Diffusion Maps

Simple and Elegant

RR Coifman, S Lafon, AB Lee et al.: Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps. Proceedings of the National Academy of Sciences 102, 7426—7431, 2005. [doi:10.1073/pnas.0500334102]
RR Coifman and S Lafon: Diffusion maps. Applied and Computational Harmonic Analysis 21, 5—30, 2006. [doi:10.1016/j.acha.2006.04.006]
B Nadler, S Lafon, RR Coifman et al.: Diffusion maps, spectral clustering and reaction coordinates of dynamical systems. Applied and Computational Harmonic Analysis 21, 113—127, 2006. [doi:10.1016/j.acha.2005.07.004]
E Barter and T Gross: Manifold cities: social variables of urban areas in the UK. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, 20180615, 2019. [doi:10.1098/rspa.2018.0615]
AK Fahimipour and T Gross: Mapping the bacterial metabolic niche space. Nature Communications 11, 4887, 2020. [doi:10.1038/s41467-020-18695-z]
A Ryabov, B Blasius, H Hillebrand et al.: Trait reconstruction and estimation of functional diversity from ecolocical monitoring data. Proc. Nat. Sci. USA 119, e2118156119, 2022. [doi:10.1073/pnas.2118156119]
A Ghafourian, O Georgiou, E Barter et al.: Wireless localization with diffusion maps. Scientific Reports 10, 20655, 2020. [doi:10.1038/s41598-020-77695-7]
\bibitem{coifman2005geometric} RR Coifman, S Lafon, AB Lee et al.: Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps. Proceedings of the National Academy of Sciences 102, 7426--7431, 2005. [doi:10.1073/pnas.0500334102]
\bibitem{coifman2006diffusion} RR Coifman and S Lafon: Diffusion maps. Applied and Computational Harmonic Analysis 21, 5--30, 2006. [doi:10.1016/j.acha.2006.04.006]
\bibitem{nadler2006diffusion} B Nadler, S Lafon, RR Coifman et al.: Diffusion maps, spectral clustering and reaction coordinates of dynamical systems. Applied and Computational Harmonic Analysis 21, 113--127, 2006. [doi:10.1016/j.acha.2005.07.004]
\bibitem{barter2019manifold} E Barter and T Gross: Manifold cities: social variables of urban areas in the UK. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, 20180615, 2019. [doi:10.1098/rspa.2018.0615]
\bibitem{fahimipour2020mapping} AK Fahimipour and T Gross: Mapping the bacterial metabolic niche space. Nature Communications 11, 4887, 2020. [doi:10.1038/s41467-020-18695-z]
\bibitem{ryabov2021trait} A Ryabov, B Blasius, H Hillebrand et al.: Trait reconstruction and estimation of functional diversity from ecolocical monitoring data. Proc. Nat. Sci. USA 119, e2118156119, 2022. [doi:10.1073/pnas.2118156119]
\bibitem{ghafourian2020wireless} A Ghafourian, O Georgiou, E Barter et al.: Wireless localization with diffusion maps. Scientific Reports 10, 20655, 2020. [doi:10.1038/s41598-020-77695-7]

American Physical Society

RR Coifman, S Lafon, AB Lee et al., Proceedings of the National Academy of Sciences 102, 7426—7431, (2005). [doi:10.1073/pnas.0500334102]
RR Coifman and S Lafon, Applied and Computational Harmonic Analysis 21, 5—30, (2006). [doi:10.1016/j.acha.2006.04.006]
B Nadler, S Lafon, RR Coifman et al., Applied and Computational Harmonic Analysis 21, 113—127, (2006). [doi:10.1016/j.acha.2005.07.004]
E Barter and T Gross, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, 20180615, (2019). [doi:10.1098/rspa.2018.0615]
AK Fahimipour and T Gross, Nature Communications 11, 4887, (2020). [doi:10.1038/s41467-020-18695-z]
A Ryabov, B Blasius, H Hillebrand et al., Proc. Nat. Sci. USA 119, e2118156119, (2022). [doi:10.1073/pnas.2118156119]
A Ghafourian, O Georgiou, E Barter et al., Scientific Reports 10, 20655, (2020). [doi:10.1038/s41598-020-77695-7]
\bibitem{coifman2005geometric} RR Coifman, S Lafon, AB Lee et al., Proceedings of the National Academy of Sciences \textbf{102}, 7426--7431, (2005). [doi:10.1073/pnas.0500334102]
\bibitem{coifman2006diffusion} RR Coifman and S Lafon, Applied and Computational Harmonic Analysis \textbf{21}, 5--30, (2006). [doi:10.1016/j.acha.2006.04.006]
\bibitem{nadler2006diffusion} B Nadler, S Lafon, RR Coifman et al., Applied and Computational Harmonic Analysis \textbf{21}, 113--127, (2006). [doi:10.1016/j.acha.2005.07.004]
\bibitem{barter2019manifold} E Barter and T Gross, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences \textbf{475}, 20180615, (2019). [doi:10.1098/rspa.2018.0615]
\bibitem{fahimipour2020mapping} AK Fahimipour and T Gross, Nature Communications \textbf{11}, 4887, (2020). [doi:10.1038/s41467-020-18695-z]
\bibitem{ryabov2021trait} A Ryabov, B Blasius, H Hillebrand et al., Proc. Nat. Sci. USA \textbf{119}, e2118156119, (2022). [doi:10.1073/pnas.2118156119]
\bibitem{ghafourian2020wireless} A Ghafourian, O Georgiou, E Barter et al., Scientific Reports \textbf{10}, 20655, (2020). [doi:10.1038/s41598-020-77695-7]

