The Study Of Semi-supervised Subspace Clustering And Its Applications

The ubiquitous large,complex and high dimensional datasets in computer vision and machine learning generates the problem of subspace clustering,which aims to partition the data into several low dimensional subspaces.By utilizing relatively limited labeled data and sufficient unlabeled data,the semi-supervised subspace clustering is more effective,practical and becoming more popular.For accurate semi-supervised subspace clustering,the label information should be fully used to predict the unknown label.Therefore,it is of great importance to infer the unknown label by using the given label in semi-supervised clustering.In this work,a new regularity combing the labels and the affinity is proposed to ensure the coherence of the affinity between data points from the same subspace as well as the discrimination of cluster labels for data points from different subspaces.By combining it with the manifold smoothing term of the existing methods and the Gaussian fields and harmonic functions method,a new unified optimization framework for semi-supervised subspace clustering is given.Analysis shows the proposed model fully combines the affinity and the labels to guide each other so that both are discriminative between clusters and coherent within clusters.Additionally,linear regression as one of the most important machine learning technique,can typically map image features to continuous or discrete values.Therefore,based on the work in chapter 3,a classifier-like linear regression mapping in the process of learning the affinity is learned by a semi-supervised way,which can transform the affinity into label matrix.This not only guarantees the the property of discriminative between clusters and coherent within clusters,but also can learn a linear mapping to convert the affinity into a label matrix.Extensive experiments show that our method outperforms the existing state-of-the-art methods,thus suggests that the property of discriminative between clusters and coherent within clusters of our method is advantageous to semi-supervised subspace clustering,and it is practical to learn a linear mapping as a classifier to convert the affinity into a label matrix by a semi-supervised way.