Abstract
This chapter is devoted to presentation of results, which were obtained for the data considered with the use of clustering algorithms. Clustering consists in grou** of similar observations, while separating the dissimilar ones. (The groups obtained therefrom are referred to, exactly, as clusters.) Hence, we might suspect that the observations we analyse should fall into different clusters, and that first of all depending upon whether they represent “bot” or “human” behavior, based on the apparently obvious assumption that bots are more similar to (at least some) bots than to humans and that humans are more similar to (at least some) humans than to bots. Therefrom the attempts we report on in the present chapter.
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Notes
- 1.
And so, for instance, among the hierarchical aggregation algorithms it is known that single linkage is the only one that tends to produce chain-like, frequently multi-armed groups of relatively low overall spatial density, while virtually all the other algorithms from this group tend to form compact and dense clusters.
- 2.
We speak here, of course, of the so-called “internal [partition quality] indices”, which do not refer to any “model” or “ideal” partition, but serve to assess a given partition against the general principles, forming the basis of understanding how a “good partition”, for a given set of data, should look. In contrast, the so-called “external indices” are used to evaluate the partitions obtained through clustering algorithms with respect to some reference partition.
- 3.
These two numbers need not always be the same, since at some iterations there may be clusters that disappear, when no object is assigned to a centre.
- 4.
A dendrogram, as explained before, is a graphical illustration of the mergers of clusters along the functioning of the hierarchical merger algorithms, starting with all observations being separate clusters and ending with all of them forming one all-embracing cluster.
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- 6.
- 7.
Meaning the comparison of distance of an observation to the particular centroids, divided by the distance to the farthest centroid for this observation, and identification of situations, when the distances to two closest centroids are very similar, and these centroids correspond to clusters of different types (i.e. “bot” and “human”).
References
Ball, G., & Hall, D. (1965). ISODATA, a novel method of data analysis and pattern classification. Technical report NTIS AD 699616. Stanford Research Institute, Stanford, CA.
Bezdek, J. C. (1981). Pattern recognition with fuzzy objective function algorithms. Plenum Press.
Chen, Ch., Wang, Y., Hu, W., & Zheng, Z. (2020). Robust multi-view k-means clustering with outlier removal. Knowledge-Based Systems, 210, 106518. https://doi.org/10.1016/j.knosys.2020.106518
Ester, M., Kriegel, H.-P., Sander, J., & Xu, X. (1996). A density-based algorithm for discovering clusters in large spatial databases with noise. In E. Simoudis, J. Han, U. M. Fayyad (Eds.), Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (KDD-96) (pp. 226–231). AAAI Press.
Florek, K., Łukaszewicz, J., Perkal, J., Steinhaus, H., & Zubrzycki, S. (1951b). Sur la liaison et la division des points d’un ensemble fini. Colloquium Mathematicum, 2.
Florek, K., Łukaszewicz, J., Perkal, J., Steinhaus, H., & Zubrzycki, S. (1951a). Taksonomia wrocławska. Przegl. Antropol., 17.
Forgy, E. W. (1965). Cluster analysis of multivariate data: Efficiency versus interpretability of classifications. Abstract in Biometrics, 21, 768. Biometric Society Meeting, Riverside, California, 1965.
Gagolewski, M., Bartoszuk, M., & Cena, A. (2016). Genie: A new, fast, and outlier-resistant hierarchical clustering algorithm. Information Sciences, 363, 8–23.
Halkidi, M., Batistakis, Y., & Vazirgiannis, M. (2001). On clustering validation techniques. Journal of Intelligent Information Systems, 171(2–3), 107–145.
Hämäläinen, J., Jauhiainen, S., & Kaerkkaeinen, T. (2017). Comparison of internal clustering validation indices for prototype-based clustering. Algorithms, 10(3). https://doi.org/10.3390/a10030105
Jiarui, X., & Chen, L. (2015). Detecting crowdsourcing click fraud in search advertising based on clustering analysis. In 2015 IEEE 12th International Conference on Ubiquitous Intelligence and Computing and 2015 IEEE 12th International Conference on Autonomic and Trusted Computing and 2015 IEEE 15th International Conference on Scalable Computing and Communications and Its Associated Workshops (UIC-ATC-ScalCom) (pp. 894–900). https://doi.org/10.1109/UIC-ATC-ScalCom-CBDCom-IoP.2015.172
Kryszczuk, K., & Hurley, P. (2010). Estimation of the number of clusters using multiple clustering validity indices. In Multiple classifier systems. Lecture Notes in Computer Science (Vol. 5997, pp. 114–123). Springer.
