CBSDPEF ֤ੜݩʢ݀ʣͷ CJSUI͔ΒEFBUI·Ͱ ઢΛҾ͘ 0 1 2 3 4 4 3 2 1 QFSTJTUFODFEJBHSBN CJSUI EFBUI ֤ੜݩͷCJSUI C ͱ EFBUI E Λ࣍ݩฏ໘্ͷ C E ͱͯ͠දݱ ü ͍ઢˠOPJTZ ü ͍ઢˠSPCVTU ü ର֯ઢʹ͍ۙˠOPJTZ ü ର֯ઢ͔Βԕ͍ˠSPCVTU t = 0 t = 1 t = 2 t = 3 t = 4 34 / 46
data,” Bulletin of the American Mathematical Society 46.2, pp. 255–308, 2009. • F. Chazal and B. Michel, “An introduction to topological data analysis: fundamental and practical aspects for data scientists,” arXiv preprint, arXiv:1710.04019, 2017. • C. J. Carstens and K. J. Horadam, “Persistent homology of collaboration networks,” Mathematical problems in engineering 2013, 2013. • M. Gidea, “Topological Data Analysis of Critical Transitions in Financial Networks,” International Conference and School on Network Science, Springer, Cham, pp.47–59, 2017. • P. Bubenik, “Statistical topological data analysis using persistence landscapes,” The Journal of Machine Learning Research archive, 16(1), pp. 77–102, 2015. 43 / 46
Multi-Scale Kernel for Topological Machine Learning,” IEEE Conference on Computer Vision and Pattern Recognition, pp. 4741–4748, 2015. • G. Kusano, K. Fukumizu and Y. Hiraoka. “Persistence weighted Gaussian kernel for topological data analysis,” Proceedings of the 33rd International Conference on Machine Learning (ICML), 2016. • H. Adams, S. Chepushtanova, T. Emerson, E. Hanson, M. Kirby, F. Motta, R. Neville, C. Peterson, P. Shipman and L. Ziegelmeier, “Persistence Images: A Stable Vector Representation of Persistent Homology,” http://arxiv.org/abs/1507.06217. 44 / 46