Abstract
The design of validity index of fuzzy clustering has always been a historical problem in fuzzy clustering field. When the distribution of cluster centers is very close, it is difficult for the existing fuzzy clustering validity indexes to obtain a reasonable cluster number, and the separation mechanism of these indexes is too simple. In order to solve the above problems, we propose a novel fuzzy clustering validity index called TLW (Tang-Li-Wang) index. Firstly, compactness is expressed as the ratio of the membership weighted distance value to the sample variance of the dataset. Secondly, the sum of the maximum distance between cluster centers and the mean distance is used in separateness, and the sample variance of cluster centers is introduced, and the two are multiplied to describe the separateness. Thirdly, on the basis of considering compactness and separateness, the introduction of cluster number can alleviate the phenomenon that the index value may change monotonically with the increase of cluster number. Finally, the classical FCM (Fuzzy C-Mean) algorithm is used to conduct experiments on indexes. Comparative experiments and analyses were carried out on 17 typical datasets and 12 clustering validity indexes. From the experimental results of normal simple datasets and high-dimensional difficult datasets, the proposed index shows some advantages. All in all, these results verify that the proposed TLW index has better accuracy and stronger stability.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Tang, Y.M., Pan, Z.F., Pedrycz, W., Ren, F.J., Song, X.C.: Viewpoint-based kernel fuzzy clustering with weight information granules. IEEE Trans. Emerg. Top. Comput. Intell. 7(2), 342–356 (2023)
Tang, Y.M., Ren, F.J., Pedrycz, W.: Fuzzy C-means clustering through SSIM and patch for image segmentation. Appl. Soft Comput. 87, 105928, 1–16 (2020)
Tang, Y.M., Li, L., Liu, X.P.: State-of-the-art development of complex systems and their simulation methods. Complex Syst. Model. Simulat. 1(4), 271–290 (2021)
Tang, Y.M., Huang, J.J., Pedrycz, W., et al.: A fuzzy cluster validity index induced by triple center relation. IEEE Trans. Cybernet. 53(8), 5024–5036 (2023)
Wu, C.H., Ouyang, C.S., Chen, L.W., et al.: A new fuzzy clustering validity index with a median factor for centroid-based clustering. IEEE Trans. Fuzzy Syst. 23(3), 701–718 (2014)
Wan, Y.T., Ma, A.L., Zhang, L.P., Zhong, Y.F.: Multiobjective sine cosine algorithm for remote sensing image spatial-spectral clustering. IEEE Trans. Cybernet. 52(10), 11172–11186 (2022)
Rathore, P., Ghafoori, Z., Bezdek, J.C., Palaniswami, M., Leckie, C.: Approximating Dunn’s cluster validity indices for partitions of big data. IEEE Trans. Cybernet. 49(5), 1629–1641 (2019)
Salem, S.A., Nandi, A.K.: Development of assessment criteria for clustering algorithms. Pattern Anal. Appl. 12(1), 79–98 (2009)
Calinski, R.B., Harabasz, J.: A dendrite method for cluster analysis. Commun. Stat. 3(1), 1–27 (1974)
Bezdek, J.C.: Numerical taxonomy with fuzzy sets. J. Math. Biol. 7(1), 57–71 (1974)
Dunn, J.C.: A fuzzy relative of the ISODA TA process and its use in detecting compact well-separated clusters. Cybern. Syst. 3(3), 32–57 (1973)
Roubens, M.: Pattern classification problems and fuzzy sets. Fuzzy Sets Syst. 1(4), 239–253 (1978)
Fukuyama, Y., Sugeno, M.: A new method of choosing the number of cluster for the fuzzy c-means method. In: 5th Fuzzy Systems Symposium Kobe, pp. 247–250 (1989)
**e, X.L., Beni, G.: A validity measure for fuzzy clustering. IEEE Trans. Pattern Anal. Mach. Intell. 13(8), 841–847 (1991)
Davies, D.L., Bouldin, D.W.: A cluster separation measure. IEEE Trans. Pattern Anal. Mach. Intell. 1(2), 224–227 (1979)
Wu, C.H., Ouyang, C.S., Chen, L.W., et al.: A new fuzzy clustering validity index with a median factor for centroid-based clustering. IEEE Trans. Fuzzy Syst. 23(3), 701–718 (2015)
Liu, Y., Jiang, Y., Hou, T., et al.: A new robust fuzzy clustering validity index for imbalanced data sets. Inf. Sci. 547, 579–591 (2021)
Mittal, H., Saraswat, M.: A new fuzzy cluster validity index for hyperellipsoid or hyperspherical shape close clusters with distant centroids. IEEE Trans. Fuzzy Syst. 29(11), 3249–3258 (2020)
Zhu, E., Ma, R.: An effective partitional clustering algorithm based on new clustering validity index. Appl. Soft Comput. 71, 608–621 (2018)
Maulik, U., Bandyopadhyay, S.: Performance evaluation of some clustering algorithms and validity indices. IEEE Trans. Pattern Anal. Mach. Intell. 24(12), 1650–1654 (2002)
Liang, J., Bai, L., Dang, C., et al.: The K-means-type algorithms versus imbalanced data distributions. IEEE Trans. Fuzzy Syst. 20(4), 728–745 (2012)
Tang, Y.M., Ren, F.J.: Fuzzy systems based on universal triple I method and their response functions. Int. J. Inf. Technol. Decis. Mak. 16(2), 443–471 (2017)
Tang, Y.M., Zhang, L., Bao, G.Q., Ren, F.J., Pedrycz, W.: Symmetric implicational algorithm derived from intuitionistic fuzzy entropy. Iranian J. Fuzzy Syst. 19(4), 27–44 (2022)
Tang, Y.M., Pan, Z.H., Hu, X.H., Pedrycz, W., Chen, R.H.: Knowledge-induced multiple kernel fuzzy clustering. IEEE Trans. Pattern Anal. Mach. Intell. (2023). https://doi.org/10.1109/TPAMI.2023.3298629
Tang, Y.M., Pedrycz, W.: Oscillation bound estimation of perturbations under Bandler-Kohout subproduct. IEEE Trans. Cybernet. 52(7), 6269–6282 (2022)
Acknowledgment
It was subsidized from National Natural Science Foundation of China (62176083, 62176084) and Fundamental Research Funds for Central Universities of China (PA2023GDSK0061).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Tang, Y., Wang, X., Li, B., Hu, X., **e, W. (2024). Compactness and Separateness Driven Fuzzy Clustering Validity Index Called TLW. In: Sun, Y., Lu, T., Wang, T., Fan, H., Liu, D., Du, B. (eds) Computer Supported Cooperative Work and Social Computing. ChineseCSCW 2023. Communications in Computer and Information Science, vol 2013. Springer, Singapore. https://doi.org/10.1007/978-981-99-9640-7_13
Download citation
DOI: https://doi.org/10.1007/978-981-99-9640-7_13
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-99-9639-1
Online ISBN: 978-981-99-9640-7
eBook Packages: Computer ScienceComputer Science (R0)