We propose a novel approach based on predictive quantization (PQ) for online summarization of multiple time-varying data streams. A synopsis over a sliding window of most recent entries is computed in one pass and dynamically updated in constant time. The correlation between consecutive data elements is effectively taken into account without the need for preprocessing. We extend PQ to multiple streams and propose structures for real-time summarization and querying of a massive number of streams. Queries on any subsequence of a sliding window over multiple streams are processed in real time. We examine each component of the proposed approach, prediction, and quantization separately and investigate the space-accuracy trade-off for synopsis generation. Complementing the theoretical optimality of PQ-based approaches, we show that the proposed technique, even for very short prediction windows, significantly outperforms the current techniques for a wide variety of query types on both synthetic and real data sets.

Clustering has been shown to be effective in analyzing functional relationships of genes. However, no single clustering method with single distance metric is capable of capturing all types of relationships that a gene may have with other genes. In this paper we introduce a framework which groups genes around a query gene, and ranks them in order corresponding to different levels of similarity utilizing multiple metrics. The focus of our efforts is to create gene centric clusters. The notion of Strong Group (SG) is presented as a cluster definition where no two genes are distant from each other, greater than a threshold value. The genes are then ranked on their frequency of co-occurrence. The grouping and rankings are drawn by applying set operations over results of multiple distance metrics, each capturing particular similarities such as shifted relationships, negative correlations and strong positive relationships. The effectiveness of the algorithm is demonstrated on two case studies. In the first one, a single yeast cell cycle dataset is used. It is shown that different combination of set operations reveals different kinds of interactions between genes. Finally, to provide further analysis on our techniques, we have tested them on multiple microarray datasets obtained from Stanford Microarray Database.

An effective analysis of clinical trials data involves analyzing different types of data such as heterogeneous and high dimensional time series data. The current time series analysis methods generally assume that the series at hand have sufficient length to apply statistical techniques to them. Other ideal case assumptions are that data are collected in equal length intervals, and while comparing time series, the lengths are usually expected to be equal to each other. However, these assumptions are not valid for many real data sets, especially for the clinical trials data sets. An addition, the data sources are different from each other, the data are heterogeneous, and the sensitivity of the experiments varies by the source. Approaches for mining time series data need to be revisited, keeping the wide range of requirements in mind. In this paper, we propose a novel approach for information mining that involves two major steps: applying a data mining algorithm over homogeneous subsets of data, and identifying common or distinct patterns over the information gathered in the first step. Our approach is implemented specifically for heterogeneous and high dimensional time series clinical trials data. Using this framework, we propose a new way of utilizing frequent itemset mining, as well as clustering and declustering techniques with novel distance metrics for measuring similarity between time series data. By clustering the data, we find groups of analytes (substances in blood) that are most strongly correlated. Most of these relationships already known are verified by the clinical panels, and, in addition, we identify novel groups that need further biomedical analysis. A slight modification to our algorithm results an effective declustering of high dimensional time series data, which is then used for "feature selection." Using industry-sponsored clinical trials data sets, we are able to identify a small set of analytes that effectively models the state of normal health.