Visualizing Big Data via a Mixture of PARAMAP and Isomap

Ulas Akkucuk

Abstract


Dimensionality reduction aims to represent higher dimensional data by a lower-dimensional structure. A well-known approach by Carroll, Parametric Mapping or PARAMAP (Shepard and Carroll, 1966) relies on iterative minimization of a loss function measuring the smoothness or continuity of the mapping from the lower dimensional representation to the original data. The algorithm was revitalized with important modifications (Akkucuk and Carroll, 2006). However improved, the approach still involved the need to make a large number of random starts. In this paper we discuss the use of a variant of the Isomap method (Tenenbaum et al., 2000) to obtain a starting framework, consisting of a core set of landmark points. These core set of landmark points are used to construct a rational start for running PARAMAP algorithm only once. Since Isomap is faster and less prone to local optimum problems than PARAMAP, and the iterative process involved in adding new points to the configuration will be less time consuming (since only one starting configuration is used), we believe the resulting method should be better suited to deal with large data sets, and more inclined to obtain a satisfactory solution in reasonable time.


Keywords


PARAMAP, Isomap, Nonlinear Mapping, Dimension Reduction, Big Data, Data Mining

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References


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International Journal of Decision Sciences & Applications- by Umit Hacioglu is licensed under aCreative Commons Attribution-NonCommercial 4.0 International License.

 

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