Proud

Abstract

We present PROUD -A PRObabilistic approach to processing similarity queries over Uncertain Data streams, where the data streams here are mainly time series streams. In contrast to data with certainty, an uncertain series is an ordered sequence of random variables. The distance between two uncertain series is also a random variable. We use a general uncertain data model, where only the mean and the deviation of each random variable at each timestamp are available. We derive mathematical conditions for progressively pruning candidates to reduce the computation cost. We then apply PROUD to a streaming environment where only sketches of streams, like wavelet synopses, are available. Extensive experiments are conducted to evaluate the effectiveness of PROUD and compare it with Det, a deterministic approach that directly processes data without considering uncertainty. The results show that, compared with Det, PROUD offers a flexible trade-off between false positives and false negatives by controlling a threshold, while maintaining a similar computation cost. In contrast, Det does not provide such flexibility. This trade-off is important as in some applications false negatives are more costly, while in others, it is more critical to keep the false positives low.

A Weighted DTW Approach for Similarity Matching over Uncertain Time Series

“…Yeh et al use a different data model than [13] and propose an approach named PROUD to deal with the uncertain time series in [16] Instead of using sample points for each element, the elements of each timestamp are treated as random variables with means and deviations. The distance between two points is represented by Euclidean distance.…”

“…There is a growing interest in studying uncertain time series. Distance measurements for uncertain time series are rare [13], [14], [15], [16], [17]. The issue of probabilistic bounded range query (PBRQ) for uncertain time series data is first discussed in [10].…”

“…Here DB is a set of uncertain time series, and DIST () means a distance measurement. Note that the approaches in [13], [16] have different definitions for DIST ().…”

“…In this section, we propose a new distance measure for uncertain time series. We use a general uncertain time series model in [16], [17], in which the value of uncertain time series at a time point is considered as a random variable. For a random variable at a time point, it contains a mean and a deviation.…”

“…Like classical time series, the similarity matching is also a fundamental and crucial issue in the analysis of uncertain time series data [14], [15]. Some efforts have been made to give solutions to similarity measurements of uncertain time series based on different models of uncertain time series (i.e., [13], [16], [17]). Uncertain time series matching algorithms can be applied in processing data (skyline queries on uncertain time series [18] and in solving some application problems (e.g., CPU utilization time patterns of several MapReduce applications in [19].…”