Effective and Efficient Summarization for Non-hierarchical Data
Xiang Ji, Yan Xiao, Kaijun Ren, Wang Xiang, Bo Ming Tang · 2021
Data cubes are ubiquitous in domains including meteorology, sales and demography, and data summarization is an important service that can be used to compress data cubes and extract insight. Existing data summarization methods require presupposed hierarchies for the data cube dimensions, which do not exist for many types of data (e.g., rainfall and temperature). To tackle this problem, we first define the non-hierarchical data summarization (NHDS) problem, which covers data cube using rectangle regions with an error bound and minimizes the summary size. We then show that the NHDS problem is NP-hard and design the Mark and Select (MS) algorithm to find an approximate solution. MS first identifies the qualified rectangles and then selects among the rectangles to cover the data cube. To improve efficiency, we show that it suffices to find only some of the qualified rectangles, devise a procedure to avoid checking rectangles that do not contribute to the result, save unnecessary computation during rectangle selection using sub-modularity. We conducted experiments on both real and synthetic datasets. The results show that MS significantly outperforms a state-of-the-art baseline in summary size, error and running time.