Harvard

Coifman, R. R., Lafon, S., Lee, A. B., Maggioni, M., Nadler, B. et al. (2005) ‘Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps’. Proceedings of the National Academy of Sciences, 102(21), 7426—7431. [doi:10.1073/pnas.0500334102]
Coifman, R. R., and Lafon, S. (2006) ‘Diffusion maps’. Applied and Computational Harmonic Analysis, 21(1), 5—30. [doi:10.1016/j.acha.2006.04.006]
Nadler, B., Lafon, S., Coifman, R. R., and Kevrekidis, I. G. (2006) ‘Diffusion maps, spectral clustering and reaction coordinates of dynamical systems’. Applied and Computational Harmonic Analysis, 21(1), 113—127. [doi:10.1016/j.acha.2005.07.004]
Barter, E., and Gross, T. (2019) ‘Manifold cities: social variables of urban areas in the UK’. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475(2221), 20180615. [doi:10.1098/rspa.2018.0615]
Fahimipour, A. K., and Gross, T. (2020) ‘Mapping the bacterial metabolic niche space’. Nature Communications, 11(1), 4887. [doi:10.1038/s41467-020-18695-z]
Ryabov, A., Blasius, B., Hillebrand, H., Olenina, I., and Gross, T. (2022) ‘Trait reconstruction and estimation of functional diversity from ecolocical monitoring data’. Proc. Nat. Sci. USA, 119(43), e2118156119. [doi:10.1073/pnas.2118156119]
Ghafourian, A., Georgiou, O., Barter, E., and Gross, T. (2020) ‘Wireless localization with diffusion maps’. Scientific Reports, 10(1), 20655. [doi:10.1038/s41598-020-77695-7]
\bibitem{coifman2005geometric} Coifman, R. R., Lafon, S., Lee, A. B., Maggioni, M., Nadler, B. et al. (2005) ‘Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps'. \textit{Proceedings of the National Academy of Sciences}, 102(21), 7426--7431. [doi:10.1073/pnas.0500334102]
\bibitem{coifman2006diffusion} Coifman, R. R., and Lafon, S. (2006) ‘Diffusion maps'. \textit{Applied and Computational Harmonic Analysis}, 21(1), 5--30. [doi:10.1016/j.acha.2006.04.006]
\bibitem{nadler2006diffusion} Nadler, B., Lafon, S., Coifman, R. R., and Kevrekidis, I. G. (2006) ‘Diffusion maps, spectral clustering and reaction coordinates of dynamical systems'. \textit{Applied and Computational Harmonic Analysis}, 21(1), 113--127. [doi:10.1016/j.acha.2005.07.004]
\bibitem{barter2019manifold} Barter, E., and Gross, T. (2019) ‘Manifold cities: social variables of urban areas in the UK'. \textit{Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, 475(2221), 20180615. [doi:10.1098/rspa.2018.0615]
\bibitem{fahimipour2020mapping} Fahimipour, A. K., and Gross, T. (2020) ‘Mapping the bacterial metabolic niche space'. \textit{Nature Communications}, 11(1), 4887. [doi:10.1038/s41467-020-18695-z]
\bibitem{ryabov2021trait} Ryabov, A., Blasius, B., Hillebrand, H., Olenina, I., and Gross, T. (2022) ‘Trait reconstruction and estimation of functional diversity from ecolocical monitoring data'. \textit{Proc. Nat. Sci. USA}, 119(43), e2118156119. [doi:10.1073/pnas.2118156119]
\bibitem{ghafourian2020wireless} Ghafourian, A., Georgiou, O., Barter, E., and Gross, T. (2020) ‘Wireless localization with diffusion maps'. \textit{Scientific Reports}, 10(1), 20655. [doi:10.1038/s41598-020-77695-7]

