DeepAI
Log In Sign Up

Fuzzy Clustering with Similarity Queries

06/04/2021
by   Wasim Huleihel, et al.
0

The fuzzy or soft k-means objective is a popular generalization of the well-known k-means problem, extending the clustering capability of the k-means to datasets that are uncertain, vague, and otherwise hard to cluster. In this paper, we propose a semi-supervised active clustering framework, where the learner is allowed to interact with an oracle (domain expert), asking for the similarity between a certain set of chosen items. We study the query and computational complexities of clustering in this framework. We prove that having a few of such similarity queries enables one to get a polynomial-time approximation algorithm to an otherwise conjecturally NP-hard problem. In particular, we provide probabilistic algorithms for fuzzy clustering in this setting that asks O(𝗉𝗈𝗅𝗒(k)log n) similarity queries and run with polynomial-time-complexity, where n is the number of items. The fuzzy k-means objective is nonconvex, with k-means as a special case, and is equivalent to some other generic nonconvex problem such as non-negative matrix factorization. The ubiquitous Lloyd-type algorithms (or, expectation-maximization algorithm) can get stuck at a local minima. Our results show that by making few similarity queries, the problem becomes easier to solve. Finally, we test our algorithms over real-world datasets, showing their effectiveness in real-world applications.

READ FULL TEXT

page 1

page 2

page 3

page 4

06/08/2016

Clustering with Same-Cluster Queries

We propose a framework for Semi-Supervised Active Clustering framework (...
12/19/2017

Approximate Correlation Clustering Using Same-Cluster Queries

Ashtiani et al. (NIPS 2016) introduced a semi-supervised framework for c...
08/14/2019

Correlation Clustering with Same-Cluster Queries Bounded by Optimal Cost

Several clustering frameworks with interactive (semi-supervised) queries...
12/07/2022

On the Global Solution of Soft k-Means

This paper presents an algorithm to solve the Soft k-Means problem globa...
04/17/2021

Fuzzy Discriminant Clustering with Fuzzy Pairwise Constraints

In semi-supervised fuzzy clustering, this paper extends the traditional ...
08/11/2015

Answering Fuzzy Conjunctive Queries over Finitely Valued Fuzzy Ontologies

Fuzzy Description Logics (DLs) provide a means for representing vague kn...
05/20/2016

Fast Randomized Semi-Supervised Clustering

We consider the problem of clustering partially labeled data from a mini...