• Optics and Precision Engineering
  • Vol. 32, Issue 7, 1045 (2024)
Yunlong GAO1, Jianpeng LI2, Xingshen ZHENG1, Guifang SHAO1..., Qingyuan ZHU1 and Chao CAO3,*|Show fewer author(s)
Author Affiliations
  • 1Pen-Tung Sah Institute of Micro-Nano Science and Technology, Xiamen University, Xiamen3602, China
  • 2Department of Automation, Xiamen University, Xiamen36110, China
  • 3Third Institute of Oceanography, Ministry of Natural Resources, Xiamen61005, China
  • show less
    DOI: 10.37188/OPE.20243207.1045 Cite this Article
    Yunlong GAO, Jianpeng LI, Xingshen ZHENG, Guifang SHAO, Qingyuan ZHU, Chao CAO. Fuzzy C-means clustering algorithm based on adaptive neighbors information[J]. Optics and Precision Engineering, 2024, 32(7): 1045 Copy Citation Text show less

    Abstract

    Traditional FCM algorithms cluster based on raw data, risking distortion from noise, outliers, or other disruptions, which can degrade clustering outcomes. To bolster FCM's resilience, this study introduces a fuzzy C-means clustering algorithm that leverages adaptive neighbor information. This concept hinges on the similarity between data points, treating each point as a potential neighbor to others, albeit with varying degrees of similarity. By integrating the neighbor information of sample points, labeled GX, and that of cluster centers, labeled GV, into the standard FCM framework, the algorithm gains additional insights into data structure. This aids in steering the clustering process and enhances the algorithm's robustness. Three iterative methods are presented to implement this enhanced clustering model. When compared to leading clustering techniques, our approach demonstrates over a 10% improvement in clustering efficacy on select benchmark datasets. It undergoes thorough evaluation across different dimensions, including parameter sensitivity, convergence rate, and through ablation studies, confirming its practicality and efficiency.
    minU,M i=1nk=1cuikhxi-mk22(1)

    View in Article

    s.t.k=1cuik=1,   0uik1(1)

    View in Article

    uik=1k=1cxi-mk2xi-mk22h-1(2)

    View in Article

    mk=i=1nuikhxii=1nuikh(3)

    View in Article

    minU,M i=1nk=1cuikxi-mk22(5)

    View in Article

    s.t.k=1cuik=1,   uik0,1(4)

    View in Article

    uik=1,      xi-mk22=min1jcxi-mj220,                        otherwise(5)

    View in Article

    minU,M i=1nk=1cuikxi-mk2+γUF2(8)

    View in Article

    s.t.k=1cuik=1,   0uik1(6)

    View in Article

    minU,M i=1nk=1cuikminxi-mk2,ε+γUF2(10)

    View in Article

    s.t.k=1cuik=1,   0uik1(7)

    View in Article

    minU,M,Z i=1nk=1cuikzi-mk22+γUF2+(12)

    View in Article

    βi=1nxi-zi22,s.t.  k=1cuik=1,   0uik1(8)

    View in Article

    minsiT1=1,0si1 k=1nxj-xk22sjk+λsjk2(9)

    View in Article

    Gxj=minS k=1nxj-xk22sjk+λsjk2(15)

    View in Article

     s.t.   sjk0,k=1nsjk=1(10)

    View in Article

    Gvi=minS' k=1nvi-xk22sjk'+λsjk'2(17)

    View in Article

       s.t.    sjk'0,k=1nsjk'=1(11)

    View in Article

    minU,V J=i=1cj=1nuijmxj-vi22+αGxj-Gvi2(19)

    View in Article

    minU,V J=i=1cj=1Nuijmxj-vi22+αGxj-Gvi2Gxj=minS k=1Nxj-xk22sjk+λsjk2     s.t.    sjk0,k=1Nsjk=1Gvi=minS' k=1Nvi-xk22sjk'+λsjk'2     s.t.    sjk'0,k=1Nsjk'=1(13)

    View in Article

    djk=xj-xk22(14)

    View in Article

    GX=minj=1Nk=1Nsjkdjk+λSF2=(22)

    View in Article

    LSj,η,βj=12Sj+dj2λj22-ηSjT-1-βjTSj(16)

    View in Article

    λj=k2dj,k+1-12i=1kdji(17)

    View in Article

    λ=1Nj=1N(k2dj,k+1-12i=1kdji)(18)

    View in Article

    η=1k+12kλji=1kdji(19)

    View in Article

    sji=-dji2λj+η+(20)

    View in Article

    L=i=1cj=1nuijmxj-vi2+αGxj-Gvi2+                           j=1nλji=1cuij-1.                            (21)(28)

    View in Article

    Luij=mxj-vi2+αGxj-Gvi2uijm-1+λj=0(22)

    View in Article

    uijm-1=-λjmxj-vi2+αGxj-Gvi2(23)

    View in Article

    uij=-λjm1m-11xj-vi2+αGxj-Gvi21m-1(24)

    View in Article

    uij=1k=1cxj-vi2+αGxj-Gvi2xj-vk2+αGxj-Gvi21m-1(25)

    View in Article

    Lvi=j=1n-2uijmxj-vi=0(26)

    View in Article

    -2j=1nuijmxj+2j=1nuijmvi=0(27)

    View in Article

    vi=k=1nuikmxkk=1nuik(28)

    View in Article

    minU,V J=i=1cj=1Nuijmxj-vi22+αGxi-Gvi2(29)

    View in Article

    minU,V J=i=1cj=1Nuijmxj-vi22(30)

    View in Article

    minU,V J=i=1cj=1Nuijmxj-vi22+αGvi2(31)

    View in Article

    minU,V J=i=1cj=1Nuijmxj-vi22+αGxi2(32)

    View in Article

    Yunlong GAO, Jianpeng LI, Xingshen ZHENG, Guifang SHAO, Qingyuan ZHU, Chao CAO. Fuzzy C-means clustering algorithm based on adaptive neighbors information[J]. Optics and Precision Engineering, 2024, 32(7): 1045
    Download Citation