Extreme learning machine for out-of-sample extension in Laplacian eigenmaps

• Spectral manifold learning does not allow for out of sample embedding.
• We propose the use of extreme learning machine (ELM) as out-of-sample extension.
• ELM is compared to the well-known Nyström method for Laplacian eigenmap.
• Reconstruction accuracy is assessed on several public image datasets.
• ELM is shown to yield better reconstruction accuracy and computation time.

Manifold learning techniques have shown a great potential for computer vision problems; however, they do not extend easily to points different from the ones on which they were trained (out-of-sample). On the other hand, extreme learning machine (ELM) is a powerful method that allows to perform nonlinear, multivariate regression. This paper discusses the effectiveness of ELM for the out-of-sample problem and compares it to the state-of-the-art solution : the Nyström extension. Both methods are evaluated through the reconstruction of the manifold learnt using Laplacian eigenmaps, via experiments on a wide range of publicly available image datasets. We show that when reducing the data dimension to its intrinsic dimension, the ELM offers a better approximation of the embedded coordinates, also with reduced computational costs during testing.