scholarly journals A New Binary Adaptive Elitist Differential Evolution Based Automatic k-Medoids Clustering for Probability Density Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
D. Pham-Toan ◽  
T. Vo-Van ◽  
A. T. Pham-Chau ◽  
T. Nguyen-Trang ◽  
D. Ho-Kieu
Keyword(s):  
Differential Evolution ◽  
Probability Density ◽  
Probability Density Functions ◽  
Computational Time ◽  
Density Functions ◽  
Number Of Clusters ◽  
Computational Burden ◽  
Clustering Problem ◽  
Chromosome Representation

This paper proposes an evolutionary computing based automatic partitioned clustering of probability density function, the so-called binary adaptive elitist differential evolution for clustering of probability density functions (baeDE-CDFs). Herein, the k-medoids based representative probability density functions (PDFs) are preferred to the k-means one for their capability of avoiding outlier effectively. Moreover, addressing clustering problem in favor of an evolutionary optimization one permits determining number of clusters “on the run”. Notably, the application of adaptive elitist differential evolution (aeDE) algorithm with binary chromosome representation not only decreases the computational burden remarkably, but also increases the quality of solution significantly. Multiple numerical examples are designed and examined to verify the proposed algorithm’s performance, and the numerical results are evaluated using numerous criteria to give a comprehensive conclusion. After some comparisons with other algorithms in the literature, it is worth noticing that the proposed algorithm reveals an outstanding performance in both quality of solution and computational time in a statistically significant way.

scholarly journals Clustering for Probability Density Functions by New k-Medoids Method

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
D. Ho-Kieu ◽  
T. Vo-Van ◽  
T. Nguyen-Trang
Keyword(s):  
Probability Density ◽  
Clustering Algorithm ◽  
Real Life ◽  
Probability Density Functions ◽  
Rand Index ◽  
Computational Time ◽  
Adjusted Rand Index ◽  
Density Functions ◽  
Potential Applications ◽  
Iteration Number

This paper proposes a novel and efficient clustering algorithm for probability density functions based on k-medoids. Further, a scheme used for selecting the powerful initial medoids is suggested, which speeds up the computational time significantly. Also, a general proof for convergence of the proposed algorithm is presented. The effectiveness and feasibility of the proposed algorithm are verified and compared with various existing algorithms through both artificial and real datasets in terms of adjusted Rand index, computational time, and iteration number. The numerical results reveal an outstanding performance of the proposed algorithm as well as its potential applications in real life.

scholarly journals An R Code for Implementing Non-hierarchical Algorithm for Clustering of Probability Density Functions

2018 ◽  
Vol 2 (3) ◽  
pp. 174
Author(s):  
Diem Ngoc Tran ◽  
Tom Vinant ◽  
Théo Marc Colombani ◽  
Diem Ho-Kieu
Keyword(s):  
Probability Density ◽  
Clustering Algorithm ◽  
Simulated Data ◽  
Probability Density Functions ◽  
Computational Time ◽  
Density Functions ◽  
Data Set ◽  
Hierarchical Algorithm ◽  
Creative Commons ◽  
Clustering Quality

This paper aims to present a code for implementation of non-hierarchical algorithm to cluster probability density functions in one dimension for the first time in R environment. The structure of code consists of 2 primary steps: executing the main clustering algorithm and evaluating the clustering quality. The code is validated on one simulated data set and two applications. The numerical results obtained are highly compatible with that on MATLAB software regarding computational time. Notably, the code mainly serves for educational purpose and desires to extend the availability of algorithm in several environments so as having multiple choices for whom interested in clustering.  This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Improving fuzzy clustering algorithm for probability density functions and applying in image recognition

2020 ◽  
Vol 15 (3) ◽  
pp. 249-261
Author(s):  
Dinh Phamtoan ◽  
Tai Vovan
Keyword(s):  
Probability Density ◽  
Image Recognition ◽  
Fuzzy Clustering ◽  
Clustering Algorithm ◽  
Probability Density Functions ◽  
Density Functions ◽  
Number Of Clusters ◽  
Fuzzy Clustering Algorithm ◽  
Different Types ◽  
Specific Cluster

This study introduces a measure called coefficient of within-cluster proximity (CWP) to evaluate the similarity of probability density functions (DFs) within clusters. After surveying the under and upper, and the computational problems of CWP, a fuzzy clustering algorithm for DFs is proposed. This algorithm can determine the suitable number of clusters and find the probability for each DF to belong to specific cluster. The convergence of the algorithm is considered in theory and illustrated by the numerical examples. The algorithm is applied to image recognition. The results show strong advantages of it in comparison to other algorithms. They also indicate the potential of the proposed approach in application to the data of different types.

scholarly journals A Differential Evolution-Based Clustering for Probability Density Functions

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 41325-41336 ◽  
Author(s):  
Ho Kieu Diem ◽  
Vo Duy Trung ◽  
Nguyen Thoi Trung ◽  
Vo Van Tai ◽  
Nguyen Trang Thao
Keyword(s):  
Differential Evolution ◽  
Probability Density ◽  
Probability Density Functions ◽  
Density Functions

scholarly journals Modeling Diameter Distributions with Six Probability Density Functions in Pinus halepensis Mill. Plantations Using Low-Density Airborne Laser Scanning Data in Aragón (Northeast Spain)

2021 ◽  
Vol 13 (12) ◽  
pp. 2307
Author(s):  
J. Javier Gorgoso-Varela ◽  
Rafael Alonso Ponce ◽  
Francisco Rodríguez-Puerta
Keyword(s):  
Probability Density ◽  
Linear Models ◽  
Pinus Halepensis ◽  
Beta Function ◽  
Probability Density Functions ◽  
Lidar Data ◽  
Density Functions ◽  
Minimum Diameter ◽  
Location Parameters ◽  
Diameter Distributions

