Topological analysis of data
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Murphy KP (2012) Machine learning: a probabilistic perspective. MIT Press, Cambridge
Newman M, Barabasi A-L, Watts DJ (2006) The structure and dynamics of networks. Princeton studies in complexity. Princeton University Press, Princeton
Zanin M, Papo D, Sousa PA, Menasalvas E, Nicchi A, Kubik E, Boccaletti S (2016) Combining complex networks and data mining: why and how. Phys Rep 635:1-44
Gonzalez MC, Hidalgo CA, Barabasi A-L (2008) Understanding individual human mobility patterns. Nature 453(7196):779-782
Gao J, Barzel B, Barabási A-L (2016) Universal resilience patterns in complex networks. Nature 530(7590):307-312
Gates AJ, Rocha LM (2016) Control of complex networks requires both structure and dynamics. Sci Rep 6:24456
Carleo G, Troyer M (2017) Solving the quantum many-body problem with artificial neural networks. Science 355(6325):602-606. doi: 10.1126/science.aag2302
Carlsson G, Zomorodian A, Collins A, Guibas LJ (2005) Persistence barcodes for shapes. Int J Shape Model 11(02):149-187
Poincaré H (1895) Analysis situs. J Éc Polytech 1:1-123
Steenrod SE-N, Eilenberg S (1952) Foundations of algebraic topology. Princeton University Press, Princeton
Kovalevsky VA (1989) Finite topology as applied to image analysis. Comput Vis Graph Image Process 46(2):141-161
Edelsbrunner H, Letscher D, Zomorodian A (2002) Topological persistence and simplification. Discrete Comput Geom 28(4):511-533
Ghrist R (2008) Barcodes: the persistent topology of data. Bull Am Math Soc 45(1):61-75. doi: 10.1090/S0273-0979-07-01191-3
Cohen-Steiner D, Edelsbrunner H, Harer J (2007) Stability of persistence diagrams. Discrete Comput Geom 37(1):103-120
Chan JM, Carlsson G, Rabadan R (2013) Topology of viral evolution. Proc Natl Acad Sci 110(46):18566-18571
Giusti C, Pastalkova E, Curto C, Itskov V (2015) Clique topology reveals intrinsic geometric structure in neural correlations. Proc Natl Acad Sci 112(44):13455-13460. doi: 10.1073/pnas.1506407112
Yoo J, Kim EY, Ahn YM, Ye JC (2016) Topological persistence vineyard for dynamic functional brain connectivity during resting and gaming stages. J Neurosci Methods 267:1-13
Carstens C, Horadam K (2013) Persistent homology of collaboration networks. Math Probl Eng 2013:815035
Schebesch KB, Stecking RW (2017) Topological data analysis for extracting hidden features of client data. In: Operations research proceedings 2015. Springer, Berlin, pp 483-489
Hiraoka Y, Nakamura T, Hirata A, Escolar EG, Matsue K, Nishiura Y (2016) Hierarchical structures of amorphous solids characterized by persistent homology. Proc Natl Acad Sci 113(26):7035-7040. doi: 10.1073/pnas.1520877113
Donato I, Gori M, Pettini M, Petri G, De Nigris S, Franzosi R, Vaccarino F (2016) Persistent homology analysis of phase transitions. Phys Rev E 93(5):052138
Lloyd S, Garnerone S, Zanardi P (2016) Quantum algorithms for topological and geometric analysis of data. Nat Commun 7:10138
Nakamura T, Hiraoka Y, Hirata A, Escolar EG, Nishiura Y (2015) Persistent homology and many-body atomic structure for medium-range order in the glass. Nanotechnology 26(30):304001
Singh G, Memoli F, Carlsson G (1991) Mapper: a topological mapping tool for point cloud data. In: Eurographics symposium on point-based graphics
Singh G, Mémoli F, Carlsson GE (2007) Topological methods for the analysis of high dimensional data sets and 3d object recognition. In: SPBG, pp 91-100
Petri G, Scolamiero M, Donato I, Vaccarino F (2013) Topological strata of weighted complex networks. PLoS ONE 8(6):66506
Dean J, Ghemawat S (2008) Mapreduce: simplified data processing on large clusters. Commun ACM 51(1):107-113
Nicolau M, Levine AJ, Carlsson G (2011) Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival. Proc Natl Acad Sci 108(17):7265-7270
Lum P, Singh G, Lehman A, Ishkanov T, Vejdemo-Johansson M, Alagappan M, Carlsson J, Carlsson G (2013) Extracting insights from the shape of complex data using topology. Sci Rep 3:1236
Li L, Cheng W-Y, Glicksberg BS, Gottesman O, Tamler R, Chen R, Bottinger EP, Dudley JT (2015) Identification of type 2 diabetes subgroups through topological analysis of patient similarity. Sci Transl Med 7(311):311ra174
Rucco M, Merelli E, Herman D, Ramanan D, Petrossian T, Falsetti L, Nitti C, Salvi A (2015) Using topological data analysis for diagnosis pulmonary embolism. J Theor Appl Comput Sci 9(1):41-55
