Online unit clustering is a clustering problem where classification of points is done in an online fashion, but the exact location of clusters can be modified dynamically. We study several variants and generalizations of the online unit clustering problem, which are inspired by variants of packing and scheduling problems in the literature.

In Online Sum-Radii Clustering, n demand points arrive online and must be irrevocably assigned to a cluster upon arrival. The cost of each cluster is the sum of a fixed opening cost and its radius, and the objective is to minimize the total cost of the clusters opened by the algorithm. We show that the deterministic competitive ratio of Online Sum-Radii Clustering for general metric spaces is Θ...

Due to the constant increase of the complexity and size of the complex networks studied, the need for distributed implementations of network clustering methods is getting more urgent each year. Here we present the online version of CFinder, which can locate overlapping communities in directed, weighted or undirected networks based on the clique percolation method (CPM). Due to the local nature ...

Clique clustering is the problem of partitioning a graph into cliques so that some objective function is optimized. In online clustering, the input graph is given one vertex at a time, and any vertices that have previously been clustered together are not allowed to be separated. The objective here is to maintain a clustering the never deviates too far in the objective function compared to the o...

We study the online clustering problem where data items arrive in an online fashion. The algorithm maintains a clustering of data items into similarity classes. Upon arrival of v, the relation between v and previously arrived items is revealed, so that for each u we are told whether v is similar to u. The algorithm can create a new cluster for v and merge existing clusters. When the objective i...

Given an example-feature set, representing the information context present in a dataset, is it possible to reconstruct the information context in the form of clusters to a certain degree of compromise, if the examples are processed randomly without repetition in a sequential online manner? A general transductive inductive learning strategy which uses constraint based multivariate Chebyshev ineq...

Approximating the k-means clustering objective with an online learning algorithm is an open problem. We introduce a family of online clustering algorithms by extending algorithms for online supervised learning, with access to expert predictors, to the unsupervised learning setting. Instead of computing prediction errors in order to re-weight the experts, the algorithms compute an approximation ...

We introduce a novel algorithmic approach to content recommendation based on adaptive clustering of exploration-exploitation (“bandit”) strategies. We provide a sharp regret analysis of this algorithm in a standard stochastic noise setting, demonstrate its scalability properties, and prove its effectiveness on a number of artificial and real-world datasets. Our experiments show a significant in...

We introduce a set of clustering algorithms whose performance function is such that the algorithms overcome one of the weaknesses of K-means, its sensitivity to initial conditions which leads it to converge to a local optimum rather than the global optimum. We derive online learning algorithms and illustrate their convergence to optimal solutions which K-means fails to find. We then extend the ...

The problem of online clustering is considered in the case where each data point is a sequence generated by a stationary ergodic process. Data arrive in an online fashion so that the sample received at every timestep is either a continuation of some previously received sequence or a new sequence. The dependence between the sequences can be arbitrary. No parametric or independence assumptions ar...