Compressive Mining: Fast and Optimal Data Mining in the Compressed Domain

Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance estimation when the data are represented using different sets of coefficients is still a largely unexplored area. This work studies the optimization problems related to obtaining the \emph{tightest} lower/upper bound on Euclidean distances when each data object is potentially compressed using a different set of orthonormal coefficients. Our technique leads to tighter distance estimates, which translates into more accurate search, learning and mining operations \textit{directly} in the compressed domain. We formulate the problem of estimating lower/upper distance bounds as an optimization problem. We establish the properties of optimal solutions, and leverage the theoretical analysis to develop a fast algorithm to obtain an \emph{exact} solution to the problem. The suggested solution provides the tightest estimation of the $L_2$-norm or the correlation. We show that typical data-analysis operations, such as k-NN search or k-Means clustering, can operate more accurately using the proposed compression and distance reconstruction technique. We compare it with many other prevalent compression and reconstruction techniques, including random projections and PCA-based techniques. We highlight a surprising result, namely that when the data are highly sparse in some basis, our technique may even outperform PCA-based compression. The contributions of this work are generic as our methodology is applicable to any sequential or high-dimensional data as well as to any orthogonal data transformation used for the underlying data compression scheme.Comment: 25 pages, 20 figures, accepted in VLD

Coding of non-stationary sources as a foundation for detecting change points and outliers in binary time-series

An interesting scheme for estimating and adapting distributions in real-time for non-stationary data has recently been the focus of study for several different tasks relating to time series and data mining, namely change point detection, outlier detection and online compression/sequence prediction. An appealing feature is that unlike more sophisticated procedures, it is as fast as the related stationary procedures which are simply modified through discounting or windowing. The discount scheme makes older observations lose their influence on new predictions. The authors of this article recently used a discount scheme for introducing an adaptive version of the Context Tree Weighting compression algorithm. The mentioned change point and outlier detection methods rely on the changing compression ratio of an online compression algorithm. Here we are beginning to provide theoretical foundations for the use of these adaptive estimation procedures that have already shown practical promise

A Framework for Developing Real-Time OLAP algorithm using Multi-core processing and GPU: Heterogeneous Computing

The overwhelmingly increasing amount of stored data has spurred researchers seeking different methods in order to optimally take advantage of it which mostly have faced a response time problem as a result of this enormous size of data. Most of solutions have suggested materialization as a favourite solution. However, such a solution cannot attain Real- Time answers anyhow. In this paper we propose a framework illustrating the barriers and suggested solutions in the way of achieving Real-Time OLAP answers that are significantly used in decision support systems and data warehouses