Synonyms
MDS
Definition
Multidimensional scaling (MDS) is a mathematical dimension reduction technique that best preserves the interpoint distances by analyzing gram matrix. Given any two points pi and pj in a dataset P, MSD aims to minimize the following objective function:
where d(pi, pj)d(pi, pj) and d′(pi, pj)d′(pi, pj) represent the distance between points pi and pj in original space and the lower dimensional subspace, respectively.
Key Points
Multidimensional scaling (MDS) is a set of related statistical techniques often used in data visualization and analysis for exploring similarities or dissimilarities in data. An MDS algorithm starts with a matrix of point-point (dis)similarities and then assigns a location of each point in a low-dimensional space. The points are arranged in this subspace so that the distances between pairs of points have their original distance maximally retained....
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Cox MF, Cox MAA. Multidimensional scaling. Boca Raton: Chapman and Hall; 2001.
Young FW, Hamer RM. Multidimensional scaling: history, theory and applications. New York: Erlbaum; 1987.
Zhu X, Huang Z, Shen HT, Cheng J, Xu C. Dimensionality reduction by mixed kernel canonical correlation analysis. Pattern Recog (PR). 2012;45(8):3003–16.
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Shen, H.T. (2018). Multidimensional Scaling. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_548
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DOI: https://doi.org/10.1007/978-1-4614-8265-9_548
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