Kernel estimators of density function of directional data
Journal of Multivariate Analysis - Memorial volume dedicated to P. R. Krishnaiah
Regular Article: Computing Fourier Transforms and Convolutions on the 2-Sphere
Advances in Applied Mathematics
Journal of Multivariate Analysis
Estimation of densities and derivatives of densities with directional data
Journal of Multivariate Analysis
Application of fast spherical Fourier transform to density estimation
Journal of Multivariate Analysis
Gauss mixture vector quantization
ICASSP '01 Proceedings of the Acoustics, Speech, and Signal Processing, 2001. on IEEE International Conference - Volume 03
Gaussian mixture density modeling, decomposition, and applications
IEEE Transactions on Image Processing
On the Construction of Invertible Filter Banks on the 2-Sphere
IEEE Transactions on Image Processing
IEEE Transactions on Signal Processing
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In this paper, we derive an explicit form of the convolution theorem for functions on an n-sphere. Our motivation comes from the design of a probability density estimator for n-dimensional random vectors. We propose a probability density function (pdf) estimation method that uses the derived convolution result on Sn. Random samples are mapped onto the n-sphere and estimation is performed in the new domain by convolving the samples with the smoothing kernel density. The convolution is carried out in the spectral domain. Samples are mapped between the n-sphere and the n-dimensional Euclidean space by the generalized stereographic projection. We apply the proposed model to several synthetic and real-world data sets and discuss the results.