Unsupervised Learning of the Set of Local Maxima

TL;DR

This paper introduces an unsupervised learning method that identifies local maxima in data, learning a set indicator and a comparator function to improve anomaly detection without labeled data.

Contribution

It proposes a novel unsupervised approach that jointly learns a set indicator and comparator function based on local maxima, outperforming traditional one-class classifiers.

Findings

Outperforms one-class classifiers in anomaly detection

Efficiently identifies local maxima as an indicator

Provides an unsupervised additional signal

Abstract

This paper describes a new form of unsupervised learning, whose input is a set of unlabeled points that are assumed to be local maxima of an unknown value function v in an unknown subset of the vector space. Two functions are learned: (i) a set indicator c, which is a binary classifier, and (ii) a comparator function h that given two nearby samples, predicts which sample has the higher value of the unknown function v. Loss terms are used to ensure that all training samples x are a local maxima of v, according to h and satisfy c(x)=1. Therefore, c and h provide training signals to each other: a point x' in the vicinity of x satisfies c(x)=-1 or is deemed by h to be lower in value than x. We present an algorithm, show an example where it is more efficient to use local maxima as an indicator function than to employ conventional classification, and derive a suitable generalization bound. Our experiments show that the method is able to outperform one-class classification algorithms in the task of anomaly detection and also provide an additional signal that is extracted in a completely unsupervised way.