scholarly journals A Clustering Method for Data in Cylindrical Coordinates

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Kazuhisa Fujita
Keyword(s):  
Color Image ◽  
Synthetic Data ◽  
Von Mises Distribution ◽  
Clustering Method ◽  
Cylindrical Coordinates ◽  
Gaussian Distributions ◽  
Image Quantization ◽  
Log Likelihood ◽  
Optimization Function ◽  
Von Mises

We propose a new clustering method for data in cylindrical coordinates based on the k-means. The goal of the k-means family is to maximize an optimization function, which requires a similarity. Thus, we need a new similarity to obtain the new clustering method for data in cylindrical coordinates. In this study, we first derive a new similarity for the new clustering method by assuming a particular probabilistic model. A data point in cylindrical coordinates has radius, azimuth, and height. We assume that the azimuth is sampled from a von Mises distribution and the radius and the height are independently generated from isotropic Gaussian distributions. We derive the new similarity from the log likelihood of the assumed probability distribution. Our experiments demonstrate that the proposed method using the new similarity can appropriately partition synthetic data defined in cylindrical coordinates. Furthermore, we apply the proposed method to color image quantization and show that the methods successfully quantize a color image with respect to the hue element.

scholarly journals An IMM Filter Defined in the Linear-Circular Domain, Application to Maneuver Detection with Heading Only

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Karim El mokhtari ◽  
Serge Reboul ◽  
Georges Stienne ◽  
Jean Bernard Choquel ◽  
Benaissa Amami ◽  
...  
Keyword(s):  
A Priori ◽  
Synthetic Data ◽  
Real Data ◽  
Circular Domain ◽  
Circular Data ◽  
Von Mises Distribution ◽  
A Posteriori ◽  
Circular Distributions ◽  
Vehicle Maneuver ◽  
Von Mises

In this article, we propose a multimodel filter for circular data. The so-called Circular Interacting Multimodel filter is derived in a Bayesian framework with the circular normal von Mises distribution. The aim of the proposed filter is to obtain the same performance in the circular domain as the classical IMM filter in the linear domain. In our approach, the mixing and fusion stages of the Circular Interacting Multimodel filter are, respectively, defined from the a priori and from the a posteriori circular distributions of the state angle knowing the measurements and according to a set of models. We propose in this article a set of circular models that will be used in order to detect the vehicle maneuvers from heading measurements. The Circular Interacting Multimodel filter performances are assessed on synthetic data and we show on real data a vehicle maneuver detection application.

scholarly journals Problematic usage of the Zhang and Luck mixture model

2018 ◽  
Author(s):  
Wei Ji Ma
Keyword(s):  
Uniform Distribution ◽  
Synthetic Data ◽  
Real Data ◽  
Von Mises Distribution ◽  
Candidate Model ◽  
Model Mismatch ◽  
Variable Precision ◽  
Model Free ◽  
True Model ◽  
Von Mises

A common method, due to Zhang and Luck (2008), for analyzing delayed-estimation data with a circular stimulus variable is to fit a mixture of a Von Mises distribution and a uniform distribution. The uniform distribution represents random guesses, presumably made when an item is not kept in memory. When I generate synthetic data from a variable-precision model with zero guessing, the method estimates the guess rate to be nonzero and often high. This is due to model mismatch: the fitted model is not matched to the data-generating (true) model. In real data, this could be a problem if one considers the variable-precision model a plausible candidate model and draws conclusions based on the estimated guess rates. I describe five solutions to this problem: analyzing the residual, ruling out the variable-precision model, robust inference, fitting a hybrid model, and using model-free statistics. I hope that these solutions can contribute to good data analysis practices in the study of working memory.

scholarly journals Spatial Correlation for DoA Characterization Using Von Mises, Cosine, and Gaussian Distributions

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Wamberto J. L. Queiroz ◽  
Francisco Madeiro ◽  
Waslon Terllizzie A. Lopes ◽  
Marcelo S. Alencar
Keyword(s):  
Spatial Correlation ◽  
Antenna Arrays ◽  
Electromagnetic Waves ◽  
Mutual Coupling ◽  
Coupling Effect ◽  
Exact Expression ◽  
Von Mises Distribution ◽  
Angle Of Arrival ◽  
Gaussian Distributions ◽  
Von Mises

This paper presents mathematical expressions for the spatial correlation between elements of linear and circular antenna arrays, considering cosine, Gaussian, and Von Mises distributions, for the direction of arrival (DoA) of the electromagnetic waves at the receiver antenna. The expressions obtained for the Von Mises distribution can include or not the mutual coupling effect between the elements and are simpler than those obtained for the cosine and the Gaussian distributions of the angle of arrival. The Von Mises distribution produces spatial correlation expressions in terms of Bessel and trigonometric functions. An exact expression for the spatial correlation, taking into account the mutual coupling, for the circular and linear arrays and an arbitrary number of elements are presented. It can be verified, by numerical evaluation of the expressions, that the coupling between the elements correlates the electromagnetic field, and a separation of half wavelength could not be enough to decorrelate them.

