Semi-supervised learning using multiple one-dimensional embedding based adaptive interpolation

We propose a novel semi-supervised learning scheme using adaptive interpolation on multiple one-dimensional (1-D) embedded data. For a give high dimensional data set, we smoothly map it onto several different one-dimensional (1-D) sequences, so that the labeled subset is converted to a 1-D subset for each of these sequences. Applying the cubic interpolation of the labeled subset, we obtain a subset of unlabeled points, which are assigned to the same label in all interpolations. Selecting a proportion of these points at random and adding them to the current labeled subset, we build a larger labeled subset for the next interpolation. Repeating the embedding and interpolation, we enlarge the labeled subset gradually, and finally reach a labeled set with a reasonable large size, based on which the final classifier is constructed. We explore the use of the proposed scheme in the classification of handwritten digits and show promising results.