Efficient real time OD matrix estimation based on Principal Component Analysis

Djukic, Tamara; Flötteröd, Gunnar; Lint, Hans van; Hoogendoorn, Serge P.

doi:10.1109/itsc.2012.6338720

Cited by 62 publications

(43 citation statements)

References 16 publications

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“…Singular value decomposition based methods have found applications in many ITS applications including missing data imputation [4], [12] and estimation [13]. By applying SVD, network profile matrix A can be represented as A = USV T , where the columns of matrix U ∈ R n×n and matrix V ∈ R p×p are called the left singular vectors and the right singular vectors of A respectively.…”

Section: A Singular Value Decompositionmentioning

confidence: 99%

“…The previous studies related to low-dimensional models such as in [3], [13], [19], [20], [22]- [26] only consider lossy compression. In lossy compression, there is no bound on the maximum absolute error (MAE).…”

Section: Introductionmentioning

confidence: 99%

“…These studies do not typically compare the reconstruction efficiency of various low-dimensional models for a given road network [3], [13], [19], [20]. Furthermore, the proposed methods do not provide any upper bound on the maximum loss of information.…”

Section: Introductionmentioning

confidence: 99%

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Near-Lossless Compression for Large Traffic Networks

Asif

Srinivasan

Mitrović

et al. 2015

IEEE Trans. Intell. Transport. Syst.

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Abstract-With advancements in sensor technologies, intelligent transportation systems (ITS) can collect traffic data with high spatial and temporal resolution. However, the size of the networks combined with the huge volume of the data puts serious constraints on the system resources. Low-dimensional models can help ease these constraints by providing compressed representations for the networks. In this study, we analyze the reconstruction efficiency of several low-dimensional models for large and diverse networks. The compression performed by low-dimensional models is lossy in nature. To address this issue, we propose a near-lossless compression method for traffic data by applying the principle of lossy plus residual coding. To this end, we first develop low-dimensional model of the network. We then apply Huffman coding in the residual layer. The resultant algorithm guarantees that the maximum reconstruction error will remain below a desired tolerance limit. For analysis, we consider a large and heterogeneous test network comprising of more than 18000 road segments. The results show that the proposed method can efficiently compress data obtained from a large and diverse road network, while maintaining the upper bound on the reconstruction error.

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Section: A Singular Value Decompositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Near-Lossless Compression for Large Traffic Networks

Asif

Srinivasan

Mitrović

et al. 2015

IEEE Trans. Intell. Transport. Syst.

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“…Previous studies related to low-dimensional representations for traffic networks mainly deal with PCA [3,[9][10][11][12]. Djukic et al applied PCA on small network with OD pair data [9,10].…”

Section: Introductionmentioning

confidence: 99%

“…Djukic et al applied PCA on small network with OD pair data [9,10]. In another study, Asif et al applied different subspace methods for compression of traffic speed [11].…”

Section: Introductionmentioning

confidence: 99%

CUR decomposition for compression and compressed sensing of large-scale traffic data

Mitrović

Asif

Rasheed

et al. 2013

16th International IEEE Conference on Intelligent Transportation Systems (ITSC 2013)

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Abstract-Intelligent Transportation Systems (ITS) often operate on large road networks, and typically collect traffic data with high temporal resolution. Consequently, ITS need to handle massive volumes of data, and methods to represent that data in more compact representations are sorely needed. Subspace methods such as Principal Component Analysis (PCA) can create accurate low-dimensional models. However, such models are not readily interpretable, as the principal components usually involve a large number of links in the traffic network. In contrast, the CUR matrix decomposition leads to low-dimensional models where the components correspond to individual links in the network; the resulting models can be easily interpreted, and can also be used for compressed sensing of the traffic network. In this paper, the CUR matrix decomposition is applied for two purposes: (1) compression of traffic data; (2) compressed sensing of traffic data. In the former, only data from a "random" subset of links and time instances is stored. In the latter, data for the entire traffic network is inferred from measurements at a "random" subset of links. Numerical results for a large traffic network in Singapore demonstrate the feasibility of the proposed approach.

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Traffic matrix estimation: Advanced‐Tomogravity method based on a precise gravity model

Zhou

Tan

et al. 2014

Int J Communication

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SummaryTraffic matrix (TM) is extremely important in many networking operations. This paper proposes a novel approach of TM estimation in large‐scale IP networks, termed as Advanced‐Tomogravity method, which is based on a precise gravity model and the tomography method. First, the precise gravity model is proposed on the basis of the existing generalized gravity model by introducing a relativity factor vector parameter, which defines the relativity between the solution of the existing generalized gravity model and its real TM. The solution obtained from this precise gravity model is then refined by the basic model of the tomography method. By mathematical analysis, we give the explicit expression of the relativity factor vector parameter in the proposed precise gravity model by the Moore–Penrose inverse and the minimum‐norm least‐square solution. The vector parameter is subsequently determined with the aid of small amount of historical real data of TM. A general algorithm of the proposed approach is therefore designed. Finally, our approach is validated by simulation using the real data of the Abilene Network. The simulation results indicate that it reduces the relative errors to less than one‐half, better tracks not only the dynamic fluctuations but also the overall mean behavior of traffic flow. Copyright © 2014 John Wiley & Sons, Ltd.

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Efficient real time OD matrix estimation based on Principal Component Analysis

Cited by 62 publications

References 16 publications

Near-Lossless Compression for Large Traffic Networks

Near-Lossless Compression for Large Traffic Networks

CUR decomposition for compression and compressed sensing of large-scale traffic data

Traffic matrix estimation: Advanced‐Tomogravity method based on a precise gravity model

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