Online Clustering Via Inequality

Given an example-feature set, representing the information context present in a dataset, is it possible to reconstruct the information context in the form of clusters to a certain degree of compromise, if the examples are processed randomly without repetition in a sequential online manner? A general transductive inductive learning strategy which uses constraint based multivariate Chebyshev inequality is proposed. Theoretical convergence in the reconstruction error to a finite value with increasing number of (a) processed examples and (b) generated clusters, respectively, is shown. Upper bounds for these error rates are also proved. Nonparametric estimates of these error from a sample of random sequences of example set, empirically point to a stable number of clusters.