Chicago

Coifman, R. R., Lafon, S., Lee, A. B., Maggioni, M., Nadler, B. et al. “Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps.” Proceedings of the National Academy of Sciences 102, no. 21 (2005) 7426—7431. [doi:10.1073/pnas.0500334102]
Coifman, Ronald R., and Lafon, Stéphane. “Diffusion maps.” Applied and Computational Harmonic Analysis 21, no. 1 (2006) 5—30. [doi:10.1016/j.acha.2006.04.006]
Nadler, Boaz, Lafon, Stéphane, Coifman, Ronald R., and Kevrekidis, Ioannis G.. “Diffusion maps, spectral clustering and reaction coordinates of dynamical systems.” Applied and Computational Harmonic Analysis 21, no. 1 (2006) 113—127. [doi:10.1016/j.acha.2005.07.004]
Barter, Edmund, and Gross, Thilo. “Manifold cities: social variables of urban areas in the UK.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2221 (2019) 20180615. [doi:10.1098/rspa.2018.0615]
Fahimipour, Ashkaan K., and Gross, Thilo. “Mapping the bacterial metabolic niche space.” Nature Communications 11, no. 1 (2020) 4887. [doi:10.1038/s41467-020-18695-z]
Ryabov, Alexey, Blasius, Bernd, Hillebrand, Helmit, Olenina, Irina, and Gross, Thilo. “Trait reconstruction and estimation of functional diversity from ecolocical monitoring data.” Proc. Nat. Sci. USA 119, no. 43 (2022) e2118156119. [doi:10.1073/pnas.2118156119]
Ghafourian, Amin, Georgiou, Orestis, Barter, Edmund, and Gross, Thilo. “Wireless localization with diffusion maps.” Scientific Reports 10, no. 1 (2020) 20655. [doi:10.1038/s41598-020-77695-7]
\bibitem{coifman2005geometric} Coifman, R. R., Lafon, S., Lee, A. B., Maggioni, M., Nadler, B. et al. ‘‘Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps.'' \textit{Proceedings of the National Academy of Sciences} 102, no.~21 (2005) 7426--7431. [doi:10.1073/pnas.0500334102]
\bibitem{coifman2006diffusion} Coifman, Ronald R., and Lafon, St\'{e}phane. ‘‘Diffusion maps.'' \textit{Applied and Computational Harmonic Analysis} 21, no.~1 (2006) 5--30. [doi:10.1016/j.acha.2006.04.006]
\bibitem{nadler2006diffusion} Nadler, Boaz, Lafon, St\'{e}phane, Coifman, Ronald R., and Kevrekidis, Ioannis G.. ‘‘Diffusion maps, spectral clustering and reaction coordinates of dynamical systems.'' \textit{Applied and Computational Harmonic Analysis} 21, no.~1 (2006) 113--127. [doi:10.1016/j.acha.2005.07.004]
\bibitem{barter2019manifold} Barter, Edmund, and Gross, Thilo. ‘‘Manifold cities: social variables of urban areas in the UK.'' \textit{Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences} 475, no.~2221 (2019) 20180615. [doi:10.1098/rspa.2018.0615]
\bibitem{fahimipour2020mapping} Fahimipour, Ashkaan K., and Gross, Thilo. ‘‘Mapping the bacterial metabolic niche space.'' \textit{Nature Communications} 11, no.~1 (2020) 4887. [doi:10.1038/s41467-020-18695-z]
\bibitem{ryabov2021trait} Ryabov, Alexey, Blasius, Bernd, Hillebrand, Helmit, Olenina, Irina, and Gross, Thilo. ‘‘Trait reconstruction and estimation of functional diversity from ecolocical monitoring data.'' \textit{Proc. Nat. Sci. USA} 119, no.~43 (2022) e2118156119. [doi:10.1073/pnas.2118156119]
\bibitem{ghafourian2020wireless} Ghafourian, Amin, Georgiou, Orestis, Barter, Edmund, and Gross, Thilo. ‘‘Wireless localization with diffusion maps.'' \textit{Scientific Reports} 10, no.~1 (2020) 20655. [doi:10.1038/s41598-020-77695-7]

BibTex

@article{coifman2005geometric,
  title = {Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps},
  year = {2005},
  author = {Coifman, R. R. and Lafon, S. and Lee, A. B. and Maggioni, M. and Nadler, B. and Warner, F. and Zucker, S. W.},
  doi = {10.1073/pnas.0500334102},
  number = {21},
  journal = {Proceedings of the National Academy of Sciences},
  volume = {102},
  pages = {7426--7431},
}

@article{coifman2006diffusion,
  title = {Diffusion maps},
  year = {2006},
  author = {Coifman, Ronald R. and Lafon, St\'{e}phane},
  doi = {10.1016/j.acha.2006.04.006},
  number = {1},
  journal = {Applied and Computational Harmonic Analysis},
  volume = {21},
  pages = {5--30},
}

