An efficient automatic clustering algorithm for probability density functions and its applications in surface material classification

Thao Nguyen‐Trang, Tai Vo‐ Van and Ha Che‐Ngoc

Statistica Neerlandica, 2024, vol. 78, issue 1, 244-260

Abstract: Clustering is a technique used to partition a dataset into groups of similar elements. In addition to traditional clustering methods, clustering for probability density functions (CDF) has been studied to capture data uncertainty. In CDF, automatic clustering is a clever technique that can determine the number of clusters automatically. However, current automatic clustering algorithms update the new probability density function (pdf) fi(t)$$ {f}_i(t) $$ based on the weighted mean of all previous pdfs fj(t−1),j=1,2,…,N$$ {f}_j\left(t-1\right),j=1,2,\dots, N $$, resulting in slow convergence. This paper proposes an efficient automatic clustering algorithm for pdfs. In the proposed approach, the update of fi(t)$$ {f}_i(t) $$ is based on the weighted mean of f1(t),f2(t),…,fi−1(t),fi(t−1),fi+1(t−1),…,fN(t−1)$$ \left\{{f}_1(t),{f}_2(t),\dots, {f}_{i-1}(t),{f}_i\left(t-1\right),{f}_{i+1}\left(t-1\right),\dots, {f}_N\left(t-1\right)\right\} $$, where N$$ N $$ is the number of pdfs and i=1,2,…,N$$ i=1,2,\dots, N $$. This technique allows for the incorporation of recently updated pdfs, leading to faster convergence. This paper also pioneers the applications of certain CDF algorithms in the field of surface image recognition. The numerical examples demonstrate that the proposed method can result in a rapid convergence at some early iterations. It also outperforms other state‐of‐the‐art automatic clustering methods in terms of the Adjusted Rand Index and the Normalized Mutual Information. Additionally, the proposed algorithm proves to be competitive when clustering material images contaminated by noise. These results highlight the applicability of the proposed method in the problem of surface image recognition.

Date: 2024
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