Liadan O'Callaghan

Clustering data streams: Theory and practice

The data stream model has recently attracted attention for its applicability to numerous types of data, including telephone records, Web documents, and clickstreams. For analysis of such data, the ability to process the data in a single pass, or a small number of passes, while using little memory, is crucial. We describe such a streaming algorithm that effectively clusters large data streams. We also provide empirical evidence of the algorithms performance on synthetic and real data streams.

Streaming-data algorithms for high-quality clustering

Streaming data analysis has recently attracted attention in numerous applications including telephone records, Web documents and click streams. For such analysis, single-pass algorithms that consume a small amount of memory are critical. We describe such a streaming algorithm that effectively clusters large data streams. We also provide empirical evidence of the algorithms performance on synthetic and real data streams.

Maintaining variance and k-medians over data stream windows

The sliding window model is useful for discounting stale data in data stream applications. In this model, data elements arrive continually and only the most recent <i>N</i> elements are used when answering queries. We present a novel technique for solving two important and related problems in the sliding window model---maintaining variance and maintaining a <i>k</i>--median clustering. Our solution to the problem of maintaining variance provides a continually updated estimate of the variance of the last <i>N</i> values in a data stream with relative error of at most ε using <i>O</i>(1/<inf>ε</inf>2 log <i>N</i>) memory. We present a constant-factor approximation algorithm which maintains an approximate <i>k</i>--median solution for the last <i>N</i> data points using <i>O</i>(<i>k</i>/τ4 <i>N</i>^2τ log² <i>N</i>) memory, where τ < 1/2 is a parameter which trades off the space bound with the approximation factor of <i>O</i>(2^{<i>O</i>(1/τ)}).

Better streaming algorithms for clustering problems

We study clustering problems in the streaming model, where the goal is to cluster a set of points by making one pass (or a few passes) over the data using a small amount of storage space. Our main result is a randomized algorithm for the k--Median problem which produces a constant factor approximation in one pass using storage space O(k poly log n). This is a significant improvement of the previous best algorithm which yielded a 2O(1/ε) approximation using O(nε) space. Next we give a streaming algorithm for the k--Median problem with an arbitrary distance function. We also study algorithms for clustering problems with outliers in the streaming model. Here, we give bicriterion guarantees, producing constant factor approximations by increasing the allowed fraction of outliers slightly.

A k -Median Algorithm with Running Time Independent of Data Size

AbstractWe give a sampling-based algorithm for the k-Median problem, with running time O(k

Computing Shortest Paths with Uncertainty

(\frac{{k^2 }}{ \in } \log k)^2

Truth revelation in approximately efficient combinatorial auctions

log