Learning Isometric Separation Maps

Maximum Variance Unfolding (MVU) and its variants have been very successful in embedding data-manifolds in lower dimensionality spaces, often revealing the true intrinsic dimensions. In this paper we show how to also incorporate supervised class information into an MVU-like method without breaking its convexity. We call this method the Isometric Separation Map and we show that the resulting kernel matrix can be used for a binary/multiclass Support Vector Machine in a semi-supervised (transductive) framework. We also show that the method always finds a kernel matrix that linearly separates the training data exactly without projecting them in infinite dimensional spaces.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Nikolaos Vasiloglou, Alexander G. Gray, David V. Anderson
• Keywords: CORR 2008, Education, Kernel Matrix, Lower Dimensionality Spaces, True Intrinsic Dimensions