Multi-Dimensional Regression Analysis of Time-Series Data Streams

Real-time production systems and other dynamic environments often generate tremendous (potentially in nite) amount of stream data; the volume of data is too huge to be stored on disks or scanned multiple times. Can we perform on-line, multi-dimensional analysis and data mining of such data to alert people about dramatic changes of situations and to initiate timely, high-quality responses? This is a challenging task. In this paper, we investigate methods for online, multi-dimensional regression analysis of time-series stream data, with the following contributions: (1) our analysis shows that only a small number of compressed regression measures instead of the complete stream of data need to be registered for multi-dimensional linear regression analysis, (2) to facilitate on-line stream data analysis, a partially materialized data cube model, with regression as measure, and a tilt time frame as its time dimension, is proposed to minimize the amount of data to be retained in memory or stored on disks, and (3) an exception-guided drilling approach is developed for on-line, multi-dimensional exceptionbased regression analysis. Based on this design, algorithms are proposed for eÆcient analysis of time-series data streams. Our performance study compares the proposed algorithms and identi es the most memoryand timeeÆcient The work was supported in part by grants from U.S. National Science Foundation, the University of Illinois, and Microsoft Research. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and/or special permission from the Endowment. Proceedings of the 28th VLDB Conference, Hong Kong, China, 2002 one for multi-dimensional stream data analysis.