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The magnitude of a metric space is a novel invariant that provides a measure of the 'effective size' of a space across multiple scales, while also capturing numerous geometrical properties, such as curvature, density, or entropy.
On the evolution of random graphs
P. Erdős, A. Rényi, et al · 1960
Earlier work this paper cites.
Nonnegative Matrices
H. Minc · 1988
Earlier work this paper cites.
Measuring biological diversity
A. R. Solow and S. Polasky · 1994
Earlier work this paper cites.
Algorithm 748: Enclosing zeros of continuous functions
G. Alefeld, F. A. Potra, and Y. Shi · 1995
Earlier work this paper cites.
Reliable fidelity and diversity metrics for generative models
M. F. Naeem, S. J. Oh, Y. Uh, Y. Choi, and J. Yoo · 2002
Earlier work this paper cites.
Distinguishing enzyme structures from non-enzymes without alignments
P. D. Dobson and A. J. Doig · 2003
Earlier work this paper cites.
Evaluation of text generation: A survey
A. Celikyilmaz, E. Clark, and J. Gao · 2006
Earlier work this paper cites.
A kernel method for the two-sample-problem
A. Gretton, K. Borgwardt, M. Rasch, B. Schölkopf, and A. Smola · 2006
Earlier work this paper cites.
Low discrepancy sequences in high dimensions: How well are their projections distributed?
X. Wang and I. H. Sloan · 2007
Earlier work this paper cites.
Collective classification in network data
P. Sen, G. Namata, M. Bilgic, L. Getoor, B. Galligher, and T. Eliassi-Rad · 2008
Earlier work this paper cites.
Cholesky factorization
N. J. Higham · 2009
Earlier work this paper cites.
Mixture discrepancy for quasi-random point sets
Y.-D. Zhou, K.-T. Fang, and J.-H. Ning · 2012
Earlier work this paper cites.
The magnitude of metric spaces
T. Leinster · 2013
Earlier work this paper cites.
Positive definite metric spaces
M. W. Meckes · 2013
Earlier work this paper cites.
On the magnitude of spheres, surfaces and other homogeneous spaces
S. Willerton · 2014
Earlier work this paper cites.
Geodesic exponential kernels: When curvature and linearity conflict
A. Feragen, F. Lauze, and S. Hauberg · 2015
Earlier work this paper cites.
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C. Szegedy, V. Vanhoucke, S. Ioffe, J. Shlens, and Z. Wojna · 2016
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L. Theis, A. v. d. Oord, and M. Bethge · 2016
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Ecological diversity: Measuring the unmeasurable
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M. S. M. Sajjadi, O. Bachem, M. Lucic, O. Bousquet, and S. Gelly · 2018
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Cited alongside, same era.
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Magnitude homology of enriched categories and metric spaces
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The q-spread dimension and the maximum diversity of square grid metric spaces
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Evaluating the evaluation of diversity in natural language generation
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Parallel black-box optimization of expensive high-dimensional multimodal functions via magnitude
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