Semisupervised data classification via the Mumford–Shah–Potts-type model

Abstract

• A semisupervised data classification was proposed based on the Mumford–Shah–Potts-type model. • We used the ADMM-type and primal-dual-type methods to solving the proposed model. • Some propositions of proposed model and numerical methods were discussed. • We arranged some numerical comparisons to illustrate the efficiency of our proposed methods. More and more high dimensional data are widely used in many real world applications. This kind of data are obtained from different feature extractors, which represent distinct perspectives of the data. How to classify such data efficiently is a challenge. Despite of existence of millions of unlabeled data samples, it is believed that labeling a handful of data such as the semisupervised scheme will remarkably improve the searching performance. However, the performance of semisupervised data classification highly relies on proposed models and related numerical methods. Following from the extension of the Mumford–Shah–Potts-type model in the spatially continuous setting, we propose some efficient data classification algorithms based on the alternating direction method of multipliers and the primal-dual method to efficiently deal with the nonsmoothing problem in the proposed model. The convergence of the proposed data classification algorithms is established under the framework of variational inequalities. Some balanced and unbalanced classification problems are tested, which demonstrate the efficiency of the proposed algorithms.