Dimensionality Reduction and Clustering on Statistical Manifolds Export

@proceedings{lee07dim, abstract = {Dimensionality reduction and clustering on statistical manifolds is presented. Statistical manifold [16] is a 2D Riemannian manifold which is statistically defined by maps that transform a parameter domain onto a set of probability density functions. Principal component analysis (PCA) based dimensionality reduction is performed on the manifold, and therefore, estimation of a mean and a variance of the set of probability distributions are needed. First, the probability distributions are transformed by an isometric transform that maps the distributions onto a surface of hyper-sphere. The sphere constructs a Riemannian manifold with a simple geodesic distance measure. Then, a Frechet mean is estimated on the Riemannian manifold to perform the PCA on a tangent plane to the mean. Experimental results show that clustering on the Riemannian space produce more accurate and stable classification than the one on Euclidean space.}, author = {Lee, Sang-Mook and Abbott, A. L. and Araman, P. A.}, booktitle = {Computer Vision and Pattern Recognition, 2007. CVPR '07. IEEE Conference on}, citeulike-article-id = {4779777}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/CVPR.2007.383408}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4270406}, doi = {10.1109/CVPR.2007.383408}, journal = {Computer Vision and Pattern Recognition, 2007. CVPR '07. IEEE Conference on}, keywords = {clustering, manifold, onur2009, segmentation, statistical}, pages = {1--7}, posted-at = {2009-06-08 18:27:26}, priority = {2}, title = {Dimensionality Reduction and Clustering on Statistical Manifolds}, url = {http://dx.doi.org/10.1109/CVPR.2007.383408}, year = {2007} }

TY - CONF ID - lee07dim L3 - citeulike-article-id:4779777 N2 - Dimensionality reduction and clustering on statistical manifolds is presented. Statistical manifold [16] is a 2D Riemannian manifold which is statistically defined by maps that transform a parameter domain onto a set of probability density functions. Principal component analysis (PCA) based dimensionality reduction is performed on the manifold, and therefore, estimation of a mean and a variance of the set of probability distributions are needed. First, the probability distributions are transformed by an isometric transform that maps the distributions onto a surface of hyper-sphere. The sphere constructs a Riemannian manifold with a simple geodesic distance measure. Then, a Frechet mean is estimated on the Riemannian manifold to perform the PCA on a tangent plane to the mean. Experimental results show that clustering on the Riemannian space produce more accurate and stable classification than the one on Euclidean space. JF - Computer Vision and Pattern Recognition, 2007. CVPR '07. IEEE Conference on EP - 7 TI - Dimensionality Reduction and Clustering on Statistical Manifolds T2 - Computer Vision and Pattern Recognition, 2007. CVPR '07. IEEE Conference on SP - 1 KW - clustering KW - manifold KW - onur2009 KW - segmentation KW - statistical AU - Lee, Sang-Mook AU - Abbott, AL AU - Araman, PA PY - 2007/// UR - http://dx.doi.org/10.1109/CVPR.2007.383408 ER -