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We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction.
Advances in Neural Information Processing Systems
Jon M Kleinberg (2003): An impossibility theorem for clustering · 2003
Earlier work this paper cites.
Encyclopedia of Measurement and Statistics. SAGE Publications
Hervé Abdi (2007): Metric multidimensional scaling (MDS): analyzing distance matrices · 2007
Earlier work this paper cites.
In: Proceedings of the 24th international conference on Machine learning
Samuel Gerber, Tolga Tasdizen & Ross Whitaker (2007): Robust non-linear dimensionality reduction using successive 1-dimensional Laplacian eigenmaps · 2007
Earlier work this paper cites.
In: Proceedings of the twenty-fifth annual symposium on Computational geometry
Frédéric Chazal, David Cohen-Steiner, Marc Glisse, Leonidas J Guibas & Steve Y Oudot (2009): Proximity of persistence modules and their diagrams · 2009
Earlier work this paper cites.
Wiley interdisciplinary reviews: computational statistics
Hervé Abdi & Lynne J Williams (2010): Principal component analysis · 2010
Earlier work this paper cites.
Publications of the Astronomical Society of the Pacific
Stephen Bailey (2012): Principal Component Analysis with Noisy and/or Missing Data · 2012
Earlier work this paper cites.
Self published notes
David I Spivak (2012): Metric realization of fuzzy simplicial sets · 2012
Earlier work this paper cites.
Foundations of Computational Mathematics
Gunnar Carlsson & Facundo Mémoli (2013): Classifying clustering schemes · 2013
Cited alongside, same era.
Discrete & Computational Geometry
Peter Bubenik & Jonathan A Scott (2014): Categorification of persistent homology · 2014
Cited alongside, same era.
Geometriae Dedicata
Frédéric Chazal, Vin De Silva & Steve Oudot (2014): Persistence stability for geometric complexes · 2014
Cited alongside, same era.
arXiv preprint arXiv:1608.04331
Jared Culbertson, Dan P Guralnik, Jakob Hansen & Peter F Stiller (2016): Consistency constraints for overlapping data clustering · 2016
Cited alongside, same era.
Cambridge University Press, 10.1017/CBO9780511525858
Tom Leinster (2016): Basic Category Theory · 2016
Cited alongside, same era.
Journal of Open Source Software
Leland McInnes, John Healy, Nathaniel Saul & Lukas Großberger (2018): UMAP: Uniform Manifold Approximation and Projection · 2018
Later among the works it cites.
Cambridge University Press, 10.1017/9781108668804
Brendan Fong & David I. Spivak (2019): An Invitation to Applied Category Theory: Seven Sketches in Compositionality · 2019
Later among the works it cites.
Journal of Applied and Computational Topology
Adam Brown, Omer Bobrowski, Elizabeth Munch & Bei Wang (2020): Probabilistic convergence and stability of random mapper graphs · 2020
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Advances in Mathematics
Tobias Fritz (2020): A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics · 2020
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PhD Thesis at Western University (Ontario)
Luis N Scoccola (2020): Locally Persistent Categories And Metric Properties Of Interleaving Distances · 2020
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Topological Data Analysis and Beyond Workshop at NeurIPS 2020
Dan Shiebler (2020): Functorial Clustering via Simplicial Complexes · 2020
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Andrew J Blumberg & Michael Lesnick (2017): Universality of the homotopy interleaving distance · 2017
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Discrete Applied Mathematics
Jared Culbertson, Dan P Guralnik & Peter F Stiller (2018): Functorial hierarchical clustering with overlaps · 2017
Cited alongside, same era.
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