Kernel density estimation and its application

Węglarczyk, Stanisław

doi:10.1051/itmconf/20182300037

Cited by 275 publications

(150 citation statements)

References 32 publications

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“…Multivariate non-parametric kernel density estimation was performed to visualize the distribution of BM samples ( 28 , 29 ). Multivariate non-parametric kernel density estimation enables better exploratory data analysis by reconstructing probabilistic density functions using the sample data in a non-parametric way ( 30 , 31 ). A multivariate probabilistic density function

is estimated as:…”

Section: Methodsmentioning

confidence: 99%

Brain Metastases From Lung Adenocarcinoma May Preferentially Involve the Distal Middle Cerebral Artery Territory and Cerebellum

et al. 2020

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Although whole-brain radiation therapy (WBRT) is the mainstay of treatment for brain metastases (BMs), the concept of saving eloquent cortical lesions has been promoted. If BMs from lung cancer are spatially biased to certain regions, this approach can be justified more. We evaluated whether BMs from lung cancer show a preference for certain brain regions and if their distribution pattern differs according to the histologic subtype of the primary lung cancer. In this retrospective study, 562 BMs in 80 patients were analyzed (107 BMs from small cell carcinoma, 432 from adenocarcinoma, and 23 from squamous cell carcinoma). Kernel density estimation was performed to investigate whether BM spatial patterns differed among lung cancer subtypes. Further, we explored more detailed subregions where BMs from adenocarcinomas occur frequently using one-way analysis of variance. Finally, we divided our cohort into those with fewer (≤10) and more (>10) BMs and evaluated whether this biased pattern was maintained across limited and extensive stages. For small cell carcinoma, BMs were biased to the cerebellum, but this did not reach statistical significance. For adenocarcinoma, BMs were found more frequently near the distal middle cerebral artery (MCA) territory and cerebellum than in other arterial territories ( p < 0.01). The precentral and postcentral gyri were the most significant subregions within the distal anterior cerebral artery (ACA) and MCA territories ( p < 0.01). Crus I and Lobule VI were significant regions within the cerebellum ( p < 0.01). Regardless of the number of BMs, the affinity to the distal MCA territory and cerebellum was maintained. The present data confirm that BMs from lung adenocarcinoma may preferentially involve the distal MCA territory and cerebellum.

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is estimated as:…”

Section: Methodsmentioning

confidence: 99%

Brain Metastases From Lung Adenocarcinoma May Preferentially Involve the Distal Middle Cerebral Artery Territory and Cerebellum

et al. 2020

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“…Here, we use kernel density estimation to evaluate the probability density function of a random variable, which gives a better approximation of the studied probability distribution compared to a traditional histogram [52,53]. Our method applies KDE to calculate probability density by each of the shapelets in the subset.…”

Section: Kernel Density Estimator (Kde)mentioning

confidence: 99%

“…Then, we generalize the local shapelets for discovering robust and high dimensional state shapes of dFNC, which we call 'statelets'. The method uses a kernel density estimator (KDE) to compute the probability density of the shapelets, which are later used to check the eligibility of shapelets to be interpreted as statelets [25]. We aim to approximate a corset of shapes for the dynamics rather than subgrouping the time series using the shapelets similarity.…”

Section: Introductionmentioning

confidence: 99%

Statelets: High dimensional predominant shapes in dynamic functional network connectivity

Rahaman

Damaraju

Saha

et al. 2020

Preprint

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Dynamic functional network connectivity (dFNC) analysis has been attracting interest over the past years by elucidating crucial details of brain activation patterns in severe neurological or psychiatric disorders. Consequently, a considerable amount of work has been conducted to analyze dFNC and leverage it for an improved understanding of neuro-dynamics and cognition. However, state-of-art methods mostly focus on fixed patterns of connectivity that reoccur. Such approaches do not capture the more transient feature space of the brain's neural system and its dynamic properties. Likewise, the dynamical system approaches to model the system continuously and do not well capture unmodelled heterogeneity across subjects and time. Here, we seek an improved understanding of these connectivity states and the mechanism through which their dynamics vary across individuals. Relying on the concept of shapelets to model the temporal dynamics of functional associations between intrinsic brain networks, we develop the 'statelet' - a high dimensional state-shape representation of dynamics. We handle scale differences using the earth mover distance as our similarity metric and utilizing kernel density estimation to build a probability density profile for each shapelet. Unlike clustering the time series, we approximate short, variable-length connectivity patterns using the probability density profile of the shapelets from lower dimensions. We apply the proposed approach to study patients with schizophrenia (SZ) exhibit and identify reduced modularity increased statelet recurrence in their brain network organization relative to healthy controls (HC). An analysis of the connections' consistency across time reveals significant differences within visual, sensorimotor, and default mode regions where HC subjects show higher consistency than SZ. The introduced statelet-approach enables the handling of dynamic information in cross-modal applications to study healthy and disordered brains and multi-modal fusion within a single dataset.

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“…The use of KDE has a significant advantage of directly evaluating the data without previously applying a model onto it [38]. In contrast to the commonly used histogram as an estimation of a datasets density, the shape of the kernel density estimation is continuous and seems to be a reasonable estimation of the "true" PDF [39]. According to Sheather [40], the bias of kernel density estimation is one order better compared to a histogram estimator.…”

Section: Probability Density Functionsmentioning

confidence: 99%

“…Each observed sample is first replaced with a uniform kernel K, which is here based on the normal Gaussian distribution, which is the most frequently used kernel [39]:…”

Section: Probability Density Functionsmentioning

confidence: 99%

Improving air leakage prediction of buildings using the fan pressurization method with the Weighted Line of Organic Correlation

Kölsch

Walker

2020

Building and Environment

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Kernel density estimation and its application

Cited by 275 publications

References 32 publications

Brain Metastases From Lung Adenocarcinoma May Preferentially Involve the Distal Middle Cerebral Artery Territory and Cerebellum

Brain Metastases From Lung Adenocarcinoma May Preferentially Involve the Distal Middle Cerebral Artery Territory and Cerebellum

Statelets: High dimensional predominant shapes in dynamic functional network connectivity

Improving air leakage prediction of buildings using the fan pressurization method with the Weighted Line of Organic Correlation

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