Semisupervised learning is the primary method of making use of unlabeled samples for learning, and is a very active research field in machine learning. This article focuses on the applied research of geometric information in the semisupervised learning. The main work includes the integration of geometric information and tag information, graphbased inductive algorithm, affine manifold alignment, image segmentation by multiresolution RandomWalk, comparative effects and analysis of geometric information in semisupervised learning.Semisupervised learning mainly digs the hidden information in the unlabeled data to improve the classifier accuracy, and usually contains the integration of label information and geometric information. In most algorithms the coefficient for melting the two parts is fixed. In this paper, we point out that the weights of the labeled information and manifold structural information could be changed with the proportion of the labeled points in order to effectively improve the learning accuracy.Graphbased learning is a very active direction of semisupervised learning in recent years. It describes the sample space by graph, and uses neighbors to spread label information in point cloud. For the restriction of the graph feature, most of these algorithms are transductive that they can't produce an explicit mapping. By introducing the mixed model and local linear coordinate into the semisupervised learning, we propose the semisupervised local linear coordination algorithm. The algorithm is an inductive graphbased method, and achieves better performance than linear methods by local linear transformation.Manifold alignment is to find the hidden space of two or more data sets, and align them in a global coordination where the corresponding pairwise relationship could be found easily. Most of manifold alignment algorithms can only give the predictive value of the training set instead of producing a mapping defined everywhere. We present a manifold affine alignment algorithm, which facilitates direct mapping of new data points.As the constraints of memory consumption and time of segmentation, most of the semisupervised image segmentation algorithms can not be directly applied to large images. In this paper, a semisupervised image segmentation algorithm based on multiresolution RandomWalk is proposed. Low frequency subdivision is used here to approximate the segmentation probability of the original image, while the controversial area is quickly identified, then the accurate segmentation is imposed on the disputed area. The algorithm offers a better solution to semisupervised segmentation on large images, and is robust in complex background environment.In order to better study the relationship between the geometric information and the semisupervised learning effect, a framework for integrating the geometric information and tag information is present here. The methods based on mixed model are also incorporated into the framework by the definition of middle variable. The comparison and analysis of geometric information's impact on semisupervised learning is performed through the experiments.
