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| Fast but Not Bad Initial Configuration for Metric Multidimensional Scaling |
| Shuo Xu, Xiaodong Qiao, Lijun Zhu, Yunliang Zhang, Lin Li |
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Abstract The Multidimensional Scaling (MDS) has become a standard technique in multivariate data analysis and
is widely used in a variety of disciplines. The objective of MDS is to find a configuration matrix so that
given pairwise dissimilarities can be preserved as faithfully as possible. But since there exist a lot of nonglobal
minima for (s)stress, many optimization iterative algorithms are liable to converge to local minima.
Thus, the choice of a good initial configuration is crucial. Through closer examination on currently used
initial configurations, we find that all these configurations require extensive preprocessing and usually are
computationally expensive, thus not appropriate for large scale applications. To overcome this problem,
we conjecture that several approximating scalable solutions for classical MDS can be used to initialize
the configuration for metric MDS at lower complexity, but should have comparative performance with
classical MDS. Finally, extensive simulation experimental results verify our assumptions.
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