Kernel density estimation for directional–linear data

García‐Portugués, Eduardo; Crujeiras, Rosa M.; González–Manteiga, Wenceslao

doi:10.1016/j.jmva.2013.06.009

Cited by 62 publications

(51 citation statements)

References 25 publications

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“…With these conditions, the PDF estimate has the properties of a probability density function [10,11]. Although any kernel that satisfies these conditions is viable, the simplest and most convenient usable kernel is ( ) , which is commonly referred to as the von Mises kernel, created with the von Mises -Fisher directional probability distribution on the L-sphere in mind:…”

Section: ) Directional Kernel Density Estimationmentioning

confidence: 99%

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Directional Kernel Density Estimation for Classification of Breast Tissue Spectra

Pardo

Real

Krishnaswamy

et al. 2017

IEEE Trans. Med. Imaging

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Abstract-In Breast Conserving Therapy, surgeons measure the thickness of healthy tissue surrounding an excised tumor (surgical margin) via post-operative histological or visual assessment tests that, for lack of enough standardization and reliability, have recurrence rates in the order of 33%. Spectroscopic interrogation of these margins is possible during surgery, but algorithms are needed for parametric or dimension reduction processing. One methodology for tumor discrimination based on dimensionality reduction and nonparametric estimation -in particular, Directional Kernel Density Estimation -is proposed and tested on spectral image data from breast samples. Once a hyperspectral image of the tumor has been captured, a surgeon assists by establishing Regions of Interest where tissues are qualitatively differentiable. After proper normalization, Directional KDE is used to estimate the likelihood of every pixel in the image belonging to each specified tissue class. This information is enough to yield, in almost real time and with 98% accuracy, results that coincide with those provided by histological H&E validation performed after the surgery.

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Section: ) Directional Kernel Density Estimationmentioning

confidence: 99%

“…or, in other words, using the von Mises kernel provides a generalized estimator of directional densities, being the estimate a mixture of von Mises -Fisher directional density probability functions [10]:…”

Section: ) Directional Kernel Density Estimationmentioning

confidence: 99%

Directional Kernel Density Estimation for Classification of Breast Tissue Spectra

Pardo

Real

Krishnaswamy

et al. 2017

IEEE Trans. Med. Imaging

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“…The circular Wasserstein distance ∆ is used to compare the distribution of phases to another distribution with circular symmetry, it corresponds to the minimal distance from all linear Wasserstein distances on an unfolded circle for all possible starting points on the circle (Rabin et al, 2011). Circular and circular-linear kernel density estimations use von Mises and Gaussian kernels with adaptive concentration and smoothing parameters (García-Portugués et al, 2013).…”

Section: Discussionmentioning

confidence: 99%

Hippocampal spike-time correlations and place-field overlaps during open field foraging

Monsalve‐Mercado

Roudi²

2019

Preprint

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Phase precessing place cells encode spatial information on fine timescales via the timing of their spikes. This phase code has been extensively studied on linear tracks and for short runs in the open field. However, less is known about the phase code on unconstrained trajectories lasting tens of minutes, typical of open field foraging.In previous work (Monsalve-Mercado and Leibold, 2017), an analytic expression was derived for the spike-time cross-correlation between phase precessing place cells during natural foraging in the open field. This expression makes two predictions on how this phase code differs from the linear track case: cross-correlations are symmetric with respect to time, and they represent the distance between pairs of place fields in that the theta-filtered cross-correlations around zero time-lag are positive for cells with nearby fields while they are negative for those with fields further apart. Here we analyze several available open field recordings and show that these predictions hold for pairs of CA1 place cells. We also show that the relationship remains during remapping in CA1, and it is also present in place cells in area CA3. For CA1 place cells of Fmr1-null mice, which exhibit normal place fields but somewhat weaker temporal coordination with respect to theta compared to wild type, the cross-correlations still remain symmetric but the relationship to place field overlap is largely lost. The relationship discussed here describes how spatial information is communicated by place cells to downstream areas in a finer theta-timescale, relevant for learning and memory formation in behavioural tasks lasting tens of minutes in the open field.

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“…The circular Wasserstein distance ∆ is used to compare the distribution of phases to another distribution with circular symmetry, it corresponds to the minimal distance from all linear Wasserstein distances on an unfolded circle for all possible starting points on the circle (Rabin et al, ). Circular and circular‐linear kernel density estimations (CLKDEs) use von Mises and Gaussian kernels with adaptive concentration and smoothing parameters (Garcıa‐Portugues, Crujeiras, & Gonzalez‐Manteiga, ).…”

Section: Methodsmentioning

confidence: 99%

Hippocampal spike‐time correlations and place field overlaps during open field foraging

Monsalve‐Mercado

Roudi²

2019

Hippocampus

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Phase precessing place cells encode spatial information on fine timescales via the timing of their spikes. This phase code has been extensively studied on linear tracks and for short runs in the open field. However, less is known about the phase code on unconstrained trajectories lasting tens of minutes, typical of open field foraging. In previous work (Monsalve‐Mercado and Leibold, Physical Review Letters, 119, 38101 (2017)), an analytic expression was derived for the spike‐time cross‐correlation between phase precessing place cells during natural foraging in the open field. This expression makes two predictions on how this phase code differs from the linear track case: cross‐correlations are symmetric with respect to time, and they represent the distance between pairs of place fields in that the theta‐filtered cross‐correlations around zero time lag are positive for cells with nearby fields while they are negative for those with fields further apart. Here we analyze several available open field recordings and show that these predictions hold for pairs of CA1 place cells. We also show that the relationship remains during remapping in CA1, and it is also present in place cells in area CA3. For CA1 place cells of Fmr1‐null mice, which exhibit normal place fields but somewhat weaker temporal coordination with respect to theta compared to wild type, the cross‐correlations still remain symmetric but the relationship to place field overlap is largely lost. The relationship discussed here describes how spatial information is communicated by place cells to downstream areas in a finer theta‐timescale, relevant for learning and memory formation in behavioral tasks lasting tens of minutes in the open field.

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Kernel density estimation for directional–linear data

Cited by 62 publications

References 25 publications

Directional Kernel Density Estimation for Classification of Breast Tissue Spectra

Directional Kernel Density Estimation for Classification of Breast Tissue Spectra

Hippocampal spike-time correlations and place-field overlaps during open field foraging

Hippocampal spike‐time correlations and place field overlaps during open field foraging

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