Online Computing Quantile Summaries Over Uncertain Data Streams

Quantile summarization is a useful tool in data streams management and mining that can efficiently capture the distribution of the data. A quantile of a sequence of points is the point with a given rank in the sequence. Given a sequence of uncertain points S on the real line, each represented by one-dimensional probability density function (pdf), we study the problem of incrementally maintaining quantile summaries on S such that for any query with a given rank, the summaries can provide a point as the quantile within a given error. We define quantile on uncertain data with discrete or continuous pdf in terms of two error metrics under possible worlds semantics. For an answer to a quantile query on uncertain data, we give the methods for calculating the value of the error and thereby discussing the high-level features of the summaries that can answer approximate quantile query under the two error metrics. We propose an online, space efficient algorithm to compute such summary data on uncertain data streams. The experimental results show that our algorithm substantially outperforms other techniques, such as Monte Carlo and averaging methods, in terms of query error and space for storing the summary data.