| Paper: | MP-L4.4 |
| Session: | Image and Video Modeling I |
| Time: | Monday, September 17, 15:30 - 15:50 |
| Presentation: |
Lecture
|
| Title: |
UNSUPERVISED NONLINEAR MANIFOLD LEARNING |
| Authors: |
Matthieu Brucher; Université Louis Pasteur | | |
| | Christian Heinrich; Université Louis Pasteur | | |
| | Fabrice Heitz; Université Louis Pasteur | | |
| | Jean-Paul Armspach; Université Louis Pasteur | | |
| Abstract: |
This communication deals with data reduction and regression. A set of high dimensional data (e.g., images) has usually only few degrees of freedom whose corresponding variables 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 enables to project high-dimensional noisy points onto the manifold, like PCA does for linear models. We present application of our approach on several standard data sets such as the SwissRoll. |
