We consider the problem of clustering data streams. A data stream can roughly be thought of as a transient, continuously increasing sequence of time-stamped data. In order to maintain an up-to-date clustering structure, it is necessary to analyze the incoming data in an online manner, tolerating but a constant time delay. For this purpose, we develop an efficient online version of the classical...

We propose a recursive algorithm for clustering trajectories lying in multiple moving hyperplanes. Starting from a given or random initial condition, we use normalized gradient descent to update the coefficients of a time varying polynomial whose degree is the number of hyperplanes and whose derivatives at a trajectory give an estimate of the vector normal to the hyperplane containing that traj...

Clustering text data online as it comes in is a difficult problem. It is both hard to capture a meaningful notion of linguistic similarity and to cluster large amounts of data in a single pass. This problem is especially challenging because most known algorithms that ensure tight clusterings are inefficient on large datasets. While significant work has been done on text clustering, it has not b...

The notion that information moves through social networks has been widely discussed[3], however, with the growing availability of large digital corpora, the ability to quantitatively model this phenomenon is new. To this end we explore a large corpus of online news quotations looking for cases of noisy reproduction and the factors which influence such noise. An essential step in this process is...

Low-Rank Representation (LRR) has been a significant method for segmenting data that are generated from a union of subspaces. It is also known that solving LRR is challenging in terms of time complexity and memory footprint, in that the size of the nuclear norm regularized matrix is n-by-n (where n is the number of samples). In this paper, we thereby develop a novel online implementation of LRR...

The goal of this research is to explore the nature of the response relation in online learning networks. We ask whether actors choose their response partners at random or whether certain special mechanisms are at work. We compare the observed values of clustering of responses in 95 online learning networks with the predictions of two suitable Random Graph models. All the online distance learnin...

Online algorithms allow data instances to be processed in a sequential way, which is important for large-scale and real-time applications. In this paper, we propose a novel online clustering approach based on a Dirichlet process mixture of generalized Dirichlet (GD) distributions, which can be considered as an extension of the finite GD mixture model to the infinite case. Our approach is built ...