Parametric Dimensionality Reduction by Unsupervised Regression

We introduce a parametric version (pDRUR) of the recently proposed Dimensionality Reduction by Unsupervised Regression algorithm. pDRUR alternately minimizes reconstruction error by fitting parametric functions given latent coordinates and data, and by updating latent coordinates given functions (with a Gauss-Newton method decoupled over coordinates). Both the fit and the update become much faster while attaining results of similar quality, and afford dealing with far larger datasets (105 points). We show in a number of benchmarks how the algorithm efficiently learns good latent coordinates and bidirectional mappings between the data and latent space, even with very noisy or low-quality initializations, often drastically improving the result of spectral and other methods. We consider the problem of dimensionality reduction, where given a high-dimensional dataset of N points in D dimensions YD×N = (y1, . . . , yN ), we want to estimate mappings F : y → x (dimensionality reduction...

• Type: Conference
• Year: 2010
• Where: CVPR
• Authors: Miguel Carreira-perpinan, Zhengdong Lu
• Keywords: Computer Vision, CVPR 2010, Dimensionality Reduction, Latent Coordinates, Latent Points