Dimensionality reduction by unsupervised regression

We consider the problem of dimensionality reduction, where given high-dimensional data we want to estimate two mappings: from high to low dimension (dimensionality reduction) and from low to high dimension (reconstruction). We adopt an unsupervised regression point of view by introducing the unknown low-dimensional coordinates of the data as parameters, and formulate a regularised objective functional of the mappings and low-dimensional coordinates. Alternating minimisation of this functional is straightforward: for fixed low-dimensional coordinates, the mappings have a unique solution; and for fixed mappings, the coordinates can be obtained by finite-dimensional nonlinear minimisation. Besides, the coordinates can be initialised to the output of a spectral method such as Laplacian eigenmaps. The model generalises PCA and several recent methods that learn one of the two mappings but not both; and, unlike spectral methods, our model provides out of-sample mappings by construction. Exper...

• Type: Conference
• Year: 2008
• Where: CVPR
• Authors: Miguel Á. Carreira-Perpiñán, Zhengdong Lu
• Keywords: Computer Vision, CVPR 2008, Dimensionality Reduction