An extension of the von mises distribution

1982 ◽  
Vol 11 (15) ◽  
pp. 1695-1706 ◽  
Author(s):  
E.A. Yfantis ◽  
L.E. Borgman
Keyword(s):  
Von Mises Distribution ◽  
Von Mises

Error-in-variables model of Malacca wind direction data with the von Mises distribution in southwest monsoon

2021 ◽  
Vol 15 (9) ◽  
pp. 471-479
Author(s):  
Nurkhairany Amyra Mokhtar ◽  
Basri Badyalina ◽  
Kerk Lee Chang ◽  
Fatin Farazh Ya'acob ◽  
Ahmad Faiz Ghazali ◽  
...  
Keyword(s):  
Wind Direction ◽  
Southwest Monsoon ◽  
Von Mises Distribution ◽  
Error In Variables ◽  
Von Mises

scholarly journals STATISTICAL MODEL FOR THE RELATIONSHIP BETWEEN MAIZE KERNEL ORIENTATION AND SEED LEAF AZIMUTH

2015 ◽  
Vol 52 (3) ◽  
pp. 359-370
Author(s):  
ADRIAN KOLLER ◽  
GUILHERME TORRES ◽  
MICHAEL BUSER ◽  
RANDY TAYLOR ◽  
BILL RAUN ◽  
...  
Keyword(s):  
Simulation Models ◽  
Circular Statistics ◽  
Von Mises Distribution ◽  
Canopy Closure ◽  
Canopy Architecture ◽  
Maize Kernel ◽  
Angular Data ◽  
Significant Yield ◽  
Von Mises ◽  
The Relationship

SUMMARYHand-planted plots of across-row-oriented corn seeds (Zeamays L.) produce highly structured leaf canopies and have shown significant yield advantage over randomly planted plots in prior studies. For further investigation of the phenomenon by simulation, the objective of this study was to develop a probabilistic model for the correlation between seed orientation and initial plant orientation. In greenhouse trials, the azimuthal orientation of kernels of four different hybrids was recorded at planting. At collar setting of the seed leaf, the orientation of the seed leaf was determined and the angular data subjected to the analytical methods of circular statistics. The results indicate that the correlation between seed azimuth and seed leaf azimuth can be described by a von Mises distribution. The probabilistic seed to seed leaf azimuth model described herein may be implemented in simulation models to investigate the effect of canopy architecture, canopy closure and light interception efficiency of corn under conditions of seed oriented planting.

scholarly journals TCLUST: Trimming Approach of Robust Clustering Method

2014 ◽  
Vol 8 (4) ◽  
Author(s):  
Muhamad Alias Md. Jedi ◽  
Robiah Adnan
Keyword(s):  
Clustering Algorithm ◽  
Likelihood Function ◽  
R Package ◽  
Clustering Method ◽  
Number Of Clusters ◽  
Robust Clustering ◽  
Scatter Matrix ◽  
Group Assignment ◽  
Log Likelihood ◽  
Clustering Approach

TCLUST is a method in statistical clustering technique which is based on modification of trimmed k-means clustering algorithm. It is called “crisp” clustering approach because the observation is can be eliminated or assigned to a group. TCLUST strengthen the group assignment by putting constraint to the cluster scatter matrix. The emphasis in this paper is to restrict on the eigenvalues, λ of the scatter matrix. The idea of imposing constraints is to maximize the log-likelihood function of spurious-outlier model. A review of different robust clustering approach is presented as a comparison to TCLUST methods. This paper will discuss the nature of TCLUST algorithm and how to determine the number of cluster or group properly and measure the strength of group assignment. At the end of this paper, R-package on TCLUST implement the types of scatter restriction, making the algorithm to be more flexible for choosing the number of clusters and the trimming proportion.

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