Accurate and precise aggregation counting

AbstractAggregation counting is any procedure designed to solve the following problem: a number n of agents produces a fixed length binary message, and a central station produces an estimate of n from the bit-by-bit OR of the messages, which is therefore duplicate-insensitive. Such procedures are applicable to a situation where each of n independent sensors broadcasts the message to be used to estimate the count. A mathematically brilliant solution to this problem, due to Flajolet and Martin (1985) [1], is unfortunately affected by substantial bias and error. In this note we outline an alternative approach, which uses the Flajolet–Martin technique as a preparatory step and substantially reduces both error and bias. Specifically, the standard deviation of the count estimate drops from ∼110% to ∼20% of the estimated value

Spectra: Robust Estimation of Distribution Functions in Networks

Distributed aggregation allows the derivation of a given global aggregate property from many individual local values in nodes of an interconnected network system. Simple aggregates such as minima/maxima, counts, sums and averages have been thoroughly studied in the past and are important tools for distributed algorithms and network coordination. Nonetheless, this kind of aggregates may not be comprehensive enough to characterize biased data distributions or when in presence of outliers, making the case for richer estimates of the values on the network. This work presents Spectra, a distributed algorithm for the estimation of distribution functions over large scale networks. The estimate is available at all nodes and the technique depicts important properties, namely: robust when exposed to high levels of message loss, fast convergence speed and fine precision in the estimate. It can also dynamically cope with changes of the sampled local property, not requiring algorithm restarts, and is highly resilient to node churn. The proposed approach is experimentally evaluated and contrasted to a competing state of the art distribution aggregation technique.Comment: Full version of the paper published at 12th IFIP International Conference on Distributed Applications and Interoperable Systems (DAIS), Stockholm (Sweden), June 201

Approximation with Error Bounds in Spark

We introduce a sampling framework to support approximate computing with estimated error bounds in Spark. Our framework allows sampling to be performed at the beginning of a sequence of multiple transformations ending in an aggregation operation. The framework constructs a data provenance tree as the computation proceeds, then combines the tree with multi-stage sampling and population estimation theories to compute error bounds for the aggregation. When information about output keys are available early, the framework can also use adaptive stratified reservoir sampling to avoid (or reduce) key losses in the final output and to achieve more consistent error bounds across popular and rare keys. Finally, the framework includes an algorithm to dynamically choose sampling rates to meet user specified constraints on the CDF of error bounds in the outputs. We have implemented a prototype of our framework called ApproxSpark, and used it to implement five approximate applications from different domains. Evaluation results show that ApproxSpark can (a) significantly reduce execution time if users can tolerate small amounts of uncertainties and, in many cases, loss of rare keys, and (b) automatically find sampling rates to meet user specified constraints on error bounds. We also explore and discuss extensively trade-offs between sampling rates, execution time, accuracy and key loss

Ambient Sound Helps: Audiovisual Crowd Counting in Extreme Conditions

Visual crowd counting has been recently studied as a way to enable people counting in crowd scenes from images. Albeit successful, vision-based crowd counting approaches could fail to capture informative features in extreme conditions, e.g., imaging at night and occlusion. In this work, we introduce a novel task of audiovisual crowd counting, in which visual and auditory information are integrated for counting purposes. We collect a large-scale benchmark, named auDiovISual Crowd cOunting (DISCO) dataset, consisting of 1,935 images and the corresponding audio clips, and 170,270 annotated instances. In order to fuse the two modalities, we make use of a linear feature-wise fusion module that carries out an affine transformation on visual and auditory features. Finally, we conduct extensive experiments using the proposed dataset and approach. Experimental results show that introducing auditory information can benefit crowd counting under different illumination, noise, and occlusion conditions. The dataset and code will be released. Code and data have been made availabl

PDANet: Pyramid Density-aware Attention Net for Accurate Crowd Counting

Crowd counting, i.e., estimating the number of people in a crowded area, has attracted much interest in the research community. Although many attempts have been reported, crowd counting remains an open real-world problem due to the vast scale variations in crowd density within the interested area, and severe occlusion among the crowd. In this paper, we propose a novel Pyramid Density-Aware Attention-based network, abbreviated as PDANet, that leverages the attention, pyramid scale feature and two branch decoder modules for density-aware crowd counting. The PDANet utilizes these modules to extract different scale features, focus on the relevant information, and suppress the misleading ones. We also address the variation of crowdedness levels among different images with an exclusive Density-Aware Decoder (DAD). For this purpose, a classifier evaluates the density level of the input features and then passes them to the corresponding high and low crowded DAD modules. Finally, we generate an overall density map by considering the summation of low and high crowded density maps as spatial attention. Meanwhile, we employ two losses to create a precise density map for the input scene. Extensive evaluations conducted on the challenging benchmark datasets well demonstrate the superior performance of the proposed PDANet in terms of the accuracy of counting and generated density maps over the well-known state of the arts