Large-scale manifold learning

This paper examines the problem of extracting lowdimensional manifold structure given millions of highdimensional face images. Specifically, we address the computational challenges of nonlinear dimensionality reduction via Isomap and Laplacian Eigenmaps, using a graph containing about 18 million nodes and 65 million edges. Since most manifold learning techniques rely on spectral decomposition, we first analyze two approximate spectral decomposition techniques for large dense matrices (Nystr?om and Column-sampling), providing the first direct theoretical and empirical comparison between these techniques. We next show extensive experiments on learning low-dimensional embeddings for two large face datasets: CMU-PIE (35 thousand faces) and a web dataset (18 million faces). Our comparisons show that the Nystr?om approximation is superior to the Column-sampling method. Furthermore, approximate Isomap tends to perform better than Laplacian Eigenmaps on both clustering and classification with...

• Type: Conference
• Year: 2008
• Where: CVPR
• Authors: Ameet Talwalkar, Sanjiv Kumar, Henry A. Rowley
• Keywords: Approximate Spectral Decomposition, Computer Vision, CVPR 2008, Laplacian Eigenmaps, Large Dense Matrices, Large Face Datasets, Nonlinear Dimensionality Reduction