Automatic fuzzy genetic algorithm in clustering for images based on the extracted intervals
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Automatic fuzzy genetic algorithm in clustering for images based on the extracted intervals Dinh Phamtoan1,2,3 · Tai Vovan4 Received: 14 March 2020 / Revised: 22 August 2020 / Accepted: 24 September 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This research proposes the method to extract the characteristics of images to become the intervals. These intervals are used to build the automatic fuzzy genetic algorithm for images (AFGI). In the proposed model, the overlap measure is the criterion to evaluate the closeness of intervals, and the new Davies and Bouldin index is the objective function. The AFGI can determine the proper number of clusters, the images in each cluster, and the probability to belong to clusters of images at the same time. The experiments with different types of images illustrate the steps of AFGI, and show its significant benefit in comparing to other algorithms. Keywords Cluster analysis · Fuzzy genetic algorithm · Image processing · Interval data · Pattern recognition · Unsupervised learning
1 Introduction In the information age, the problem of storage, extraction and recognition data are one of the big challenges to the scientists. For this problem, clustering technique has a basic role. Therefore, it is especially interested in many statisticians [3, 13, 35, 38, 42]. Building cluster is to divide a dataset into groups according to certain characteristics of the elements. Cluster analysis for discrete elements (CDE) was studied in the first time with many great contributions both theory and application [3, 4, 28, 35, 36, 39]. With the big and complex data such as images, each object needs to be considered as a distribution, clustering for the Tai Vovan
[email protected] Dinh Phamtoan [email protected] 1
University of Science, Ho Chi Minh City, Vietnam
2
Vietnam National University, Ho Chi Minh City, Vietnam
3
Faculty of Engineering, Van lang University, Ho Chi Minh City, Vietnam
4
College of Natural Science, Can Tho University, Can Tho, Vietnam
Multimedia Tools and Applications
probability density functions (CDF) is proposed. In image recognition, CDF has given more benefit than CDE. The important results in the recent years for CDF were studied in [4, 35, 37, 38]. In the both CDE and CDF, statisticians have been used a lot of different measures as the criteria for clustering. Regarding CDF, the problem for finding the proper number of groups has been settled. There are two kinds of cluster analysis: crisp and fuzzy clustering. In the crisp clustering, each element belongs to a cluster with probability as 1. Therefore, some boundary elements maybe not evaluated precisely. In the fuzzy clustering, each element can belong to one or more clusters with different levels of membership. The higher level of membership in one cluster is, the greater probability of element belonging to that cluster is. This shows the flexibility and advantages of the fuzzy clustering in comparison with the crisp cluster. In the both CDE and CDF, the fuzz
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