Nonparametric kernel smoothing classification to enhance optical correlation decision performances

Author(s):  
Matthieu Saumard ◽  
Marwa Elbouz ◽  
Michael Aron ◽  
Ayman Alfalou
Sensors ◽  
2019 ◽  
Vol 19 (23) ◽  
pp. 5092
Author(s):  
Matthieu Saumard ◽  
Marwa Elbouz ◽  
Michaël Aron ◽  
Ayman Alfalou ◽  
Christian Brosseau

Optical correlation has a rich history in image recognition applications from a database. In practice, it is simple to implement optically using two lenses or numerically using two Fourier transforms. Even if correlation is a reliable method for image recognition, it may jeopardize decision making according to the location, height, and shape of the correlation peak within the correlation plane. Additionally, correlation is very sensitive to image rotation and scale. To overcome these issues, in this study, we propose a method of nonparametric modelling of the correlation plane. Our method is based on a kernel estimation of the regression function used to classify the individual images in the correlation plane. The basic idea is to improve the decision by taking into consideration the energy shape and distribution in the correlation plane. The method relies on the calculation of the Hausdorff distance between the target correlation plane (of the image to recognize) and the correlation planes obtained from the database (the correlation planes computed from the database images). Our method is tested for a face recognition application using the Pointing Head Pose Image Database (PHPID) database. Overall, the results demonstrate good performances of this method compared to competitive methods in terms of good detection and very low false alarm rates.


2022 ◽  
Vol 23 (S1) ◽  
Author(s):  
Xifang Sun ◽  
Donglin Wang ◽  
Jiaqiang Zhu ◽  
Shiquan Sun

Abstract Background DNA methylation has long been known as an epigenetic gene silencing mechanism. For a motivating example, the methylomes of cancer and non-cancer cells show a number of methylation differences, indicating that certain features characteristics of cancer cells may be related to methylation characteristics. Robust methods for detecting differentially methylated regions (DMRs) could help scientists narrow down genome regions and even find biologically important regions. Although some statistical methods were developed for detecting DMR, there is no default or strongest method. Fisher’s exact test is direct, but not suitable for data with multiple replications, while regression-based methods usually come with a large number of assumptions. More complicated methods have been proposed, but those methods are often difficult to interpret. Results In this paper, we propose a three-step nonparametric kernel smoothing method that is both flexible and straightforward to implement and interpret. The proposed method relies on local quadratic fitting to find the set of equilibrium points (points at which the first derivative is 0) and the corresponding set of confidence windows. Potential regions are further refined using biological criteria, and finally selected based on a Bonferroni adjusted t-test cutoff. Using a comparison of three senescent and three proliferating cell lines to illustrate our method, we were able to identify a total of 1077 DMRs on chromosome 21. Conclusions We proposed a completely nonparametric, statistically straightforward, and interpretable method for detecting differentially methylated regions. Compared with existing methods, the non-reliance on model assumptions and the straightforward nature of our method makes it one competitive alternative to the existing statistical methods for defining DMRs.


Author(s):  
Ryo Okui ◽  
Takahide Yanagi

Abstract This paper proposes nonparametric kernel-smoothing estimation for panel data to examine the degree of heterogeneity across cross-sectional units. We first estimate the sample mean, autocovariances and autocorrelations for each unit and then apply kernel smoothing to compute their density functions. The dependence of the kernel estimator on bandwidth makes asymptotic bias of very high order affect the required condition on the relative magnitudes of the cross-sectional sample size (N) and the time-series length (T). In particular, it makes the condition on N and T stronger and more complicated than those typically observed in the long-panel literature without kernel smoothing. We also consider a split-panel jackknife method to correct bias and construction of confidence intervals. An empirical application illustrates our procedure.


Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Jingwei Cai

We consider nonparametric spot volatility estimation for diffusion models with discrete high frequency observations. Our estimator is carried out in two steps. First, using the local average of the range-based variance, we propose a crude estimator of the spot volatility. Second, we use usual nonparametric kernel smoothing to reconstruct the volatility function from the crude estimator. By inference, we find such a double smoothing operation can effectively reduce the estimation error.


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