Transductive-Inductive Cluster Approximation Via Multivariate Chebyshev Inequality

Shriprakash Sinha

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arXiv · 1101.3755

Transductive-Inductive Cluster Approximation Via Multivariate Chebyshev Inequality

Shriprakash Sinha

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Abstract

Approximating adequate number of clusters in multidimensional data is an open area of research, given a level of compromise made on the quality of acceptable results. The manuscript addresses the issue by formulating a transductive inductive learning algorithm which uses multivariate Chebyshev inequality. Considering clustering problem in imaging, theoretical proofs for a particular level of compromise are derived to show the convergence of the reconstruction error to a finite value with increasing (a) number of unseen examples and (b) the number of clusters, respectively. Upper bounds for these error rates are also proved. Non-parametric estimates of these error from a random sample of sequences empirically point to a stable number of clusters. Lastly, the generalization of algorithm can be applied to multidimensional data sets from different fields.

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Shriprakash Sinha. 2011-01-19. Transductive-Inductive Cluster Approximation Via Multivariate Chebyshev Inequality. https://arxiv.org/abs/1101.3755

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