#### Authors

Rob Fergus, Yair Weiss, Antonio Torralba

#### Abstract

With the advent of the Internet it is now possible to collect hundreds of millions of images. These images come with varying degrees of label information. Clean labels can be manually obtained on a small fraction,noisy labels may be extracted automatically from surrounding text, while for most images there are no labels at all. Semi-supervised learning is a principled framework for combining these different label sources. However, it scales polynomially with the number of images, making it impractical for use on gigantic collections with hundreds of millions of images and thousands of classes. In this paper we show how to utilize recent results in machine learning to obtain highly efficient approximations for semi-supervised learning that are linear in the number of images.  Specifically, we use the convergence of the eigenvectors of the normalized graph Laplacian to eigenfunctions of weighted Laplace-Beltrami operators. We combine this with a label sharing framework obtained from Wordnet to propagate label information to classes lacking manual annotations. Our algorithm enables us to apply semi-supervised learning to a database of 80 million images with 74 thousand classes.