Distance between Sets

Levandowsky, M.; Winter, David J.

doi:10.1038/234034a0

Cited by 619 publications

(257 citation statements)

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“…Ruddell et al (2007) also found the Jaccard (1901) similarity coefficient to be the best among a range of similarity indices in the context of comprehensively measuring social stability. Additionally, its complement from unity is a true distance metric (Levandowsky and Winter, 1971). This paper, therefore, introduces and studies its use in quantifying fMRI reproducibility in Section 2.1.…”

Section: Introductionmentioning

confidence: 99%

A re-defined and generalized percent-overlap-of-activation measure for studies of fMRI reproducibility and its use in identifying outlier activation maps

Maitra

2010

NeuroImage

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Functional Magnetic Resonance Imaging (fMRI) is a popular noninvasive modality to investigate activation in the human brain. The end result of most fMRI experiments is an activation map corresponding to the given paradigm. These maps can vary greatly from one study to the next, so quantifying the reliability of identified activation over several fMRI studies is important. The percent overlap of activation (Rombouts et al., 1998 andMachielsen et al., 2000) is a global reliability measure between activation maps drawn from any two fMRI studies. A slightly modified but more intuitive measure is provided by the Jaccard (1901) coefficient of similarity, whose use we study in this paper. A generalization of these measures is also proposed to comprehensively summarize the reliability of multiple fMRI studies. Finally, a testing mechanism to flag potentially anomalous studies is developed. The methodology is illustrated on studies involving left-and righthand motor task paradigms performed by a right-hand dominant male subject several times over a period of two months, with excellent results. KeywordsEigenvalues, Reliability, Intra-class correlation coefficient, Outlier detection, Percent overlap, Principal components, Finger-thumb opposition experiment, Summarized multiple Jaccard similarity coefficient, Dice coefficient, Perron-Frobenius theorem Disciplines Statistics and ProbabilityComments NOTICE:this is the author's version of a work that was accepted for publication in NeuroImage. 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 NeuroImage, [v.50, iss.1,(2010) AbstractFunctional Magnetic Resonance Imaging (fMRI) is a popular non-invasive modality to investigate activation in the human brain. The end result of most fMRI experiments is an activation map corresponding to the given paradigm. These maps can vary greatly from one study to the next, so quantifying the reliability of identified activation over several fMRI studies is important. The percent overlap of activation (Rombouts et al., 1998;Machielsen et al., 2000) is a global reliability measure between activation maps drawn from any two fMRI studies. A slightly modified but more intuitive measure is provided by the Jaccard (1901) coefficient of similarity, whose use we study in this paper. A generalization of these measures is also proposed to comprehensively summarize the reliability of multiple fMRI studies. Finally, a testing mechanism to flag potentially anomalous studies is developed. The methodology is illustrated on studies involving left-and right-hand motor task paradigms performed by a right-hand dominant male subject several times over a period of two months, with excellent results.

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Section: Introductionmentioning

confidence: 99%

A re-defined and generalized percent-overlap-of-activation measure for studies of fMRI reproducibility and its use in identifying outlier activation maps

Maitra

2010

NeuroImage

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“…The Jaccard coefficient is often used as a measure of similarity between sets S 1 and S 2 [11,20]. It is defined as…”

Section: Jaccard and Related Coefficientsmentioning

confidence: 99%

Parallel jaccard and related graph clustering techniques

Fender

Emad

Petiton

et al. 2017

Proceedings of the 8th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems

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In this paper we propose to generalize Jaccard and related measures, often used as similarity coefficients between two sets. We define Jaccard, Dice-Sorensen and Tversky edge weights on a graph and generalize them to account for vertex weights. We develop an efficient parallel algorithm for computing Jaccard edge and PageRank vertex weights. We highlight that the weights computation can obtain more than 10× speedup on the GPU versus CPU on large realistic data sets. Also, we show that finding a minimum balanced cut for modified weights can be related to minimizing the sum of ratios of the intersection and union of nodes on the boundary of clusters. Finally, we show that the novel weights can improve the quality of the graph clustering by about 15% and 80% for multi-level and spectral graph partitioning and clustering schemes, respectively.

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“…For comparisons, we use the same metrics as in [15], namely the Boundary Displacement Error [9] (BDE) and the Jaccardindex (i.e., intersection over union, IOU) [21] (J). Fig.…”

Section: Saliency-based Evaluationmentioning

confidence: 99%

Lightweight Monocular Obstacle Avoidance by Salient Feature Fusion

Manno-Kovacs

Kovács

2017

2017 IEEE International Conference on Computer Vision Workshops (ICCVW)

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We present a monocular obstacle avoidance method based on a novel image feature map built by fusing robust saliency features, to be used in embedded systems on lightweight autonomous vehicles. The fused salient features are a textural-directional Harris based feature map and a relative focus feature map. We present the generation of the fused salient map, along with its application for obstacle avoidance. Evaluations are performed from a saliency point of view, and for the assessment of the method's applicability for obstacle avoidance in simulated environments. The presented results support the usability of the method in embedded systems on lightweight unmanned vehicles.

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Distance between Sets

Cited by 619 publications

References 2 publications

A re-defined and generalized percent-overlap-of-activation measure for studies of fMRI reproducibility and its use in identifying outlier activation maps

A re-defined and generalized percent-overlap-of-activation measure for studies of fMRI reproducibility and its use in identifying outlier activation maps

Parallel jaccard and related graph clustering techniques

Lightweight Monocular Obstacle Avoidance by Salient Feature Fusion

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