An Improved Traffic Matrix Decomposition Method with Frequency-Domain Regularization

We propose a novel network traffic matrix decomposition method named Stable Principal Component Pursuit with Frequency-Domain Regularization (SPCP-FDR), which improves the Stable Principal Component Pursuit (SPCP) method by using a frequency-domain noise regularization function. An experiment demonstrates the feasibility of this new decomposition method.Comment: Accepted to IEICE Transactions on Information and System

Scalable Tensor Factorizations for Incomplete Data

The problem of incomplete data - i.e., data with missing or unknown values - in multi-way arrays is ubiquitous in biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision, communication networks, etc. We consider the problem of how to factorize data sets with missing values with the goal of capturing the underlying latent structure of the data and possibly reconstructing missing values (i.e., tensor completion). We focus on one of the most well-known tensor factorizations that captures multi-linear structure, CANDECOMP/PARAFAC (CP). In the presence of missing data, CP can be formulated as a weighted least squares problem that models only the known entries. We develop an algorithm called CP-WOPT (CP Weighted OPTimization) that uses a first-order optimization approach to solve the weighted least squares problem. Based on extensive numerical experiments, our algorithm is shown to successfully factorize tensors with noise and up to 99% missing data. A unique aspect of our approach is that it scales to sparse large-scale data, e.g., 1000 x 1000 x 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP-WOPT on two real-world applications: a novel EEG (electroencephalogram) application where missing data is frequently encountered due to disconnections of electrodes and the problem of modeling computer network traffic where data may be absent due to the expense of the data collection process

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

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