Combining Smooth Graphs with Semi-supervised Classification

Abstract

In semi-supervised classification, many methods use the graph representation of data. Based on the graph, different methods, e.g. random walk model, spectral cluster, Markov chain, and regularization theory etc., are employed to design classification algorithms. However, all these methods use the form of graphs constructed directly from data, e.g. kNN graph. In reality, data is only the observation with noise of hidden variables. Classification results using data directly from the observation may be biased by noise. Therefore, filtering the noise before using any classification methods can give a better classification. We propose a novel method to filter the noise in high dimension data by smoothing the graph. The analysis is given from the aspects of spectral theory, Markov chain, and regularization. We show that our method can reduce the high frequency components of the graph, and also has an explanation from regularization view. A graph volume based parameter learning method can be efficiently applied to classification. Experiments on artificial and real world data set indicate that our method has a superior classification accuracy.