Unsupervised learning of the set of local maxima

Lior Wolf, Sagie Benaim, Tomer Galanti

Research output: Contribution to conferencePaperpeer-review

1 Scopus citations


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 x0 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.

Original languageEnglish
StatePublished - 2019
Event7th International Conference on Learning Representations, ICLR 2019 - New Orleans, United States
Duration: 6 May 20199 May 2019


Conference7th International Conference on Learning Representations, ICLR 2019
Country/TerritoryUnited States
CityNew Orleans


FundersFunder number
Horizon 2020 Framework ProgrammeERC CoG 725974
European Research Council


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