Lance, G. N., & Williams, W. T. (1965). Computer programs for hierarchical polythetic classification (“Association analyses”). The Computer Journal, 8, 3.
Lance, G. N., & Williams, W. T. (1966). Computer programs for hierarchical polythetic classification (“Similarity analyses”). The Computer Journal, 9, 1.
Lance, G. N., & Williams, W. T. (1967a). A general theory of classificatory sorting strategies. I: Hierarchical systems. The Computer Journal, 9.
Lance, G. N., & Williams, W. T. (1967b). A general theory of classificatory sorting strategies. II: Clustering systems. The Computer Journal, 10.
Li, S.-H., Kao, Y.-C., Zhang, Z.-C., Chuang, Y.-P., & Yen, D. C. (2015). A network behavior-based botnet detection mechanism using PSO and k-means. ACM Transactions on Management Information Systems, 6(1). https://doi.org/10.1145/2676869
Ling, R. F. (1972). On the theory and construction of k-clusters. The Computer Journal, 15(4), 326–332. https://doi.org/10.1093/comjnl/15.4.326
Lloyd, S. P. (1957). Least squares quantization in PCM. Reprinted in IEEE Transactions on Information Theory, IT-28 (1982) (2), 129–137. Bell Telephone Labs Memorandum, Murray Hill, NJ.
Long, Z.-Z., Xu, G., Du, J., Zhu, H., Yan, T., & Yu, Y.-F. (2021). Flexible subspace clustering: A joint feature selection and k-means clustering framework. Big Data Research, 23, 100170. https://doi.org/10.1016/j.bdr.2020.100170. https://www.sciencedirect.com/science/article/pii/S2214579620300381
MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. In L. M. LeCam & J. Neyman (Eds.), Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, 1965/66 (Vol. I, pp. 281–297). University of California Press.
Owsiński, J. W. (2020). Data analysis in bi-partial perspective: Clustering and beyond. Studies in Computational Intelligence (Vol. 818). Springer Nature.
Owsiński, J. W., Kacprzyk, J., Opara, K. R., Stańczak, J., & Zadrożny, S. (2017). Using a reverse engineering type paradigm in clustering. An evolutionary programming based approach. Fuzzy Sets, Rough Sets, Multisets and Clustering (pp. 137–155).
Owsiński, J. W., Stańczak, J., Opara, K., Zadrożny, S., & Kacprzyk, J. (2021). Reverse clustering. Formulation, interpretation and case studies. Studies in Computation Intelligence (Vol. 957). Springer International Publishing.
Pakhira, M. K. (2014). A linear time-complexity k-means algorithm using cluster shifting. In 2014 International Conference on Computational Intelligence and Communication Networks, Bhopal, India (pp. 1047–1051). https://doi.org/10.1109/CICN.2014.220
Rezaei, M. (2020). Improving a centroid-based clustering by using suitable centroids from another clustering. Journal of Classification, 37(2), 352–365. https://doi.org/10.1007/s00357-018-9296-4
Rojas-Thomas, J. C., & Santos, M. (2021). New internal clustering validation measure for contiguous arbitrary-shape clusters. International Journal of Intelligent Systems, 36, 5506–5529. https://doi.org/10.1002/int.22521
Saxena, A., Prasad, M., Gupta, A., Bharill, N., Patel, O. P., Tiwari, A., Er, M.-J., Ding, W.-P., & Lin, C.-T. (2017). A review of clustering techniques and developments. Neurocomputing, 267, 664–681. https://doi.org/10.1016/j.neucom.2017.06.053
Steinhaus, H. (1956). Sur la division des corps matériels en parties. Bulletin de l’Academie Polonaise des Sciences, IV(C1.III), 801–804.
Xu, D.-k., & Tian Y.-j. (2015). A comprehensive survey of clustering Algorithms. Annals of Data Science, 2, 165–193. https://doi.org/10.1007/s40745-015-0040-1
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Jastrzębska, A. et al. (2023). Clustering Analysis. In: Analysing Web Traffic. Studies in Big Data, vol 127. Springer, Cham. https://doi.org/10.1007/978-3-031-32503-8_4
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