Taking All Positive Eigenvectors Is Suboptimal in Classical Multidimensional Scaling
نویسندگان
چکیده
منابع مشابه
Taking all positive eigenvectors is suboptimal in classical multidimensional scaling
It is hard to overstate the importance of multidimensional scaling as an analysis technique in the broad sciences. Classical, or Torgerson multidimensional scaling is one of the main variants, with the advantage that it has a closed-form analytic solution. However, this solution is exact if and only if the distances are Euclidean. Conversely, there has been comparatively little discussion on wh...
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Baraminology methodology continues to mature, and in this article, the multivariate technique of classical multidimensional scaling is introduced to baraminology. The technique is applied to three datasets previously analyzed in baraminology studies, a Heliantheae/Helenieae (Asteraceae) dataset, a fossil equid dataset, and a grass (Poaceae) dataset. The results indicate that classical multidime...
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Out-of-sample embedding techniques insert additional points into previously constructed configurations. An out-of-sample extension of classical multidimensional scaling is presented. The out-of-sample extension is formulated as an unconstrained nonlinear least-squares problem. The objective function is a fourth-order polynomial, easily minimized by standard gradient-based methods for numerical ...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2016
ISSN: 1052-6234,1095-7189
DOI: 10.1137/15m102602x