---
res:
bibo_abstract:
- "This thesis presents several new developments in the field of manifold learning
and nonlinear dimensionality reduction. The main text can be divided into three
parts, the first of which presents a smoothness-based regularizer that is specifically
tuned to the Parametrized Self-Organizing Map (PSOM). The regularization approach
makes it possible to deal with noisy or missing data in a principled manner, and
it facilitates the construction of PSOMs from data that are not organized in a
grid topology.\r\nIn the second part, the manifold learning algorithm Unsupervised
Kernel Regression (UKR) is introduced as a counterpart to the classical Nadaraya-Watson
estimator. In a nutshell, UKR requires very little parameters to be chosen a priori:
In its simplest form, a UKR model is fully specified by the dimensionality of
latent space and the choice of a density kernel, and it can be regularized automatically
by using leave-one-out cross-validation without additional computational cost.
The low dimensional coordinates (latent variables) together with a mapping from
latent space to data space are retrieved by minimizing some error criterion.\r\nThe
third part presents four possible extensions to UKR, specifically\r\n1) a more
general cross-validation scheme, aimed at avoiding unsmooth manifolds,\r\n2) the
inclusion of loss functions beyond the usual squared error, which can enhance
the robustness towards outliers, and by which UKR can be tuned to specific noise
levels,\r\n3) a \"landmark\" variant which helps to reduce the computational cost,
and\r\n4) Unsupervised Local Polynomial Regression, where the Nadaraya-Watson
estimator is replaced by local linear or local quadratic regression models, the
latter showing less bias in the presence of curvature.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Stefan
foaf_name: Klanke, Stefan
foaf_surname: Klanke
dct_date: 2007^xs_gYear
dct_language: eng
dct_publisher: Bielefeld University@
dct_subject:
- Dimensionsreduktion
- Manifold learning
- Dimensionality reduction
- Unsupervised kernel regression
- Parametrized self-organizing map
dct_title: Learning manifolds with the Parametrized Self-Organizing Map and Unsupervised
Kernel Regression@
...