Theoretical Analysis of Wavelet Synopsis on Partitioned Data Sets

Wavelet synopsis is one of most popular dimensionality reduction methods and has been studied in various areas such as query optimization, approximate query answering, feature selection, etc. Currently, the size of data becomes much larger and the distributed data processing is increasingly important. The MapReduce well known as Google's data processing environment is the most popular distributed platform with good scalability and fault tolerance. Thus, recently, the algorithms to construct wavelet synopses on the MapReduce platform were proposed. In this paper, we theoretically analyze wavelet synopsis on partitioned data sets. Although the wavelet synopsis on partitioned data sets was proposed in recent work, only the algorithmic implementation and experimental results were given but there was no theoretical analysis. Thus, we study theoretical analysis of the properties of wavelet synopsis on partitioned data sets and the correctness of merging them.