Abstract
An important problem in the field of data stream analysis is change detection and monitoring. In many cases, the data stream can show changes over time which can be used for understanding the nature of several applications. We discuss the concept of velocity density estimation, a technique used to understand, visualize and determine trends in the evolution of fast data streams. We show how to use velocity density estimation in order to create both temporal velocity profiles and spatial velocity profiles at periodic instants in time. These profiles are then used in order to predict three kinds of data evolution. Methods are proposed to visualize the changing data trends in a single online scan of the data stream, and a computational requirement which is linear in the number of data points. In addition, batch processing techniques are proposed in order to identify combinations of dimensions which show the greatest amount of global evolution. We also discuss the problem of change detection in the context of graph data, and illustrate that it may often be useful to determine communities of evolution in graph environments.
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