The diameter distributions of trees in 50 temporary sample plots (TSPs) established in Pinus halepensis Mill. stands were recovered from LiDAR metrics by using six probability density functions (PDFs): the Weibull (2P and 3P), Johnson’s SB, beta, generalized beta and gamma-2P functions. The parameters were recovered from the first and the second moments of the distributions (mean and variance, respectively) by using parameter recovery models (PRM). Linear models were used to predict both moments from LiDAR data. In recovering the functions, the location parameters of the distributions were predetermined as the minimum diameter inventoried, and scale parameters were established as the maximum diameters predicted from LiDAR metrics. The Kolmogorov–Smirnov (KS) statistic (Dn), number of acceptances by the KS test, the Cramér von Misses (W2) statistic, bias and mean square error (MSE) were used to evaluate the goodness of fits. The fits for the six recovered functions were compared with the fits to all measured data from 58 TSPs (LiDAR metrics could only be extracted from 50 of the plots). In the fitting phase, the location parameters were fixed at a suitable value determined according to the forestry literature (0.75·dmin). The linear models used to recover the two moments of the distributions and the maximum diameters determined from LiDAR data were accurate, with R2 values of 0.750, 0.724 and 0.873 for dg, dmed and dmax. Reasonable results were obtained with all six recovered functions. The goodness-of-fit statistics indicated that the beta function was the most accurate, followed by the generalized beta function. The Weibull-3P function provided the poorest fits and the Weibull-2P and Johnson’s SB also yielded poor fits to the data.

scholarly journals A synergy of the velocity gradients technique and the probability density functions for identifying gravitational collapse in self-absorbing media

2021 ◽  
Vol 502 (2) ◽  
pp. 1768-1784
Author(s):  
Yue Hu ◽  
A Lazarian
Keyword(s):  
Magnetic Fields ◽  
Probability Density ◽  
Column Density ◽  
Mass Density ◽  
Probability Density Functions ◽  
Emission Lines ◽  
Density Functions ◽  
Star Forming ◽  
Velocity Gradients ◽  
Self Gravity

ABSTRACT The velocity gradients technique (VGT) and the probability density functions (PDFs) of mass density are tools to study turbulence, magnetic fields, and self-gravity in molecular clouds. However, self-absorption can significantly make the observed intensity different from the column density structures. In this work, we study the effects of self-absorption on the VGT and the intensity PDFs utilizing three synthetic emission lines of CO isotopologues 12CO (1–0), 13CO (1–0), and C18O (1–0). We confirm that the performance of VGT is insensitive to the radiative transfer effect. We numerically show the possibility of constructing 3D magnetic fields tomography through VGT. We find that the intensity PDFs change their shape from the pure lognormal to a distribution that exhibits a power-law tail depending on the optical depth for supersonic turbulence. We conclude the change of CO isotopologues’ intensity PDFs can be independent of self-gravity, which makes the intensity PDFs less reliable in identifying gravitational collapsing regions. We compute the intensity PDFs for a star-forming region NGC 1333 and find the change of intensity PDFs in observation agrees with our numerical results. The synergy of VGT and the column density PDFs confirms that the self-gravitating gas occupies a large volume in NGC 1333.

scholarly journals Interactive design of probability density functions for shape grammars

2015 ◽  
Vol 34 (6) ◽  
pp. 1-13 ◽  
Author(s):  
Minh Dang ◽  
Stefan Lienhard ◽  
Duygu Ceylan ◽  
Boris Neubert ◽  
Peter Wonka ◽  
...  
Keyword(s):  
Probability Density ◽  
Probability Density Functions ◽  
Interactive Design ◽  
Density Functions ◽  
Shape Grammars

scholarly journals The Impact of Probability Density Functions Assessment on Model Performance for Slope Stability Analysis

Geosciences ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 322
Author(s):  
Evelina Volpe ◽  
Luca Ciabatta ◽  
Diana Salciarini ◽  
Stefania Camici ◽  
Elisabetta Cattoni ◽  
...  
Keyword(s):  
Probability Density ◽  
Central Italy ◽  
Model Performance ◽  
Probability Density Functions ◽  
Slope Instability ◽  
Complex Nature ◽  
Density Functions ◽  
Umbria Region ◽  
Input Variables ◽  
The Impact

The development of forecasting models for the evaluation of potential slope instability after rainfall events represents an important issue for the scientific community. This topic has received considerable impetus due to the climate change effect on territories, as several studies demonstrate that an increase in global warming can significantly influence the landslide activity and stability conditions of natural and artificial slopes. A consolidated approach in evaluating rainfall-induced landslide hazard is based on the integration of rainfall forecasts and physically based (PB) predictive models through deterministic laws. However, considering the complex nature of the processes and the high variability of the random quantities involved, probabilistic approaches are recommended in order to obtain reliable predictions. A crucial aspect of the stochastic approach is represented by the definition of appropriate probability density functions (pdfs) to model the uncertainty of the input variables as this may have an important effect on the evaluation of the probability of failure (PoF). The role of the pdf definition on reliability analysis is discussed through a comparison of PoF maps generated using Monte Carlo (MC) simulations performed over a study area located in the Umbria region of central Italy. The study revealed that the use of uniform pdfs for the random input variables, often considered when a detailed geotechnical characterization for the soil is not available, could be inappropriate.

Sign in / Sign up

Export Citation Format

Share Document