Fast and Accurate Mining of Correlated Heavy Hitters

The problem of mining Correlated Heavy Hitters (CHH) from a two-dimensional data stream has been introduced recently, and a deterministic algorithm based on the use of the Misra--Gries algorithm has been proposed by Lahiri et al. to solve it. In this paper we present a new counter-based algorithm for tracking CHHs, formally prove its error bounds and correctness and show, through extensive experimental results, that our algorithm outperforms the Misra--Gries based algorithm with regard to accuracy and speed whilst requiring asymptotically much less space

A Parallel Space Saving Algorithm For Frequent Items and the Hurwitz zeta distribution

We present a message-passing based parallel version of the Space Saving algorithm designed to solve the $k$--majority problem. The algorithm determines in parallel frequent items, i.e., those whose frequency is greater than a given threshold, and is therefore useful for iceberg queries and many other different contexts. We apply our algorithm to the detection of frequent items in both real and synthetic datasets whose probability distribution functions are a Hurwitz and a Zipf distribution respectively. Also, we compare its parallel performances and accuracy against a parallel algorithm recently proposed for merging summaries derived by the Space Saving or Frequent algorithms.Comment: Accepted for publication. To appear in Information Sciences, Elsevier. http://www.sciencedirect.com/science/article/pii/S002002551500657

Parallel mining of time-faded heavy hitters

In this paper we present PFDCMSS (Parallel Forward Decay Count-Min Space Saving) which, to the best of our knowledge, is the world first message-passing parallel algorithm for mining time-faded heavy hitters. The algorithm is a parallel version of the recently published FDCMSS (Forward Decay Count-Min Space Saving) sequential algorithm. We formally prove its correctness by showing that the underlying data structure, a sketch augmented with a Space Saving stream summary holding exactly two counters, is mergeable. Whilst mergeability of traditional sketches derives immediately from theory, we show that, instead, merging our augmented sketch is non trivial. Nonetheless, the resulting parallel algorithm is fast and simple to implement. The very large volumes of modern datasets in the context of Big Data present new challenges that current sequential algorithms can not cope with; on the contrary, parallel computing enables near real time processing of very large datasets, which are growing at an unprecedented scale. Our algorithm's implementation, taking advantage of the MPI (Message Passing Interface) library, is portable, reliable and provides cutting-edge performance. Extensive experimental results confirm that PFDCMSS retains the extreme accuracy and error bound provided by FDCMSS whilst providing excellent parallel scalability. Our contributions are three-fold: (i) we prove the non trivial mergeability of the augmented sketch used in the FDCMSS algorithm; (ii) we derive PFDCMSS, a novel message-passing parallel algorithm; (iii) we experimentally prove that PFDCMSS is extremely accurate and scalable, allowing near real time processing of large datasets. The result supports both casual users and seasoned, professional scientists working on expert and intelligent systems

Advanced Visualization and Interaction Systems for Surgical Pre-operative Planning

The visualization of 3D models of the patient’s body emerges as a priority in surgery. In this paper two different visualization and interaction systems are presented: a virtual interface and a low cost multi-touch screen. The systems are able to interpret in real-time the user’s movements and can be used in the surgical pre-operative planning for the navigation and manipulation of 3D models of the human body built from CT images. The surgeon can visualize both the standard patient information, such as the CT image dataset, and the 3D model of the patient’s organs built from these images. The developed virtual interface is the first prototype of a system designed to avoid any contact with the computer so that the surgeon is able to visualize models of the patient’s organs and to interact with these, moving the finger in the free space. The multi-touch screen provides a custom user interface developed for doctors’ needs that allows users to interact, for surgical pre-operative planning purposes, both with the 3D model of the patient’s body built from medical images, and with the image dataset

On Frequency Estimation and Detection of Heavy Hitters in Data Streams

A stream can be thought of as a very large set of data, sometimes even infinite, which arrives sequentially and must be processed without the possibility of being stored. In fact, the memory available to the algorithm is limited and it is not possible to store the whole stream of data which is instead scanned upon arrival and summarized through a succinct data structure in order to maintain only the information of interest. Two of the main tasks related to data stream processing are frequency estimation and heavy hitter detection. The frequency estimation problem requires estimating the frequency of each item, that is the number of times or the weight with which each appears in the stream, while heavy hitter detection means the detection of all those items with a frequency higher than a fixed threshold. In this work we design and analyze ACMSS, an algorithm for frequency estimation and heavy hitter detection, and compare it against the state of the art ASKETCH algorithm. We show that, given the same budgeted amount of memory, for the task of frequency estimation our algorithm outperforms ASKETCH with regard to accuracy. Furthermore, we show that, under the assumptions stated by its authors, ASKETCH may not be able to report all of the heavy hitters whilst ACMSS will provide with high probability the full list of heavy hitters