Convolution on the n-sphere with application to PDF modeling
Convolution on the n-sphere with application to PDF modeling
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DOI：
10.1109/tsp.2009.2033329
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Ivan Dokmanic;Davor Petrinovic
中科院分区：
文献类型：
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作者：
Ivan Dokmanic;Davor Petrinovic
本文给出了n-球面上函数卷积定理的一个显式形式。我们的动机来自n维随机向量的概率密度估计的设计。我们提出了一个pdf估计方法，使用导出的卷积结果在S。将随机样本映射到n球上，并通过将样本与平滑核密度卷积来在新的域中进行估计。卷积在谱域中进行。通过广义赤平投影将样本映射到n维欧氏空间和n维球面之间。我们将该模型应用于几个合成和真实的世界数据集，并讨论了结果。
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 pdf estimation method that uses the derived convolution result on S. 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 nsphere and the n-dimensional Euclidean space by the generalized stereographic projection. We apply the proposed model to several synthetic and real world datasets and discuss the results.