Wavelet synopsis for data streams: minimizing non-euclidean error

We consider the wavelet synopsis construction problem for data streams where given n numbers we wish to estimate the data by constructing a synopsis, whose size, say B is much smaller than n. The B numbers are chosen to minimize a suitable error between the original data and the estimate derived from the synopsis. Several good one-pass wavelet construction streaming algorithms minimizing the 2 error exist. For other error measures, the problem is less understood. We provide the first one-pass small space streaming algorithms with provable error guarantees (additive approximation) for minimizing a variety of non-Euclidean error measures including all weighted p (including ) and relative error p metrics. In several previous works solutions (for weighted 2, and maximum relative error) where the B synopsis coefficients are restricted to be wavelet coefficients of the data were proposed. This restriction yields suboptimal solutions on even fairly simple examples. Other lines of research, s...

• Type: Conference
• Year: 2005
• Where: KDD
• Authors: Sudipto Guha, Boulos Harb
• Keywords: Data Mining, KDD 2005, Maximum Relative Error, Non-Euclidean Error Measures, Provable Error Guarantees