Topological analysis of data

[1]  Vitaliy Kurlin,et al.  A higher-dimensional homologically persistent skeleton , 2019, Adv. Appl. Math..

[2]  O. Sporns,et al.  Network neuroscience , 2017, Nature Neuroscience.

[3]  Sara Kališnik Verovšek,et al.  The Higher-Dimensional Skeletonization Problem , 2017, 1701.08395.

[4]  Jean M. Vettel,et al.  Cliques and cavities in the human connectome , 2016, Journal of Computational Neuroscience.

[5]  Matthias Troyer,et al.  Solving the quantum many-body problem with artificial neural networks , 2016, Science.

[6]  Mason A. Porter,et al.  A roadmap for the computation of persistent homology , 2015, EPJ Data Science.

[7]  Ulrich Bauer,et al.  Phat - Persistent Homology Algorithms Toolbox , 2014, J. Symb. Comput..

[8]  Morten L. Kringelbach,et al.  Insights into Brain Architectures from the Homological Scaffolds of Functional Connectivity Networks , 2016, Front. Syst. Neurosci..

[9]  Wei Guo,et al.  Toward automated prediction of manufacturing productivity based on feature selection using topological data analysis , 2016, 2016 IEEE International Symposium on Assembly and Manufacturing (ISAM).

[10]  A. Barabasi,et al.  Universal resilience patterns in complex networks , 2016, Nature.

[11]  Jaejun Yoo,et al.  Topological persistence vineyard for dynamic functional brain connectivity during resting and gaming stages , 2016, Journal of Neuroscience Methods.

[12]  Ernestina Menasalvas Ruiz,et al.  Combining complex networks and data mining: why and how , 2016, bioRxiv.

[13]  Ginestra Bianconi,et al.  Generalized network structures: The configuration model and the canonical ensemble of simplicial complexes. , 2016, Physical review. E.

[14]  Roberto Franzosi,et al.  Persistent homology analysis of phase transitions. , 2016, Physical review. E.

[15]  Luis Mateus Rocha,et al.  Control of complex networks requires both structure and dynamics , 2015, Scientific Reports.

[16]  Emerson G. Escolar,et al.  Hierarchical structures of amorphous solids characterized by persistent homology , 2015, Proceedings of the National Academy of Sciences.

[17]  J. Marron,et al.  Persistent Homology Analysis of Brain Artery Trees. , 2014, The annals of applied statistics.

[18]  Seth Lloyd,et al.  Quantum algorithms for topological and geometric analysis of data , 2016, Nature Communications.

[19]  Richard F. Betzel,et al.  Closures and Cavities in the Human Connectome , 2016 .

[20]  Guigang Zhang,et al.  Deep Learning , 2016, Int. J. Semantic Comput..

[21]  Matteo Rucco,et al.  Persistent Homology on RNA Secondary Structure Space , 2016, BICT.

[22]  Ulrich Bauer,et al.  Statistical Topological Data Analysis - A Kernel Perspective , 2015, NIPS.

[23]  Benjamin S. Glicksberg,et al.  Identification of type 2 diabetes subgroups through topological analysis of patient similarity , 2015, Science Translational Medicine.

[24]  Paul T. Pearson,et al.  Analyze High-Dimensional Data Using Discrete Morse Theory , 2015 .

[25]  Geoffrey E. Hinton,et al.  Deep Learning , 2015, Nature.

[26]  P. Bajardi,et al.  Unveiling patterns of international communities in a global city using mobile phone data , 2015, EPJ Data Science.

[27]  Emerson G. Escolar,et al.  Persistent homology and many-body atomic structure for medium-range order in the glass , 2015, Nanotechnology.

[28]  E. Pastalkova,et al.  Clique topology reveals intrinsic geometric structure in neural correlations , 2015, Proceedings of the National Academy of Sciences.

