4.5 Article

Globally automatic fuzzy clustering for probability density functions and its application for image data

Journal

APPLIED INTELLIGENCE
Volume 53, Issue 15, Pages 18381-18397

Publisher

SPRINGER
DOI: 10.1007/s10489-023-04470-2

Keywords

Automatic clustering; Differential evolution; Fuzzy clustering; Probability density function; Optimization

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Clustering for probability density functions (CDF) can be divided into non-fuzzy and fuzzy approaches. A new clustering algorithm called DE-AFCF is proposed to solve the fuzzy CDF problem by using Gaussian prototype and a new objective function. This method can automatically determine the number of clusters k and consider both clustering compactness and separation.
Clustering for probability density functions (CDF) can be categorized as non-fuzzy and fuzzy approaches. Regarding the second approach, the iterative refinement technique has been used for searching the optimal partition. This method could be easily trapped at a local optimum. In order to find the global optimum, a meta-heuristic optimization (MO) algorithm must be incorporated into the fuzzy CDF problem. However, no research utilizing MO to solve the fuzzy CDF problem has been proposed so far due to the lack of a reasonable encoding for converting a fuzzy clustering solution to a chromosome. To address this shortcoming, a new definition called Gaussian prototype is defined first. This type of prototype is capable of accurately representing the cluster without being overly complex. As a result, prototypes' information can be easily integrated into the chromosome via a novel prototype-based encoding method. Second, a new objective function is introduced to evaluate a fuzzy CDF solution. Finally, Differential Evolution (DE) is used to determine the optimal solution for fuzzy clustering. The proposed method, namely DE-AFCF, is the first to propose a globally automatic fuzzy CDF algorithm, which not only can automatically determine the number of clusters k but also can search for the optimal fuzzy partition matrix by taking into account both clustering compactness and separation. The DE-AFCF is also applied in some image clustering problems, such as processed image detection, and traffic image recognition.

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