Principal manifold learning by sparse grids

Christian Feuersänger, Michael Griebel
2009 Computing  
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
more » ... non-linear problem is solved by a descent method which resembles the expectation minimization 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 fatcat:xewaqii2t5cjzclxmczpl37jey