Geometric Structure Transfer Based Domain Adaptation

Most of the existing machine learning methods assume that the training data and the test data have an identical probability distribution.However,in practical application scenarios,such as computer vision,biomedicine,etc.,the assumption of the identical distribution of data is too strict to be established.Analyzing domain data with distribution divergence is one of the most challenging machine learning tasks at the moment.Domain adaptation can effectively solve the above-mentioned cross-domain data analysis problems.Domain adaptation do not force that training data and test data must obey an identical probability distribution.The problem of crossdomain information transfer under the same label space is solved by extracting the domaininvariant knowledge structure between different but related domains.This thesis focuses on the geometric structure relevance between different domains,and presents a study on the adaptive learning algorithms to solve the cross-domain classification problems.The main content and novel contributions are summarized as follows.1.A source domain semi-supervised domain adaptation method is proposed.This method uses the manifold structure information of the source domain data,so that the unlabeled source domain data can also participate in the knowledge transfer across domains.The proposed method effectively solves the domain adaptation problem when the label information of source domain data is insufficient.2.A domain adaptation method based on inter-domain invariant geometric graph is proposed.This method uses the Nystr(?)m approximation error to describe the probability distribution divergence between domains from the geometric perspective.By minimizing the Nystr(?)m approximation error,the target domain graph structure drives the adaptation of the source domain graph structure,and finally a domain-invariant geometric graph is established to connect the two domains.3.A domain adaptation shared dictionary learning method is proposed.This method uses the maximum mean discrepancy to extract the statistical common information between domains,and uses the Nystr(?)m approximation error to explore the geometric structure relationship between domains.The proposed method makes full use of the complementarity between the geometric structure and statistical information of data to fully capture the latent common semanteme between domains.4.A unified domain adaptation method based on geometric and statistical adaptation is proposed.Based on the foregoing work,this method considers the conditional distribution divergence between domains,and uses the expanded maximum mean discrepancy to measure the conditional distribution divergence.The marginal distribution divergence,the conditional distribution divergence,the geometric structure divergence and the construction of an adaptive classifier are unified under one optimization goal.The convex optimization solution of the adaptive model is given by the representer theorem in reproducing kernel Hilbert space.