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A quaternion clustering framework

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Data clustering is one of the most popular methods of data mining and cluster analysis. The goal of clustering algorithms is to partition a data set into a specific number of clusters for compressing or summarizing original values. There are a variety of clustering algorithms available in the related literature. However, the research on the clustering of data parametrized by unit quaternions, which are commonly used to represent 3D rotations, is limited. In this paper we present a quaternion clustering methodology including an algorithm proposal for quaternion based k-means along with quaternion clustering quality measures provided by an enhancement of known indices and an automated procedure of optimal cluster number selection. The validity of the proposed framework has been tested in experiments performed on generated and real data, including human gait sequences recorded using a motion capture technique.
Rocznik
Strony
133--147
Opis fizyczny
Bibliogr. 34 poz., rys., tab., wykr.
Twórcy
  • Department of Computer Engineering, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
  • Department of Control Systems and Mechatronics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Bibliografia
  • [1] Abhayasinghe, N. and Murray, I. (2014). Human gait phase recognition based on thigh movement computed using imus, 9th IEEE International Conference on Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP), Singapore, pp. 1–4.
  • [2] Austin, S.B., Melly, S.J., Sanchez, B.N., Patel, A., Buka, S. and Gortmaker, S.L. (2005). Clustering of fast-food restaurants around schools: A novel application of spatial statistics to the study of food environments, American Journal of Public Health 95(9): 1575–1581.
  • [3] Bandyopadhyay, S. and Maulik, U. (2002). Genetic clustering for automatic evolution of clusters and application to image classification, Pattern Recognition 35(6): 1197–1208.
  • [4] Berkhin, P. (2006). A survey of clustering data mining techniques, in J. Kagan et al. (Eds), Grouping Multidimensional Data, Springer, Berlin/Heidelberg, pp. 25–71.
  • [5] Caliński, T. and Harabasz, J. (1974). A dendrite method for cluster analysis, Communications in Statistics 3(1): 1–27, DOI: 10.1080/03610927408827101.
  • [6] Cantador, I. and Castells, P. (2006). Multilayered semantic social network modeling by ontology-based user profiles clustering: Application to collaborative filtering, in S. Staab and V. Svwtek (Eds), Managing Knowledge in a Word of Networks, Springer, Berlin/Heidelberg, pp. 334–349.
  • [7] Chaturvedi, N.A., Sanyal, A.K. and McClamroch, N.H. (2011). Rigid-body attitude control, IEEE Control Systems 31(3): 30–51.
  • [8] Creusot, C., Pears, N. and Austin, J. (2010). 3D face landmark labelling, Proceedings of the ACM Workshop on 3D Object Retrieval, Firenze, Italy, pp. 27–32.
  • [9] Davies, D.L. and Bouldin, D.W. (1979). A cluster separation measure, IEEE Transactions on Pattern Analysis and Machine Intelligence 1(2): 224–227, DOI: 10.1109/TPAMI.1979.4766909.
  • [10] Dunn, J.C. (1974). A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters, Journal of Cybernetics 3(3): 32–57.
  • [11] Ell, T.A. and Sangwine, S.J. (2007). Hypercomplex Fourier transforms of color images, IEEE Transactions on Image Processing 16(1): 22–35.
  • [12] Gariel, M., Srivastava, A.N. and Feron, E. (2011). Trajectory clustering and an application to airspace monitoring, IEEE Transactions on Intelligent Transportation Systems 12(4): 1511–1524.
  • [13] Grubesic, T.H. (2006). On the application of fuzzy clustering for crime hot spot detection, Journal of Quantitative Criminology 22(1): 77–105.
  • [14] Han, J., Pei, J. and Kamber, M. (2011). Data Mining: Concepts and Techniques, Elsevier, Waltham, MA.
  • [15] Himberg, J., Hyvärinen, A. and Esposito, F. (2004). Validating the independent components of neuroimaging time series via clustering and visualization, Neuroimage 22(3): 1214–1222.
