Research Of Semi-supervised Learning On Multi-manifold

As a non-linear dimensionality reduction method, manifold learning methods can discover the intrinsic low-dimensional structures of the high-dimensional data. They have been widely used in data classification to tackle the curse of dimensionality problem. However, they are unable to be used effectively when the input data lie in multiple manifolds with possible intersections. And this is a general case in the classification problem, since the data from each class may form its own manifold and different classes corresponds to different sub-manifolds. At present, the work in this area is relatively less.With the improvement of data acquisition technology, it’s easy to get a lot of unlabeled sample points. But because of the limitations of manpower and material resources, we are difficult to obtain a lot of labeled points. So, how to use a lot of unlabeled points and a small amount of labeled points to guide learning is one of the challenges for manifold learning. And, semi-supervised manifold learning methods just provide a good solution for it.However, the high-dimensional data obtained in the process of application may be polluted by noise. The performances of unsupervised and semi-supervised manifold learning methods will be affected inevitably. In the presence of noise, the real local relationship between the data points will be affected. Thereby, the extracted geometric features may be inaccurate. Currently, there have been some effective improvements, but most of the improvements are based on unsupervised manifold learning algorithm. Few work are done on the semi-supervised algorithms.So, this paper mainly focuses on the multi-manifold problem and the robustness problem of semi-supervised manifold learning. More concretely, the main contributions of this paper are as follows:1. A novel approach called semi-supervised learning on multiple-manifold(SSL-MM) is proposed to solve multi-manifold problem. SSL-MM constructs the local geometry of each point by solving a sparse optimization model which can greatly reduce the undesirable effect of those neighbors sampled from different manifolds. Then, SSL-MM predicts the class labels of the unlabeled data by preserving the learned local geometry in the low-dimensional space in which the label information of partially data is given. At the same time, this paper gives plentiful comparative experiments on several real-world data sets to show that the improvement and efficiency of SSL-MM.2. For the robustness problem of semi-supervised manifold, we propose a framework for robust semi-supervised manifold learning(RSSML). The noisy levels of the labeled points are firstly predicted, and then a regularization term is constructed to reduce the impact of labeled points containing noise. A new robust semi-supervised optimization model is proposed by adding the regularization term to the classical semi-supervised optimization model. At last, numerical experiments on real-world data sets show that RSSML leads to considerable improvements for classification and the robustness to noisy data.