(g, F)-the K-cover Maps (g, F)-k-deleted Graph And Independent Component Analysis And Its Applications

Two parts are involved in this paper. Firstly, we investigate the existence problem of a bipartite graph to be ( g ,f)- k-covered graphs and ( g ,f)- k-deleted graphs based on the problem of factors in graphs. a necessary and sufficient condition for a bipartite graph G=(X,Y) to be (g, f)-2-covered,(g, f)-3-covered graph,and(g, f)-3-deleted graph is given respectively when g≤f. Secondly, we put a new algorithm unifying independent component analysis (ICA),statistical parameter mapping (SPM) and principal component analysis (PCA),which is based on the ICA and related theory, and whose application in resting functional magnetic resonance imaging (fMRI) with united ICA, SPM, and PCA, for localizing epileptic activities of two lipoma foci. The thesis consists of five chapters.In chapter 1, we introduce the research headway of graph theory, some primary conception of the problem of the factors in graphs and main work in the problem of the factors in graphs.In chapter 2, we research ( g ,f)- k- covered graphs (k=2, 3). In section 2.2, a necessary and sufficient condition for a bipartite graph to be (g, f)-2-covered is given when g≤f, and a necessary and sufficient condition for a bipartite graph to be f-2-covered are obtained when f(X)=f(Y).In section 2.3, we discussed the condition that a bipartite graph is (g, f)-3-covered when g≤f , we get the analogous result in section 2.2. In section 2.4, we put two new problems.In chapter 3, we research ( g ,f)- 3- deleted graphs. A necessary and sufficient condition for a bipartite graph to be (g, f)-3-covered is given when g≤f, and a necessary and sufficient condition for a bipartite graph to be f-3-covered are obtained when f(X)=f(Y).In the last, we put a new problem.In chapter 4, we introduce the higher order statistic analysis theory and information theory related to ICA theory, the object function of ICA, and several representative optimizing algorithm of ICA.In chapter 5,we report a novel algorithm and its application in resting magnetic resonance imaging with unified ICA, SPM, and PCA,for localizing two epileptic...