DRSP : Dimension Reduction For Similarity Matching And Pruning Of Time Series Data Streams

Similarity matching and join of time series data streams has gained a lot of relevance in today's world that has large streaming data. This process finds wide scale application in the areas of location tracking, sensor networks, object positioning and monitoring to name a few. However, as the size of the data stream increases, the cost involved to retain all the data in order to aid the process of similarity matching also increases. We develop a novel framework to addresses the following objectives. Firstly, Dimension reduction is performed in the preprocessing stage, where large stream data is segmented and reduced into a compact representation such that it retains all the crucial information by a technique called Multi-level Segment Means (MSM). This reduces the space complexity associated with the storage of large time-series data streams. Secondly, it incorporates effective Similarity Matching technique to analyze if the new data objects are symmetric to the existing data stream. And finally, the Pruning Technique that filters out the pseudo data object pairs and join only the relevant pairs. The computational cost for MSM is O(l*ni) and the cost for pruning is O(DRF*wsize*d), where DRF is the Dimension Reduction Factor. We have performed exhaustive experimental trials to show that the proposed framework is both efficient and competent in comparison with earlier works.Comment: 20 pages,8 figures, 6 Table

Temporal validation of particle filters for video tracking

This is the author’s version of a work that was accepted for publication in Journal Computer Vision and Image Understanding. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal Computer Vision and Image Understanding, 131 (2015) DOI: 10.1016/j.cviu.2014.06.016A novel approach to determine adaptively the temporal consistency of Particle Filters.The proposed method is demonstrated on online performance evaluation of tracking.Temporal consistency is modeled by convolutions of mixtures of Gamma distributions.The proposed method does not need thresholds and can be used on large datasets. We present an approach for determining the temporal consistency of Particle Filters in video tracking based on model validation of their uncertainty over sliding windows. The filter uncertainty is related to the consistency of the dispersion of the filter hypotheses in the state space. We learn an uncertainty model via a mixture of Gamma distributions whose optimum number is selected by modified information-based criteria. The time-accumulated model is estimated as the sequential convolution of the uncertainty model. Model validation is performed by verifying whether the output of the filter belongs to the convolution model through its approximated cumulative density function. Experimental results and comparisons show that the proposed approach improves both precision and recall of competitive approaches such as Gaussian-based online model extraction, bank of Kalman filters and empirical thresholding. We combine the proposed approach with a state-of-the-art online performance estimator for video tracking and show that it improves accuracy compared to the same estimator with manually tuned thresholds while reducing the overall computational cost.This work was partially supported by the Spanish Government (EventVideo, TEC2011-25995) and by the EU Crowded Environments monitoring for Activity Understanding and Recognition (CENTAUR, FP7-PEOPLE-2012-IAPP) project under GA number 324359. Most of the work reported in this paper was done at the Centre for Intelligent Sensing in Queen Mary University of London

Tight Bounds for Adversarially Robust Streams and Sliding Windows via Difference Estimators

In the adversarially robust streaming model, a stream of elements is presented to an algorithm and is allowed to depend on the output of the algorithm at earlier times during the stream. In the classic insertion-only model of data streams, Ben-Eliezer et. al. (PODS 2020, best paper award) show how to convert a non-robust algorithm into a robust one with a roughly $1/\varepsilon$ factor overhead. This was subsequently improved to a $1/\sqrt{\varepsilon}$ factor overhead by Hassidim et. al. (NeurIPS 2020, oral presentation), suppressing logarithmic factors. For general functions the latter is known to be best-possible, by a result of Kaplan et. al. (CRYPTO 2021). We show how to bypass this impossibility result by developing data stream algorithms for a large class of streaming problems, with no overhead in the approximation factor. Our class of streaming problems includes the most well-studied problems such as the $L_2$-heavy hitters problem, $F_p$-moment estimation, as well as empirical entropy estimation. We substantially improve upon all prior work on these problems, giving the first optimal dependence on the approximation factor. As in previous work, we obtain a general transformation that applies to any non-robust streaming algorithm and depends on the so-called flip number. However, the key technical innovation is that we apply the transformation to what we call a difference estimator for the streaming problem, rather than an estimator for the streaming problem itself. We then develop the first difference estimators for a wide range of problems. Our difference estimator methodology is not only applicable to the adversarially robust model, but to other streaming models where temporal properties of the data play a central role. (Abstract shortened to meet arXiv limit.)Comment: FOCS 202