Algorithms to identify clusters and outliers based on dyadic decomposition with applications to streams

In our thesis we are concerned with multiscale decomposition of data using dyadic cube for clustering and outlier detection. We also extend multiscale decomposition to a streaming setting.; We start with the idea of dyadic decomposition of data for the purpose of multiscale clustering. The multiscale decomposition gives us scale based definitions of three basic constructs in data: clusters, outliers and noise. We introduce two new algorithms for multiscale clustering. We then introduce an algorithm for multiscale outlier detection. We present scale based definitions for outliers, based on cardinality, size and density.; Building on the previous ideas we introduce definitions for streaming outliers and streaming cluster centers. We introduce an algorithm and its modifications for detecting outliers and computing clusters for data streams. Lastly, we introduce a new algorithm, GenIc, for clustering in a streaming setting based on a generalization of incremental clustering.