Recently data mining over uncertain data streams has attracted a lot of attentions because of the widely existed imprecise data generated from a variety of streaming applications. Many applications have endless uncertain data streams which have a huge amount of data so that it is infeasible to reserve all data in memory to be visited. Therefore, we need a new technology to effectively compress uncertain data streams. Among different data compression technology, the Haar wavelet decomposition is the most popular one, but the traditional wavelet decomposition is no longer applicable on uncertain data streams. Although a significant amount of previous research explore various data reduction techniques on data streams, data reduction techniques on uncertain data streams have seldom been investigated. In this paper, we try to resolve the problem of the wavelet decomposition over uncertain data streams and propose U-HWT(Uncertain Haar Wavelet Transform),a new algorithm for compressing the uncertain data streams. U-HWT uses discrete Haar wavelet transform and emphasis on the impact of the tuple uncertainty on the decomposition. Experimental results show that U-HWT can effectively compress the uncertain data streams.Index Terms-uncertain data streams discrete wavelet transform Haar wavelet decomposition tuple uncertainty

Maintaining a synopsis structure dynamically from data stream is vital for a variety of streaming data applications, such as approximate query or data mining. In many cases, the significance of data item in streams decays with age: this item perhaps conveys critical information first, but, as time goes by, it gets less and less important until it eventually becomes useless. This characteristic is termed amnesic. Random Sampling is often used in construction of synopsis for streaming data. This paper proposed a Weighted Random Sampling based Hierarchical Amnesic Synopses which includes the amnesic characteristic of data stream in the generation of synopsis. The construction methods for weighted random sampling with and without replacement are discussed. We experimentally evaluate the proposed synopsis structure.