Singular Value Decomposition Model on Sharing Bicycles

Singular Value Decomposition (SVD) is factorization of a matrix and has been used extensively for dimension reduction in pattern recognition and information retrieval applications (Sergios & Konstantinos, 2009). SVD is a generalization of the eigendecomposition of a positive semidefinite normal matrix to any matrix via an extension of polar decomposition (Banerjee & Roy, 2014). Figure 3 is a schematic diagram of SVD.

Sharing BicyclesSingular Value DecompositionTraffic

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Initial contribute: 2020-06-29

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  • 曹敏
    • :  
    南京师范大学地理科学学院
    :  
    caomin@njnu.edu.cn
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    Detailed Description

    English {{currentDetailLanguage}} English
    The public bike-sharing (PBS) system has received increasing attention as a potential way to improve the first and last mile connections to other modes of transit and lessen the environmental impact of transportation activities (DeMaio, 2009; Ruch et al., 2014). Recently, an increasing number of cities have deployed bicycle-sharing systems to solve the first/last mile connection problem, generating a large quantity of data. Additionally, commuting regularities are usually linked to the spatial distribution or the transfer routing of bikes. In this theme, we come up with two models based on mathematical theory aiming to recognize the patterns in sharing bicycle data.
    • Singular Value Decomposition
    Singular Value Decomposition (SVD) is factorization of a matrix and has been used extensively for dimension reduction in pattern recognition and information retrieval applications (Sergios & Konstantinos, 2009). SVD is a generalization of the eigendecomposition of a positive semidefinite normal matrix to any matrix via an extension of polar decomposition (Banerjee & Roy, 2014). Figure 1 is a schematic diagram of SVD.
    Figure 3. Visualization of the matrices in SVD
    Figure 1. Visualization of the matrices in SVD
    The following figure(Figure 2) shows the procedural to apply SVD on bike sharing data. In this model, we need to construct OD matrix to transfer bicycle sharing data into the shape we need. In SVD, two kinds of patterns (Origin pattern and Destination pattern) can be found from SVD model.
    Figure 4. Flow chart of Singular Value Decomposition
    Figure 2. Flow chart of Singular Value Decomposition

    Reference:

    DeMaio, P. (2009). Bike-sharing: History, impacts, models of provision, and future. Journal of public transportation, 12(4), 3.

    Banerjee, S., & Roy, A. (2014). Linear algebra and matrix analysis for statistics. New York: Chapman and Hall/CRC.

    Kolda, T. G., and Bader, B. W. 2009. Tensor decompositions and applications. SIAM review, 51(3), 455-500. 

    Khoromskij, B., and Khoromskaia, V. 2007. Low rank Tucker-type tensor approximation to classical potentials. Open Mathematics, 5(3), 523-550.

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    曹敏 (2020). Singular Value Decomposition Model on Sharing Bicycles, Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/e5f3f969-9f35-4497-ae2b-98cc3767df59
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    Contributor(s)
    Initial contribute : 2020-06-29

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    Authorship

  • 曹敏
    • :  
    南京师范大学地理科学学院
    :  
    caomin@njnu.edu.cn
    Is authorship not correct? Feed back

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