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 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.

scholarly journals A Note on Different Types of Probabilities of Misclassification

2020 ◽  
pp. 181-186
Author(s):  
Awogbemi Clement Adeyeye
Keyword(s):  
Probability Density ◽  
Discriminant Function ◽  
Probability Density Functions ◽  
Classification Rule ◽  
Density Functions ◽  
Initial Sample ◽  
Different Types ◽  
The Status ◽  
Probability Of Misclassification

Whenever a discriminant function is constructed, the attention of a researcher is often focused on classification. The underlined interest is how well does a discriminant function perform in classifying future observations correctly. In order to assess the performance of any classification rule, probabilities of misclassification of a discriminant function serves as a basis for the procedure. Different forms of probabilities of misclassification and their associated properties were considered in this study. The misclassification probabilities were defined in terms of probability density functions (pdf) and classification regions. Apparent probability of misclassification is expressed as the proportion of observations in the initial sample which are misclassified by the sample discriminant function. Different methods of estimating probabilities of misclassification were related to each other using their individual shortcomings. The status of degrees of uncertainties associated with probabilities of misclassification and their implications were also specified.

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.

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