  In this project we further investigate the idea of reducing the
dimensionality of datasets using a Borel isomorphism with the purpose of
subsequently applying supervised learning algorithms, as originally suggested
by my supervisor V. Pestov (in 2011 Dagstuhl preprint). Any consistent learning
algorithm, for example kNN, retains universal consistency after a Borel
isomorphism is applied. A series of concrete examples of Borel isomorphisms
that reduce the number of dimensions in a dataset is provided, based on
multiplying the data by orthogonal matrices before the dimensionality reducing
Borel isomorphism is applied. We test the accuracy of the resulting classifier
in a lower dimensional space with various data sets. Working with a phoneme
voice recognition dataset, of dimension 256 with 5 classes (phonemes), we show
that a Borel isomorphic reduction to dimension 16 leads to a minimal drop in
accuracy. In conclusion, we discuss further prospects of the method.
