Hervé Abdi (2007):
Metric multidimensional scaling (MDS): analyzing distance matrices.
Encyclopedia of Measurement and Statistics. SAGE Publications.
Hervé Abdi & Lynne J Williams (2010):
Principal component analysis.
Wiley interdisciplinary reviews: computational statistics 2(4),
pp. 433–459,
doi:10.1002/wics.101.
Stephen Bailey (2012):
Principal Component Analysis with Noisy and/or Missing Data.
Publications of the Astronomical Society of the Pacific 124(919),
pp. 1015–1023,
doi:10.1086/668105.
Available at http://www.jstor.org/stable/10.1086/668105.
Mukund Balasubramanian (2002):
The isomap algorithm and topological stability.
Science 295(5552),
doi:10.1126/science.295.5552.7a.
Andrew J Blumberg & Michael Lesnick (2017):
Universality of the homotopy interleaving distance.
arXiv preprint arXiv:1705.01690.
Adam Brown, Omer Bobrowski, Elizabeth Munch & Bei Wang (2020):
Probabilistic convergence and stability of random mapper graphs.
Journal of Applied and Computational Topology,
pp. 1–42,
doi:10.1007/s41468-020-00063-x.
Peter Bubenik & Jonathan A Scott (2014):
Categorification of persistent homology.
Discrete & Computational Geometry 51(3),
pp. 600–627,
doi:10.1007/s00454-014-9573-x.
Gunnar Carlsson & Facundo Mémoli (2013):
Classifying clustering schemes.
Foundations of Computational Mathematics,
doi:10.1007/s10208-012-9141-9.
Frédéric Chazal, David Cohen-Steiner, Marc Glisse, Leonidas J Guibas & Steve Y Oudot (2009):
Proximity of persistence modules and their diagrams.
In: Proceedings of the twenty-fifth annual symposium on Computational geometry,
pp. 237–246,
doi:10.1145/1542362.1542407.
Frédéric Chazal, Vin De Silva & Steve Oudot (2014):
Persistence stability for geometric complexes.
Geometriae Dedicata 173(1),
pp. 193–214,
doi:10.1007/s10711-013-9937-z.
Jared Culbertson, Dan P Guralnik, Jakob Hansen & Peter F Stiller (2016):
Consistency constraints for overlapping data clustering.
arXiv preprint arXiv:1608.04331.
Jared Culbertson, Dan P Guralnik & Peter F Stiller (2018):
Functorial hierarchical clustering with overlaps.
Discrete Applied Mathematics 236,
pp. 108–123,
doi:10.1016/j.dam.2017.10.015.
Brendan Fong & David I. Spivak (2019):
An Invitation to Applied Category Theory: Seven Sketches in Compositionality.
Cambridge University Press,
doi:10.1017/9781108668804.
Tobias Fritz (2020):
A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics.
Advances in Mathematics 370,
pp. 107239,
doi:10.1016/j.aim.2020.107239.
Samuel Gerber, Tolga Tasdizen & Ross Whitaker (2007):
Robust non-linear dimensionality reduction using successive 1-dimensional Laplacian eigenmaps.
In: Proceedings of the 24th international conference on Machine learning,
pp. 281–288,
doi:10.1145/1273496.1273532.
Jon M Kleinberg (2003):
An impossibility theorem for clustering.
Advances in Neural Information Processing Systems,
doi:10.5555/2968618.2968676.
Tom Leinster (2016):
Basic Category Theory.
Cambridge University Press,
doi:10.1017/CBO9780511525858.
Leland McInnes, John Healy, Nathaniel Saul & Lukas Großberger (2018):
UMAP: Uniform Manifold Approximation and Projection.
Journal of Open Source Software 3(29),
pp. 861,
doi:10.21105/joss.00861.
Luis N Scoccola (2020):
Locally Persistent Categories And Metric Properties Of Interleaving Distances.
PhD Thesis at Western University (Ontario).
Available at https://ir.lib.uwo.ca/etd/7119/.
Dan Shiebler (2020):
Functorial Clustering via Simplicial Complexes.
Topological Data Analysis and Beyond Workshop at NeurIPS 2020.
Available at https://openreview.net/pdf?id=ZkDLcXCP5sV.
Joshua B Tenenbaum, Vin De Silva & John C Langford (2000):
A global geometric framework for nonlinear dimensionality reduction.
Science 290(5500),
pp. 2319–2323,
doi:10.1126/science.290.5500.2319.