We study a set of linear transformations on the Fourier series representation of a sequence that can be used as the basis for similarity queries on time-series data. We show that our set of transformations is rich enough to formulate operations such as moving average and time warping. We present a query processing algorithm that uses the underlying R-tree index of a multidimensional data set to answer similarity queries efficiently. Our experiments show that the performance of this algorithm is competitive to that of processing ordinary (exact match) queries using the index, and much faster than sequential scanning. We relate our transformations to the general framework for similarity queries of Jagadish et al.

Traditional duplicate elimination techniques are not applicable to many data stream applications. In general, precisely eliminating duplicates in an unbounded data stream is not feasible in many streaming scenarios. Therefore, we target at approximately eliminating duplicates in streaming environments given a limited space. Based on a well-known bitmap sketch, we introduce a data structure, Stable Bloom Filter, and a novel and simple algorithm. The basic idea is as follows: since there is no way to store the whole history of the stream, SBF continuously evicts the stale elements so that SBF has room for those more recent ones. After finding some properties of SBF analytically, we show that a tight upper bound of false positive rates is guaranteed. In our empirical study, we compare SBF to alternative methods. The results show that our method is superior in terms of both accuracy and time efficiency when a fixed small space and an acceptable false positive rate are given.

Result diversity is a topic of great importance as more facets of queries are discovered and users expect to find their desired facets in the first page of the results. However, the underlying questions of how 'diversity' interplays with 'quality' and when preference should be given to one or both are not well-understood. In this work, we model the problem as expectation maximization and study the challenges of estimating the model parameters and reaching an equilibrium. One model parameter, for example, is correlations between pages which we estimate using textual contents of pages and click data (when available). We conduct experiments on diversifying randomly selected queries from a query log and the queries chosen from the disambiguation topics of Wikipedia. Our algorithm improves upon Google in terms of the diversity of random queries, retrieving 14% to 38% more aspects of queries in top 5, while maintaining a precision very close to Google. On a more selective set of queries that are expected to benefit from diversification, our algorithm improves upon Google in terms of precision and diversity of the results, and significantly outperforms another baseline system for result diversification.

We study a set of linear transformations on the Fourier series representation of a sequence that can be used as the basis for similarity queries on time-series data. We show that our set of transformations is rich enough to formulate operations such as moving average and time warping. We present a query processing algorithm that uses the underlying R-tree index of a multidimensional data set to answer similarity queries efficiently. Our experiments show that the performance of this algorithm is competitive to that of processing ordinary (ex-act match) queries using the index, and much faster than sequential scanning. We relate our transformations to the general framework for similarity queries of Jagadish et al.

We propose an improvement of the known DFT-based indexing technique for fast retrieval of similar time series. We use the last few Fourier coefficients in the distance computation without storing them in the index since every coefficient at the end is the complex conjugate of a coefficient at the beginning and as strong as its counterpart. We show analytically that this observation can accelerate the search time of the index by more than a factor of two. This result was confirmed by our experiments, which were carried out on real stock prices and synthetic data.