@article{nadler2006diffusion,
  title = {Diffusion maps, spectral clustering and reaction coordinates of dynamical systems},
  year = {2006},
  author = {Nadler, Boaz and Lafon, St\'{e}phane and Coifman, Ronald R. and Kevrekidis, Ioannis G.},
  doi = {10.1016/j.acha.2005.07.004},
  number = {1},
  journal = {Applied and Computational Harmonic Analysis},
  volume = {21},
  pages = {113--127},
}

@article{barter2019manifold,
  title = {Manifold cities: social variables of urban areas in the UK},
  year = {2019},
  author = {Barter, Edmund and Gross, Thilo},
  doi = {10.1098/rspa.2018.0615},
  number = {2221},
  journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  volume = {475},
  pages = {20180615},
}

@article{fahimipour2020mapping,
  title = {Mapping the bacterial metabolic niche space},
  year = {2020},
  author = {Fahimipour, Ashkaan K. and Gross, Thilo},
  doi = {10.1038/s41467-020-18695-z},
  number = {1},
  journal = {Nature Communications},
  volume = {11},
  pages = {4887},
}

@article{ryabov2021trait,
  title = {Trait reconstruction and estimation of functional diversity from ecolocical monitoring data},
  year = {2022},
  author = {Ryabov, Alexey and Blasius, Bernd and Hillebrand, Helmit and Olenina, Irina and Gross, Thilo},
  doi = {10.1073/pnas.2118156119},
  number = {43},
  journal = {Proc. Nat. Sci. USA},
  volume = {119},
  pages = {e2118156119},
}

@article{ghafourian2020wireless,
  title = {Wireless localization with diffusion maps},
  year = {2020},
  author = {Ghafourian, Amin and Georgiou, Orestis and Barter, Edmund and Gross, Thilo},
  doi = {10.1038/s41598-020-77695-7},
  number = {1},
  journal = {Scientific Reports},
  volume = {10},
  pages = {20655},
}

RIS

TY  - JOUR
DA  - 2005
A1  - Coifman, R. R.
A2  - Lafon, S.
A3  - Lee, A. B.
A4  - Maggioni, M.
AU  - Nadler, B.
AU  - Warner, F.
AU  - Zucker, S. W.
DO  - 10.1073/pnas.0500334102
EP  - 7431
IS  - 21
J1  - Proceedings of the National Academy of Sciences
SP  - 7426
TI  - Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
VO  - 102
ER  -

TY  - JOUR
DA  - 2006
A1  - Coifman, Ronald R.
A2  - Lafon, Stéphane
DO  - 10.1016/j.acha.2006.04.006
EP  - 30
IS  - 1
J1  - Applied and Computational Harmonic Analysis
SP  - 5
TI  - Diffusion maps
VO  - 21
ER  -

TY  - JOUR
DA  - 2006
A1  - Nadler, Boaz
A2  - Lafon, Stéphane
A3  - Coifman, Ronald R.
A4  - Kevrekidis, Ioannis G.
DO  - 10.1016/j.acha.2005.07.004
EP  - 127
IS  - 1
J1  - Applied and Computational Harmonic Analysis
SP  - 113
TI  - Diffusion maps, spectral clustering and reaction coordinates of dynamical systems
VO  - 21
ER  -

TY  - JOUR
DA  - 2019
AV  - 1809.03376
A1  - Barter, Edmund
A2  - Gross, Thilo
DO  - 10.1098/rspa.2018.0615
IS  - 2221
J1  - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
SP  - 20180615
TI  - Manifold cities: social variables of urban areas in the UK
VO  - 475
ER  -

TY  - JOUR
DA  - 2020
AV  - 1908.07631
A1  - Fahimipour, Ashkaan K.
A2  - Gross, Thilo
DO  - 10.1038/s41467-020-18695-z
IS  - 1
J1  - Nature Communications
SP  - 4887
TI  - Mapping the bacterial metabolic niche space
VO  - 11
ER  -

TY  - JOUR
DA  - 2022
AV  - 2107.13792
A1  - Ryabov, Alexey
A2  - Blasius, Bernd
A3  - Hillebrand, Helmit
A4  - Olenina, Irina
AU  - Gross, Thilo
DO  - 10.1073/pnas.2118156119
IS  - 43
J1  - Proc. Nat. Sci. USA
SP  - e2118156119
TI  - Trait reconstruction and estimation of functional diversity from ecolocical monitoring data
VO  - 119
ER  -

TY  - JOUR
DA  - 2020
AV  - 1908.05216
A1  - Ghafourian, Amin
A2  - Georgiou, Orestis
A3  - Barter, Edmund
A4  - Gross, Thilo
DO  - 10.1038/s41598-020-77695-7
IS  - 1
J1  - Scientific Reports
SP  - 20655
TI  - Wireless localization with diffusion maps
VO  - 10
ER  -