Cautious Active Clustering

TL;DR

This paper introduces a cautious active clustering method that efficiently classifies points sampled from unknown distributions using localized Hermite polynomial kernels, without prior assumptions on the data or number of classes.

Contribution

It proposes a novel hierarchical classification approach leveraging localized kernels, providing theoretical guarantees without needing prior knowledge of class distributions or counts.

Findings

Effective classification in hyper-spectral images

Successful application to MNIST dataset

Theoretical guarantees measured by F-score

Abstract

We consider the problem of classification of points sampled from an unknown probability measure on a Euclidean space. We study the question of querying the class label at a very small number of judiciously chosen points so as to be able to attach the appropriate class label to every point in the set. Our approach is to consider the unknown probability measure as a convex combination of the conditional probabilities for each class. Our technique involves the use of a highly localized kernel constructed from Hermite polynomials, in order to create a hierarchical estimate of the supports of the constituent probability measures. We do not need to make any assumptions on the nature of any of the probability measures nor know in advance the number of classes involved. We give theoretical guarantees measured by the $F$-score for our classification scheme. Examples include classification in hyper-spectral images and MNIST classification.