  • [16] Huynh, D.Q. (2009). Metrics for 3D rotations: Comparison and analysis, Journal of Mathematical Imaging and Vision 35(2): 155–164, DOI: 10.1007/s10851-009-0161-2.
  • [17] Jabłoński, B. (2008a). Anisotropic filtering of multidimensional rotational trajectories as a generalization of 2D diffusion process, Multidimensional Systems and Signal Processing 19(3): 379–399, DOI: 10.1007/s11045-008-0056-1.
  • [18] Jabłoński, B. (2008b). Filtration of Images and Spatial Trajectories Using Partial Differential Equations, EXIT, Warsaw, (in Polish).
  • [19] Jabłoński, B. (2011). Application of quaternion scale space approach for motion processing, in R.S. Choraś (Ed.), Image Processing and Communications Challenges 3, Springer, Berlin/Heidelberg, pp. 141–148, DOI: 10.1007/978-3-642-23154-4_16.
  • [20] Jabłoński, B. (2012). Quaternion dynamic time warping, IEEE Transactions on Signal Processing 60(3): 1174–1183.
  • [21] Johnson, M. (2003). Exploiting Quaternions to Support Expressive Interactive Character Motion, PhD thesis, MIT, Cambridge, MA.
  • [22] Koster, K. and Spann, M. (2000). MIR: An approach to robust clustering-application to range image segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence 22(5): 430–444.
  • [23] Liao, T.W. (2005). Clustering of time series data—a survey, Pattern Recognition 38(11): 1857–1874.
  • [24] Loots, M.T., Bekker, A., Arashi, M. and Roux, J.J. (2013). On the real representation of quaternion random variables, Statistics 47(6): 1224–1240, DOI: 10.1080/02331888.2012.695376.
  • [25] Markley, F.L., Cheng, Y., Crassidis, J.L. and Oshman, Y. (2007). Averaging quaternions, Journal of Guidance, Control, and Dynamics 30(4): 1193–1197.
  • [26] Maulik, U. and Bandyopadhyay, S. (2002). Performance evaluation of some clustering algorithms and validity indices, IEEE Transactions on Pattern Analysis and Machine Intelligence 24(12): 1650–1654.
  • [27] Pei, S.-C. and Cheng, C.-M. (1999). Color image processing by using binary quaternion-moment-preserving thresholding technique, IEEE Transactions on Image Processing 8(5): 614–628.
  • [28] Piórek, M. (2018). Analysis of Chaotic Behavior in Non-linear Dynamical Systems, Springer, Cham.
  • [29] Reumerman, H.-J., Roggero, M. and Ruffini, M. (2005). The application-based clustering concept and requirements for intervehicle networks, IEEE Communications Magazine 43(4): 108–113.
  • [30] Risojević, V. and Babić, Z. (2013). Unsupervised learning of quaternion features for image classification, 11th International Conference on Telecommunication in Modern Satellite, Cable and Broadcasting Services (TELSIKS), Serbia, Nis, Vol. 1, pp. 345–348.
  • [31] Shi, L. (2005). Exploration in Quaternion Colour, PhD thesis, Simon Fraser University, Burnaby.
  • [32] Shi, L. and Funt, B. (2007). Quaternion color texture segmentation, Computer Vision and Image Understanding 107(1): 88–96.
  • [33] Wu, Z. and Leahy, R. (1993). An optimal graph theoretic approach to data clustering: Theory and its application to image segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence 15(11): 1101–1113.
  • [34] Zhou, F., De la Torre, F. and Hodgins, J.K. (2008). Aligned cluster analysis for temporal segmentation of human motion, 8th IEEE International Conference on Automatic Face & Gesture Recognition, FG’08, Amsterdam, The Netherlands, pp. 1–7.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-0004be85-f51e-43a7-9e0a-75b9fab436ad
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