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ICIP
2007
IEEE

Unsupervised Nonlinear Manifold Learning

13 years 7 months ago
Unsupervised Nonlinear Manifold Learning
This communication deals with data reduction and regression. A set of high dimensional data (e.g., images) usually has only a few degrees of freedom with corresponding variables that are used to parameterize the original data set. Data understanding, visualization and classification are the usual goals. The proposed method reduces data considering a unique set of low-dimensional variables and a user-defined cost function in the multidimensional scaling framework. Mapping of the reduced variables to the original data is also addressed, which is another contribution of this work. Typical data reduction methods, such as Isomap or LLE, do not deal with this important aspect of manifold learning. We also tackle the inversion of the mapping, which makes it possible to project high-dimensional noisy points onto the manifold, like PCA with linear models. We present an application of our approach to several standard data sets such as the SwissRoll.
Matthieu Brucher, Christian Heinrich, Fabrice Heit
Added 16 Aug 2010
Updated 16 Aug 2010
Type Conference
Year 2007
Where ICIP
Authors Matthieu Brucher, Christian Heinrich, Fabrice Heitz, Jean-Paul Armspach
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