Guo W, Banerjee AG (2016) Toward automated prediction of manufacturing productivity based on feature selection using topological data analysis. In: Assembly and manufacturing (ISAM), 2016 IEEE international symposium on. IEEE Press, New York, pp 31-36
Xia K, Wei G-W (2014) Persistent homology analysis of protein structure, flexibility, and folding. Int J Numer Methods Biomed Eng 30(8):814-844
Mamuye A, Rucco M (2016) Persistent homology on rna secondary structure space. In: Proceedings of the 9th EAI international conference on bio-inspired information and communications technologies (formerly BIONETICS). ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering), Gent, pp 189-192
Chan JM, Carlsson G, Rabadan R (2013) Topology of viral evolution. Proc Natl Acad Sci 110(46):18566-18571
Bajardi P, Delfino M, Panisson A, Petri G, Tizzoni M (2015) Unveiling patterns of international communities in a global city using mobile phone data. EPJ Data Sci 4(1):3
Giusti C, Pastalkova E, Curto C, Itskov V (2015) Clique topology reveals intrinsic geometric structure in neural correlations. Proc Natl Acad Sci 112(44):13455-13460
Sizemore A, Giusti C, Betzel RF, Bassett DS (2016) Closures and cavities in the human connectome. Preprint. arXiv:1608.03520
Bendich P, Marron J, Miller E, Pieloch A, Skwerer S (2016) Persistent homology analysis of brain artery trees. Ann Appl Stat 10(1):198
Lord L-D, Expert P, Fernandes HM, Petri G, Van Hartevelt TJ, Vaccarino F, Deco G, Turkheimer F, Kringelbach ML (2016) Insights into brain architectures from the homological scaffolds of functional connectivity networks. Front Syst Neurosci 10:85
Verovsek SK, Kurlin V, Lesnik D (2017) The higher-dimensional skeletonization problem. Preprint. arXiv:1701.08395
Kahle M (2014) Sharp vanishing thresholds for cohomology of random flag complexes. Ann Math (2) 179(3):1085-1107. doi: 10.4007/annals.2014.179.3.5
Courtney OT, Bianconi G (2016) Generalized network structures: the configuration model and the canonical ensemble of simplicial complexes. Preprint. arXiv:1602.04110
Edelsbrunner H, Harer J (2010) Computational topology - an introduction. Am. Math. Soc., Providence, p 1241
Bauer U, Kerber M, Reininghaus J, Wagner H (2014) Phat–persistent homology algorithms toolbox. In: International congress on mathematical software. Springer, Berlin, pp 137-143
Bauer U, Kerber M, Reininghaus J (2014) Clear and compress: computing persistent homology in chunks. In: Mathematics and visualization. Springer, Berlin, pp 103-117
Busaryev O, Cabello S, Chen C, Dey TK, Wang Y (2012) Annotating simplices with a homology basis and its applications. In: Scandinavian workshop on algorithm theory. Springer, Berlin, pp 189-200
Edelsbrunner H, Parsa S (2014) On the computational complexity of Betti numbers: reductions from matrix rank. In: Proceedings of the twenty-fifth annual ACM-SIAM symposium on discrete algorithms. Society for Industrial and Applied Mathematics, Philadelphia, pp 152-160
Boissonnat J-D, Dey TK, Maria C (2015) The compressed annotation matrix: an efficient data structure for computing persistent cohomology. Algorithmica 73(3):607-619
Mischaikow K, Nanda V (2013) Morse theory for filtrations and efficient computation of persistent homology. Discrete Comput Geom 50(2):330-353
Petri G, Expert P, Turkheimer F, Carhart-Harris R, Nutt D, Hellyer P, Vaccarino F (2014) Homological scaffolds of brain functional networks. J R Soc Interface 11(101):20140873
Bubenik P (2015) Statistical topological data analysis using persistence landscapes. J Mach Learn Res 16(1):77-102
Reininghaus J, Huber S, Bauer U, Kwitt R (2015) A stable multi-scale kernel for topological machine learning. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 4741-4748
Kwitt R, Huber S, Niethammer M, Lin W, Bauer U (2015) Statistical topological data analysis - a kernel perspective. In: Advances in neural information processing systems, pp 3070-3078
Otter N, Porter MA, Tillmann U, Grindrod P, Harrington HA (2015) A roadmap for the computation of persistent homology. Preprint. arXiv:1506.08903
Fasy BT, Kim J, Lecci F, Maria C, Rouvreau V (2014) TDA: statistical tools for topological data analysis
Pearson P, Muellner D, Singh G (2015) TDAmapper: analyze high-dimensional data using discrete Morse theory