On Renyi's entropy estimation with one-dimensional Gaussian kernels
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On Renyi's entropy estimation with one-dimensional Gaussian kernels. / Sarbu, Septimia.
2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) . IEEE, 2016. p. 4408-4412.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review
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TY - GEN
T1 - On Renyi's entropy estimation with one-dimensional Gaussian kernels
AU - Sarbu, Septimia
PY - 2016/5/18
Y1 - 2016/5/18
N2 - Rényi's entropies play a significant role in many signal processing applications. Plug-in kernel density estimation methods have been employed to estimate such entropies with good results. However, they become computationally intractable in higher dimensions, because of the requirement to store intermediate probability density values for a large number of data points. We propose a method to reduce the number of the samples in a plug-in kernel density estimation method for Rényi's entropies of real exponents and to improve the result of the standard plug-in kernel density method. To this end, we derive a univariate estimator, using an Hermite expansion of sums of Gaussian kernels and a hierarchical clustering of the samples. On simulated data from a univariate Gaussian distribution, our method performs better than a k-nearest neigbour algorithm and other kernel density estimation methods.
AB - Rényi's entropies play a significant role in many signal processing applications. Plug-in kernel density estimation methods have been employed to estimate such entropies with good results. However, they become computationally intractable in higher dimensions, because of the requirement to store intermediate probability density values for a large number of data points. We propose a method to reduce the number of the samples in a plug-in kernel density estimation method for Rényi's entropies of real exponents and to improve the result of the standard plug-in kernel density method. To this end, we derive a univariate estimator, using an Hermite expansion of sums of Gaussian kernels and a hierarchical clustering of the samples. On simulated data from a univariate Gaussian distribution, our method performs better than a k-nearest neigbour algorithm and other kernel density estimation methods.
KW - Gaussian kernels
KW - Hermite expansion
KW - hierarchical clustering
KW - Rényi's entropy estimation
U2 - 10.1109/ICASSP.2016.7472510
DO - 10.1109/ICASSP.2016.7472510
M3 - Conference contribution
SN - 9781479999880
SP - 4408
EP - 4412
BT - 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
PB - IEEE
ER -