60 research outputs found
Tensor Completion for Weakly-dependent Data on Graph for Metro Passenger Flow Prediction
Low-rank tensor decomposition and completion have attracted significant
interest from academia given the ubiquity of tensor data. However, the low-rank
structure is a global property, which will not be fulfilled when the data
presents complex and weak dependencies given specific graph structures. One
particular application that motivates this study is the spatiotemporal data
analysis. As shown in the preliminary study, weakly dependencies can worsen the
low-rank tensor completion performance. In this paper, we propose a novel
low-rank CANDECOMP / PARAFAC (CP) tensor decomposition and completion framework
by introducing the -norm penalty and Graph Laplacian penalty to model
the weakly dependency on graph. We further propose an efficient optimization
algorithm based on the Block Coordinate Descent for efficient estimation. A
case study based on the metro passenger flow data in Hong Kong is conducted to
demonstrate improved performance over the regular tensor completion methods.Comment: Accepted at AAAI 202
Networked Time Series Prediction with Incomplete Data
A networked time series (NETS) is a family of time series on a given graph,
one for each node. It has a wide range of applications from intelligent
transportation, environment monitoring to smart grid management. An important
task in such applications is to predict the future values of a NETS based on
its historical values and the underlying graph. Most existing methods require
complete data for training. However, in real-world scenarios, it is not
uncommon to have missing data due to sensor malfunction, incomplete sensing
coverage, etc. In this paper, we study the problem of NETS prediction with
incomplete data. We propose NETS-ImpGAN, a novel deep learning framework that
can be trained on incomplete data with missing values in both history and
future. Furthermore, we propose Graph Temporal Attention Networks, which
incorporate the attention mechanism to capture both inter-time series and
temporal correlations. We conduct extensive experiments on four real-world
datasets under different missing patterns and missing rates. The experimental
results show that NETS-ImpGAN outperforms existing methods, reducing the MAE by
up to 25%
Choose A Table: Tensor Dirichlet Process Multinomial Mixture Model with Graphs for Passenger Trajectory Clustering
Passenger clustering based on trajectory records is essential for
transportation operators. However, existing methods cannot easily cluster the
passengers due to the hierarchical structure of the passenger trip information,
including multiple trips within each passenger and multi-dimensional
information about each trip. Furthermore, existing approaches rely on an
accurate specification of the clustering number to start. Finally, existing
methods do not consider spatial semantic graphs such as geographical proximity
and functional similarity between the locations. In this paper, we propose a
novel tensor Dirichlet Process Multinomial Mixture model with graphs, which can
preserve the hierarchical structure of the multi-dimensional trip information
and cluster them in a unified one-step manner with the ability to determine the
number of clusters automatically. The spatial graphs are utilized in community
detection to link the semantic neighbors. We further propose a tensor version
of Collapsed Gibbs Sampling method with a minimum cluster size requirement. A
case study based on Hong Kong metro passenger data is conducted to demonstrate
the automatic process of cluster amount evolution and better cluster quality
measured by within-cluster compactness and cross-cluster separateness. The code
is available at https://github.com/bonaldli/TensorDPMM-G.Comment: Accepted in ACM SIGSPATIAL 2023. arXiv admin note: substantial text
overlap with arXiv:2306.1379
Modeling Heterogeneous Relations across Multiple Modes for Potential Crowd Flow Prediction
Potential crowd flow prediction for new planned transportation sites is a
fundamental task for urban planners and administrators. Intuitively, the
potential crowd flow of the new coming site can be implied by exploring the
nearby sites. However, the transportation modes of nearby sites (e.g. bus
stations, bicycle stations) might be different from the target site (e.g.
subway station), which results in severe data scarcity issues. To this end, we
propose a data driven approach, named MOHER, to predict the potential crowd
flow in a certain mode for a new planned site. Specifically, we first identify
the neighbor regions of the target site by examining the geographical proximity
as well as the urban function similarity. Then, to aggregate these
heterogeneous relations, we devise a cross-mode relational GCN, a novel
relation-specific transformation model, which can learn not only the
correlations but also the differences between different transportation modes.
Afterward, we design an aggregator for inductive potential flow representation.
Finally, an LTSM module is used for sequential flow prediction. Extensive
experiments on real-world data sets demonstrate the superiority of the MOHER
framework compared with the state-of-the-art algorithms.Comment: Accepted by the 35th AAAI Conference on Artificial Intelligence (AAAI
2021
Spatiotemporal Tensor Completion for Improved Urban Traffic Imputation
Effective management of urban traffic is important for any smart city
initiative. Therefore, the quality of the sensory traffic data is of paramount
importance. However, like any sensory data, urban traffic data are prone to
imperfections leading to missing measurements. In this paper, we focus on
inter-region traffic data completion. We model the inter-region traffic as a
spatiotemporal tensor that suffers from missing measurements. To recover the
missing data, we propose an enhanced CANDECOMP/PARAFAC (CP) completion approach
that considers the urban and temporal aspects of the traffic. To derive the
urban characteristics, we divide the area of study into regions. Then, for each
region, we compute urban feature vectors inspired from biodiversity which are
used to compute the urban similarity matrix. To mine the temporal aspect, we
first conduct an entropy analysis to determine the most regular time-series.
