Abstract
In this paper, we streamline the Grassmann multivariate time sequence (MTS) clustering for state-space dynamical modelling into three umbrella approaches: (i) Intrinsic approach where clustering is entirely constrained within the manifold, (ii) Extrinsic approach where Grassmann manifold is flattened via local diffeomorphisms or embedded into Reproducing Kernel Hilbert Spaces via Grassmann kernels, (iii) Semi-intrinsic approach where clustering algorithm is performed on Grassmann manifolds via Karcher mean. Consequently, 11 Grassmann clustering algorithms are derived and demonstrated through a comprehensive comparative study on human motion gesture derived MTS data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Hallac, D., Vare, S., Boyd, S., Leskovec, J.: Toeplitz inverse covariance-based clustering of multivariate time series data. In: ACM SIGKDD, pp. 215–223 (2017)
Liao, T.W.: Clustering of time series data—a survey. Pattern Recogn. 38(11), 1857–1874 (2005)
Silva, J.A., Faria, E.R., Barros, R.C., et al.: Data stream clustering: a survey. ACM Comput. Surv. 46(1), 13 (2013)
Veeraraghavan, A., Roy-Chowdhury, A.K., et al.: Matching shape sequences in video with applications in human movement analysis. IEEE TPAMI 27(12), 1896–1909 (2005)
Boets, J., Cock, K.D., Espinoza, M., Moor, B.D.: Clustering time series, subspace identification and cepstral distances. Commun. Inf. Sys. 5(1), 69–96 (2005)
Li, L., Prakash, B.A: Time series clustering: complex is simpler! In: ICML, pp. 185–192 (2011)
Harvey, A.C.: Time Series Models. The MIT Press, Cambridge (1993)
Kremer, H., Günnemann, S., Held, A., Seidl, T.: Mining of temporal coherent subspace clusters in multivariate time series databases. In: Tan, P.-N., Chawla, S., Ho, C.K., Bailey, J. (eds.) PAKDD 2012. LNCS (LNAI), vol. 7301, pp. 444–455. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-30217-6_37
Aggarwal, G., Chowdhury, A.K.R., Chellappa, R.: A System identification approach for video-based face recognition. In: ICPR, vol. 4, pp. 175–178 (2004)
Begelfor, E., Werman, M.: Affine invariance revisited. In: IEEE CVPR, vol. 2, pp. 2087–2094 (2006)
Hamm, J.: Subspace-based learning with Grassmann kernels. Ph.D. thesis, University of Pennsylvania (2008)
Hayat, M., Bennamoun, M., El-Sallam, A.A.: Clustering of video-patches on Grassmannian manifold for facial expression recognition from 3D videos. In: IEEE Workshop on Applications of Computer Vision, pp. 83–88 (2013)
Shirazi, S., Harandi, M.T., et al.: Clustering on Grassmann manifolds via kernel embedding with application to action analysis. In: IEEE ICIP, pp. 781–784 (2012)
Turaga, P., Veeraraghavan, A., Srivastava, A., Chellappa, R.: Statistical computations on Grassmann and Stiefel manifolds for image and video-based recognition. IEEE TPAMI 33(11), 2273–2286 (2011)
Gruber, P., Theis, F.J.: Grassmann clustering. In: 14th European Signal Processing Conference, pp. 1–5 (2006)
Caseiro, R., Martins, P., Henriques, J.F., Leite, F.S., Batista, J.: Rolling Riemannian manifolds to solve the multi-class classification problem. In: IEEE CVPR, pp. 41–48 (2013)
Edelman, A., Arias, T.A., Smith, S.T.: The geometry of algorithms with orthogonality constraints. SIAM J. Mat. Anal. App. 20(2), 303–353 (1998)
Cetingul, H.E., Vidal, R.: Intrinsic mean shift for clustering on Stiefel and Grassmann manifolds. In: IEEE CVPR, pp. 1896–1902 (2009)
Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: analysis and an algorithm. In: NIPS, pp. 849–856 (2002)
Karcher, H.: Riemannian center of mass and mollifier smoothing. Commun. Pure Appl. Math. 30(5), 509–541 (1977)
MOCAP database. http://mocap.cs.cmu.edu
Nie, F., Xu, D., Tsang, I.W., Zhang, C.: Spectral embedded clustering. In: International Joint Conference on Artificial Intelligence, pp. 1181–1186 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Oh, BS., Teoh, A.B.J., Toh, KA., Lin, Z. (2019). Grassmannian Clustering for Multivariate Time Sequences. In: Chang, CY., Lin, CC., Lin, HH. (eds) New Trends in Computer Technologies and Applications. ICS 2018. Communications in Computer and Information Science, vol 1013. Springer, Singapore. https://doi.org/10.1007/978-981-13-9190-3_72
Download citation
DOI: https://doi.org/10.1007/978-981-13-9190-3_72
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-9189-7
Online ISBN: 978-981-13-9190-3
eBook Packages: Computer ScienceComputer Science (R0)