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In this paper, we prove a crucial theorem called Mirroring Theorem whichaffirms that given a collection of samples with enough information in it suchthat it can be classified into classes and subclasses then (i) There exists amapping which classifies and subclassifies these samples (ii) There exists ahierarchical classifier which can be constructed by using Mirroring NeuralNetworks (MNNs) in combination with a clustering algorithm that can approximatethis mapping. Thus, the proof of the Mirroring theorem provides a theoreticalbasis for the existence and a practical feasibility of constructinghierarchical classifiers, given the maps. Our proposed Mirroring Theorem canalso be considered as an extension to Kolmogrovs theorem in providing arealistic solution for unsupervised classification. The techniques we develop,are general in nature and have led to the construction of learning machineswhich are (i) tree like in structure, (ii) modular (iii) with each modulerunning on a common algorithm (tandem algorithm) and (iv) selfsupervised. Wehave actually built the architecture, developed the tandem algorithm of such ahierarchical classifier and demonstrated it on an example problem.

A Mirroring Theorem and its Application to a New Method of Unsupervised Hierarchical Pattern Classification