Classification using distances from samples to linear manifolds

Abstract

A classifier is proposed wherein the distances from samples to linear manifolds (DSL) are used to perform classification. For each class, a linear manifold is built, whose dimension is high enough to pass all the training samples of the class. The distance from a query sample to a linear manifold is converted to the distance from a point to a linear subspace. And a simple and stable formula is derived to calculate the distance by virtue of the geometrical fundamental of the Gram matrix as well as the regularization technique. The query sample is assigned into the class whose linear manifold is the nearest. On one synthetic data set, thirteen binary-class data sets as well as six multi-class data sets, the experimental results show that the classification performance of DSL is of competence. On most of the data sets, DSL outperforms the comparing classifiers based on k nearest samples or subspaces, and is even superior to support vector machines on some data sets. Further experiment demonstrates that the test efficiency of DSL is also competitive to kNN and the related state-of-the-art classifiers on many data sets.