Classical Scaling Revisited
Classical Scaling Revisited
复制标题
重温经典缩放
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
R. Kimmel
中科院分区：
文献类型：
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作者：
Gil Shamai;Y. Aflalo;M. Zibulevsky;R. Kimmel
Multidimensional-scaling (MDS) is an information analysis tool. It involves the evaluation of distances between data points, which is a quadratic space-time problem. Then, MDS procedures find an embedding of the points in a low dimensional Euclidean (flat) domain, optimizing for the similarity of inter-points distances. We present an efficient solver for Classical Scaling (a specific MDS model) by extending the distances measured from a subset of the points to the rest, while exploiting the smoothness property of the distance functions. The smoothness is measured by the L2 norm of the Laplace-Beltrami operator applied to the unknown distance function. The Laplace Beltrami reflects the local differential relations between points, and can be computed in linear time. Classical-scaling is thereby reformulated into a quasi-linear space-time complexities procedure.
