We present new algorithms for$k$-means clustering on a data stream with a focus on providing fast responses to clustering queries. Compared to the state-of-the-art, our algorithms provide substantial improvements in the query time for cluster-center queries while retaining the desirable properties of provably small approximation error and low space usage. Our proposed clustering algorithms systematically reuse the “coresets” (summaries of data) computed for recent queries in answering the current clustering query, a novel technique which we refer to as coreset caching. We also present an algorithm calledOnlineCCthat integrates the coreset caching idea with a simple sequential streaming$k$-means algorithm. In practice,OnlineCCalgorithm can provide constant query time. We present both theoretical analysis and detailed experiments demonstrating the correctness, accuracy, and efficiency of all our proposed clustering algorithms.

We consider space-efficient single-pass estimation of the number of butterflies, a fundamental bipartite graph motif, from a massive bipartite graph stream where each edge represents a connection between entities in two different partitions. We present a space lower bound for any streaming algorithm that can estimate the number of butterflies accurately, as well as FLEET, a suite of algorithms for accurately estimating the number of butterflies in the graph stream. Estimates returned by the algorithms come with provable guarantees on the approximation error, and experiments show good tradeoffs between the space used and the accuracy of approximation. We also present space-efficient algorithms for estimating the number of butterflies within a sliding window of the most recent elements in the stream. While there is a significant body of work on counting subgraphs such as triangles in a unipartite graph stream, our work seems to be one of the few to tackle the case of bipartite graph streams.

A current challenge for data management systems is to support the construction and maintenance of machine learning models over data that is large, multi-dimensional, and evolving. While systems that could support these tasks are emerging, the need to scale to distributed, streaming data requires new models and algorithms. In this setting, as well as computational scalability and model accuracy, we also need to minimize the amount of communication between distributed processors, which is the chief component of latency. We study Bayesian Networks, the workhorse of graphical models, and present a communication-efficient method for continuously learning and maintaining a Bayesian network model over data that is arriving as a distributed stream partitioned across multiple processors. We show a strategy for maintaining model parameters that leads to an exponential reduction in communication when compared with baseline approaches to maintain the exact MLE (maximum likelihood estimation). Meanwhile, our strategy provides similar prediction errors for the target distribution and for classification tasks.

We present methods for k-means clustering on a stream with a focus on providing fast responses to clustering queries. Compared to the current state-of-the-art, our methods provide substantial improvement in the query time for cluster centers while retaining the desirable properties of provably small approximation error and low space usage. Our algorithms rely on a novel idea of "coreset caching" that systematically reuses coresets (summaries of data) computed for recent queries in answering the current clustering query. We present both theoretical analysis and detailed experiments demonstrating their correctness and e ciency.