Then, we conduct a joint Fourier and correlation analysis to compute its
periodicity and construct the temporal matrix. Both urban and temporal matrices
are fed into a modified CP-completion objective function. To solve this
objective, we propose an alternating least square approach that operates on the
vectorized version of the inputs. We conduct comprehensive comparative study
with two evaluation scenarios. In the first one, we simulate random missing
values. In the second scenario, we simulate missing values at a given area and
time duration. Our results demonstrate that our approach provides effective
recovering performance reaching 26% improvement compared to state-of-art CP
approaches and 35% compared to state-of-art generative model-based approaches
Tensor-variate machine learning on graphs
Traditional machine learning algorithms are facing significant challenges as the world enters the era of big data, with a dramatic expansion in volume and range of applications and an increase in the variety of data sources. The large- and multi-dimensional nature of data often increases the computational costs associated with their processing and raises the risks of model over-fitting - a phenomenon known as the curse of dimensionality. To this end, tensors have become a subject of great interest in the data analytics community, owing to their remarkable ability to super-compress high-dimensional data into a low-rank format, while retaining the original data structure and interpretability. This leads to a significant reduction in computational costs, from an exponential complexity to a linear one in the data dimensions.
An additional challenge when processing modern big data is that they often reside on irregular domains and exhibit relational structures, which violates the regular grid assumptions of traditional machine learning models. To this end, there has been an increasing amount of research in generalizing traditional learning algorithms to graph data. This allows for the processing of graph signals while accounting for the underlying relational structure, such as user interactions in social networks, vehicle flows in traffic networks, transactions in supply chains, chemical bonds in proteins, and trading data in financial networks, to name a few.
Although promising results have been achieved in these fields, there is a void in literature when it comes to the conjoint treatment of tensors and graphs for data analytics. Solutions in this area are increasingly urgent, as modern big data is both large-dimensional and irregular in structure. To this end, the goal of this thesis is to explore machine learning methods that can fully exploit the advantages of both tensors and graphs. In particular, the following approaches are introduced: (i) Graph-regularized tensor regression framework for modelling high-dimensional data while accounting for the underlying graph structure; (ii) Tensor-algebraic approach for computing efficient convolution on graphs; (iii) Graph tensor network framework for designing neural learning systems which is both general enough to describe most existing neural network architectures and flexible enough to model large-dimensional data on any and many irregular domains. The considered frameworks were employed in several real-world applications, including air quality forecasting, protein classification, and financial modelling. Experimental results validate the advantages of the proposed methods, which achieved better or comparable performance against state-of-the-art models. Additionally, these methods benefit from increased interpretability and reduced computational costs, which are crucial for tackling the challenges posed by the era of big data.Open Acces
STGC-GNNs: A GNN-based traffic prediction framework with a spatial-temporal Granger causality graph
The key to traffic prediction is to accurately depict the temporal dynamics
of traffic flow traveling in a road network, so it is important to model the
spatial dependence of the road network. The essence of spatial dependence is to
accurately describe how traffic information transmission is affected by other
nodes in the road network, and the GNN-based traffic prediction model, as a
benchmark for traffic prediction, has become the most common method for the
ability to model spatial dependence by transmitting traffic information with
the message passing mechanism. However, existing methods model a local and
static spatial dependence, which cannot transmit the global-dynamic traffic
information (GDTi) required for long-term prediction. The challenge is the
difficulty of detecting the precise transmission of GDTi due to the uncertainty
of individual transport, especially for long-term transmission. In this paper,
we propose a new hypothesis\: GDTi behaves macroscopically as a transmitting
causal relationship (TCR) underlying traffic flow, which remains stable under
dynamic changing traffic flow. We further propose spatial-temporal Granger
causality (STGC) to express TCR, which models global and dynamic spatial
dependence. To model global transmission, we model the causal order and causal
lag of TCRs global transmission by a spatial-temporal alignment algorithm. To
capture dynamic spatial dependence, we approximate the stable TCR underlying
dynamic traffic flow by a Granger causality test. The experimental results on
three backbone models show that using STGC to model the spatial dependence has
better results than the original model for 45 min and 1 h long-term prediction.Comment: 14 pages, 16 figures, 4 table
Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach
Traffic speed is central to characterizing the fluidity of the road network.
Many transportation applications rely on it, such as real-time navigation,
dynamic route planning, and congestion management. Rapid advances in sensing
and communication techniques make traffic speed detection easier than ever.
However, due to sparse deployment of static sensors or low penetration of
mobile sensors, speeds detected are incomplete and far from network-wide use.
In addition, sensors are prone to error or missing data due to various kinds of
reasons, speeds from these sensors can become highly noisy. These drawbacks
call for effective techniques to recover credible estimates from the incomplete
data. In this work, we first identify the issue as a spatiotemporal kriging
problem and propose a Laplacian enhanced low-rank tensor completion (LETC)
framework featuring both lowrankness and multi-dimensional correlations for
large-scale traffic speed kriging under limited observations. To be specific,
three types of speed correlation including temporal continuity, temporal
periodicity, and spatial proximity are carefully chosen and simultaneously
modeled by three different forms of graph Laplacian, named temporal graph
Fourier transform, generalized temporal consistency regularization, and
diffusion graph regularization. We then design an efficient solution algorithm
via several effective numeric techniques to scale up the proposed model to
network-wide kriging. By performing experiments on two public million-level
traffic speed datasets, we finally draw the conclusion and find our proposed
LETC achieves the state-of-the-art kriging performance even under low
observation rates, while at the same time saving more than half computing time
compared with baseline methods. Some insights into spatiotemporal traffic data
modeling and kriging at the network level are provided as well
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