuous period is to discover the propagation of traffic anomalies. The accuracy and effectiveness of the proposed method have been demonstrated using a real-world GPS trajectory dataset.

Tensor-Train-Based High-Order Dominant Eigen Decomposition for Multimodal Prediction Services

By leveraging neoteric analytical techniques associated with big data, numerous new data-focused computation and service models have flourished in service computing systems. Accurate future predictions based on tensor-based multivariate Markov models can vigorously support enterprise decisions. However, the computation efficiency and quick response of tensor-based multimodal prediction approach are seriously restricted by the curse of dimensionality arising from high-order tensor. Therefore, to alleviate the problem, this paper focuses on proposing a tensor-train (TT)-based computation approach with its scalable implementation for high-order dominant eigen decomposition (HODED) in multivariate Markov models. First, we present a TT-based Einstein product directly based on decomposed TT cores and guarantee that the result remains TT format. Then, we put forward a scalable implementation for TT-based Einstein product in a distributed or parallel manner. Afterwards, we propose a scalable TT-based HODED (TT-HODED) algorithm and a multimodal accurate prediction algorithm. Furthermore, a TT-based big data processing and services framework is presented to provide accurate proactive services. Experimental results based on real-world GPS trajectory dataset demonstrate that TT-HODED algorithm can significantly improve the computation efficiency and reduce the running memory on the premise of guaranteeing the almost consistent prediction accuracy compared to the original HODED algorithm.

Limitations of Recursive Logit for Inverse Reinforcement Learning of Bicycle Route Choice Behavior in Amsterdam

Used for route choice modelling by the transportation research community, recursive logit is a form of inverse reinforcement learning. By solving a large-scale system of linear equations recursive logit allows estimation of an optimal (negative) reward function in a computationally efficient way that performs for large networks and a large number of observations. In this paper we review examples of recursive logit and inverse reinforcement learning models applied to real world GPS travel trajectories and explore some of the challenges in modeling bicycle route choice in the city of Amsterdam using recursive logit as compared to a simple baseline multinomial logit model with environmental variables. We discuss conceptual, computational, numerical and statistical issues that we encountered and conclude with recommendation for further research.

Tensor-Train-Based Higher Order Dominant Z-Eigen Decomposition for Multi-Modal Prediction and Its Cloud/Edge Implementation

Accurate multi-modal predictions can vigorously support people's wise decisions. Predicting the future by leveraging eigentensor based multivariate Markov model or Z-eigenvector based multi-order Markov model has flourished in recent years. However, there is no integrated solution by combining multivariate Markov model, and multi-order Markov model with tensor-based calculation approach. Besides, the computation efficiency, and quick response of tensor-based calculation approach are seriously restricted by the curse of dimensionality arising from higher-order tensor. Therefore, this paper focuses on proposing a scalable tensor train (TT) based higher order dominant Z-eigen decomposition (HODZED) for multivariate multi-order Markov models under cloud/edge computing environments to provide quick accurate prediction. First, we propose a multivariate multi-order Markov model, and extend dominant Z-eigen decomposition to HODZED for calculating the dominant Z-eigentensor. Then, we propose two scalable TT-based HODZED (TT-HODZED), and improved TT-based HODZED (ITT-HODZED) algorithms to improve the computation efficiency. Afterwards, we present a multi-modal prediction algorithm based on the dominant Z-eigentensor. Experimental results based on the random dataset, and real-world GPS trajectory dataset demonstrate that TT-HODZED, and ITT-HODZED algorithms can significantly improve the computation efficiency, and reduce the running memory on the premise of guaranteeing the almost consistent prediction accuracy compared to the original HODZED algorithm.