@Article{ Feuersanger.Griebel:2009, author = {Chr.~Feuers\"anger and M.~Griebel}, personid = {4}, title = {Principal Manifold Learning by Sparse Grids}, journal = {Computing}, abstract = {In this paper, we deal with the construction of lower-dimensional manifolds from high-dimensional data which is an important task in data mining, machine learning and statistics. Here, we consider principal manifolds as the minimum of a regularized, non-linear empirical quantization error functional. For the discretization we use a sparse grid method in latent parameter space. This approach avoids, to some extent, the curse of dimension of conventional grids like in the GTM approach. The arising non-linear problem is solved by a descent method which resembles the expectation maximization algorithm. We present our sparse grid principal manifold approach, discuss its properties and report on the results of numerical experiments for one-, two- and three-dimensional model problems.}, doi = {10.1007/s00607-009-0045-8}, volume = {85}, number = {4}, year = {2009}, http = {http://www.springerlink.com/content/87p4p4518q2w8569/}, pdf = {http://wissrech.ins.uni-bonn.de/research/pub/feuersaenger/mani.pdf} , note = {Also available as INS Preprint no 0801}, inspreprintnum= {0801}, annote = {inspreprint,article} }