An Efficient and Versatile Variational Method for High-Dimensional Data Classification

High-dimensional data classification is a fundamental task in machine learning and imaging science. In this paper, we propose an efficient and versatile multi-class semi-supervised classification method for classifying high-dimensional data and unstructured point clouds. To begin with, a warm initialization is generated by using a fuzzy classification method such as the standard support vector machine or random labeling. Then an unconstraint convex variational model is proposed to purify and smooth the initialization, followed by a step which is to project the smoothed partition obtained previously to a binary partition. These steps can be repeated, with the latest result as a new initialization, to keep improving the classification quality. We show that the convex model of the smoothing step has a unique solution and can be solved by a specifically designed primal–dual algorithm whose convergence is guaranteed. We test our method and compare it with the state-of-the-art methods on several benchmark data sets. Thorough experimental results demonstrate that our method is superior in both the classification accuracy and computation speed for high-dimensional data and point clouds.