[29]  Ulrich Bauer,et al.  A stable multi-scale kernel for topological machine learning , 2014, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[30]  Jean-Daniel Boissonnat,et al.  The Compressed Annotation Matrix: An Efficient Data Structure for Computing Persistent Cohomology , 2013, Algorithmica.

[31]  Peter Bubenik,et al.  Statistical topological data analysis using persistence landscapes , 2012, J. Mach. Learn. Res..

[32]  Klaus B. Schebesch,et al.  Topological Data Analysis for Extracting Hidden Features of Client Data , 2015, OR.

[33]  G. Petri,et al.  Homological scaffolds of brain functional networks , 2014, Journal of The Royal Society Interface.

[34]  Emanuela Merelli,et al.  Using Topological Data Analysis for diagnosis pulmonary embolism , 2014, 1409.5020.

[35]  Kelin Xia,et al.  Persistent homology analysis of protein structure, flexibility, and folding , 2014, International journal for numerical methods in biomedical engineering.

[36]  Herbert Edelsbrunner,et al.  On the Computational Complexity of Betti Numbers: Reductions from Matrix Rank , 2014, SODA.

[37]  Ulrich Bauer,et al.  Clear and Compress: Computing Persistent Homology in Chunks , 2013, Topological Methods in Data Analysis and Visualization.

[38]  G. Carlsson,et al.  Topology of viral evolution , 2013, Proceedings of the National Academy of Sciences.

[39]  K. Mischaikow,et al.  Morse Theory for Filtrations and Efficient Computation of Persistent Homology , 2013, Discret. Comput. Geom..

[40]  C. J. Carstens,et al.  Persistent Homology of Collaboration Networks , 2013 .

[41]  P. Y. Lum,et al.  Extracting insights from the shape of complex data using topology , 2013, Scientific Reports.

[42]  Francesco Vaccarino,et al.  Topological Strata of Weighted Complex Networks , 2013, PloS one.

[43]  Kevin P. Murphy,et al.  Machine learning - a probabilistic perspective , 2012, Adaptive computation and machine learning series.

[44]  Matthew Kahle,et al.  Sharp vanishing thresholds for cohomology of random flag complexes , 2012, 1207.0149.

[45]  Chao Chen,et al.  Annotating Simplices with a Homology Basis and Its Applications , 2011, SWAT.

[46]  G. Carlsson,et al.  Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival , 2011, Proceedings of the National Academy of Sciences.

[47]  H. Poincaré,et al.  On Analysis Situs , 2010 .

[48]  Herbert Edelsbrunner,et al.  Computational Topology - an Introduction , 2009 .

[49]  Gunnar E. Carlsson,et al.  Topology and data , 2009 .

[50]  Albert-László Barabási,et al.  Understanding individual human mobility patterns , 2008, Nature.

[51]  Sanjay Ghemawat,et al.  MapReduce: simplified data processing on large clusters , 2008, CACM.

[52]  R. Ghrist.  Barcodes: The persistent topology of data , 2007 .

[53]  David Cohen-Steiner,et al.  Stability of Persistence Diagrams , 2005, Discret. Comput. Geom..

[54]  Facundo Mémoli,et al.  Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition , 2007, PBG@Eurographics.

[55]  Duncan J. Watts,et al.  The Structure and Dynamics of Networks: (Princeton Studies in Complexity) , 2006 .

[56]  Mark E. J. Newman,et al.  Structure and Dynamics of Networks , 2009 .

[57]  Leonidas J. Guibas,et al.  Persistence barcodes for shapes , 2004, SGP '04.

[58]  Herbert Edelsbrunner,et al.  Topological Persistence and Simplification , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[59]  Vladimir A. Kovalevsky,et al.  Finite topology as applied to image analysis , 1989, Comput. Vis. Graph. Image Process..

[60]  R. J. Wilson,et al.  Analysis situs , 1985 .

[61]  P. S. Aleksandrov,et al.  POINCARÉ AND TOPOLOGY , 1972 .

[62]  N. Steenrod,et al.  Foundations of Algebraic Topology , 1952 .