Improved fast gauss transform and efficient kernel density estimation

@inproceedings{citeulike:2755980, abstract = {Evaluating sums of multivariate Gaussians is a common computational task in computer vision and pattern recognition, including in the general and powerful kernel density estimation technique. The quadratic computational complexity of the summation is a significant barrier to the scalability of this algorithm to practical applications. The fast Gauss transform (FGT) has successfully accelerated the kernel density estimation to linear running time for low-dimensional problems. Unfortunately, the cost of a direct extension of the FGT to higher-dimensional problems grows exponentially with dimension, making it impractical for dimensions above 3. We develop an improved fast Gauss transform to efficiently estimate sums of Gaussians in higher dimensions, where a new multivariate expansion scheme and an adaptive space subdivision technique dramatically improve the performance. The improved FGT has been applied to the mean shift algorithm achieving linear computational complexity. Experimental results demonstrate the efficiency and effectiveness of our algorithm.}, author = {Yang, C. and Duraiswami, R. and Gumerov, N. A. and Davis, L. }, booktitle = {Computer Vision, 2003. Proceedings. Ninth IEEE International Conference on}, citeulike-article-id = {2755980}, doi = {http://dx.doi.org/10.1109/ICCV.2003.1238383}, journal = {Computer Vision, 2003. Proceedings. Ninth IEEE International Conference on}, keywords = {density, estimation, fast, gauss, kernel, nonparametric, transform}, pages = {664--671 vol.1}, posted-at = {2008-05-05 11:23:44}, priority = {5}, title = {Improved fast gauss transform and efficient kernel density estimation}, url = {http://dx.doi.org/10.1109/ICCV.2003.1238383}, year = {2003} }

TY - CONF ID - citeulike:2755980 L3 - citeulike-article-id:2755980 TI - Improved fast gauss transform and efficient kernel density estimation T2 - Computer Vision, 2003. Proceedings. Ninth IEEE International Conference on JF - Computer Vision, 2003. Proceedings. Ninth IEEE International Conference on SP - 664 EP - 671 vol.1 N2 - Evaluating sums of multivariate Gaussians is a common computational task in computer vision and pattern recognition, including in the general and powerful kernel density estimation technique. The quadratic computational complexity of the summation is a significant barrier to the scalability of this algorithm to practical applications. The fast Gauss transform (FGT) has successfully accelerated the kernel density estimation to linear running time for low-dimensional problems. Unfortunately, the cost of a direct extension of the FGT to higher-dimensional problems grows exponentially with dimension, making it impractical for dimensions above 3. We develop an improved fast Gauss transform to efficiently estimate sums of Gaussians in higher dimensions, where a new multivariate expansion scheme and an adaptive space subdivision technique dramatically improve the performance. The improved FGT has been applied to the mean shift algorithm achieving linear computational complexity. Experimental results demonstrate the efficiency and effectiveness of our algorithm. KW - density KW - estimation KW - fast KW - gauss KW - kernel KW - nonparametric KW - transform AU - Yang, C AU - Duraiswami, R AU - Gumerov, NA AU - Davis, L PY - 2003/// UR - http://dx.doi.org/10.1109/ICCV.2003.1238383 ER -