TY - GEN
T1 - Quantization of probability densities
T2 - 5th international conference on Particle Systems and Partial Differential Equations, PS-PDEs V 2016
AU - Golse, François
N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2018.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - This paper introduces a gradient flow in infinite dimension, whose long-time dynamics is expected to be an approximation of the quantization problem for probability densities, in the sense of Graf and Luschgy (Lecture Notes in Mathematics, vol 1730. Springer, Berlin, 2000). Quantization of probability distributions is a problem which one encounters in a great variety of contexts, such as signal processing, pattern or speech recognition, economics.. The present work describes a dynamical approach of the optimal quantization problem in space dimensions one and two, involving (systems of) parabolic equations. This is an account of recent work in collaboration with Caglioti et al. (Math Models Methods Appl Sci 25:1845–1885, 2015 and arXiv:1607.01198 (math.AP), to appear in Ann. Inst. H. Poincaré, Anal. Non Lin. https://doi.org/10.1016/j.anihpc.2017.12.003).
AB - This paper introduces a gradient flow in infinite dimension, whose long-time dynamics is expected to be an approximation of the quantization problem for probability densities, in the sense of Graf and Luschgy (Lecture Notes in Mathematics, vol 1730. Springer, Berlin, 2000). Quantization of probability distributions is a problem which one encounters in a great variety of contexts, such as signal processing, pattern or speech recognition, economics.. The present work describes a dynamical approach of the optimal quantization problem in space dimensions one and two, involving (systems of) parabolic equations. This is an account of recent work in collaboration with Caglioti et al. (Math Models Methods Appl Sci 25:1845–1885, 2015 and arXiv:1607.01198 (math.AP), to appear in Ann. Inst. H. Poincaré, Anal. Non Lin. https://doi.org/10.1016/j.anihpc.2017.12.003).
KW - Gradient flow
KW - Parabolic equations
KW - Quantization of probability densities
KW - Wasserstein distance
U2 - 10.1007/978-3-319-99689-9_6
DO - 10.1007/978-3-319-99689-9_6
M3 - Conference contribution
AN - SCOPUS:85059757823
SN - 9783319996882
T3 - Springer Proceedings in Mathematics and Statistics
SP - 33
EP - 52
BT - From Particle Systems to Partial Differential Equations - PSPDE V 2016
A2 - Gonçalves, Patrícia
A2 - Soares, Ana Jacinta
PB - Springer New York LLC
Y2 - 28 November 2016 through 30 November 2016
ER -