scholarly journals Human Posture Probability Density Estimation Based on Actual Motion Measurement and Eigenpostures

2005 ◽  
Vol 17 (6) ◽  
pp. 664-671 ◽  
Author(s):  
Tatsuya Harada ◽  
◽  
Taketoshi Mori ◽  
Tomomasa Sato ◽  
Keyword(s):  
Euclidean Space ◽  
Probability Density ◽  
Human Motion ◽  
Density Estimator ◽  
Probability Density Estimation ◽  
Mechanical Motion ◽  
Motion Measurement ◽  
Human Posture ◽  
Unit Quaternions ◽  
Logarithmic Mapping

We construct human posture probability density based on actual human motion measurement. Human postures in daily life were measured for two days by having subjects wear a mechanical motion capture device. Accumulated human postures were converted to unit quaternions to guarantee the uniqueness of posture representation. To represent probability density effectively, we propose eigenpostures for posture compression and use the kernel-based reduced set density estimator (RSDE) to reduce the number of posture samples and construction of posture probability density. Before compression, unit quaternions were converted to Euclidean space by logarithmic mapping. After conversion, postures were compressed in Euclidean space. Applying constructed human posture probability density for unlikely posture detection and motion segmentation, we verified its effectiveness for many different applications.

On a Gaussian process related to multivariate probability density estimation

1976 ◽  
Vol 80 (1) ◽  
pp. 135-144 ◽  
Author(s):  
B. W. Silverman
Keyword(s):  
Euclidean Space ◽  
Gaussian Process ◽  
Covariance Structure ◽  
Kernel Density ◽  
Exact Result ◽  
Uniform Continuity ◽  
Density Estimator ◽  
Probability Density Estimation ◽  
Multivariate Gaussian Process ◽  
Image Position

The multivariate Gaussian process with the same variance/covariance structure as the multivariate kernel density estimator in Euclidean space of dimension d is considered. An exact result is obtained for the limit in probability of the maximum of the normalized process. In addition weak and strong bounds are placed on the asymptotic behaviour of the maximum of the process over a multidimensional interval which is allowed to increase as the sample size increases. All the bounds obtained on the process areOnly the uniform continuity of the underlying density is assumed; the conditions on the kernel are also mild.

scholarly journals Probability density estimation using data projection

2009 ◽  
Vol 50 ◽  
Author(s):  
Mindaugas Kavaliauskas
Keyword(s):  
Computer Simulation ◽  
Probability Density ◽  
Projection Pursuit ◽  
Kernel Density ◽  
Density Estimator ◽  
Probability Density Estimation ◽  
Kolmogorov Smirnov ◽  
Computer Simulation Technique ◽  
Using Data ◽  
Smirnov Statistic

Nonparametric estimation of multivariate multimodal probability density is analysed. The projection pursuit density estimator was proposed by J.H. Friedman. Author of this paper proposes the modifications of original Friedman algorithm: employing a kernel density estimator, and a projection index based on Kolmogorov–Smirnov statistic. The efficiency of proposed modifications is analysed using computer simulation technique.

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

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