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Manifold regularization model is a semi-supervised learning model that leverages the geometric structure of a dataset, comprising a small number of labeled samples and a large number of unlabeled samples, to generate classifiers. However, the original manifold norm limits the performance of models to local regions. To address this limitation, this paper proposes an approach to improve manifold regularization based on a label propagation model. We initially enhance the probability transition matrix of the diffusion map algorithm, which can be used to estimate the Neumann heat kernel, enabling it to accurately depict the label propagation process on the manifold. Using this matrix, we establish a label propagation function on the dataset to describe the distribution of labels at different time steps. Subsequently, we extend the label propagation function to the entire data manifold. We prove that the extended label propagation function converges to a stable distribution after a sufficiently long time and can be considered as a classifier. Building upon this concept, we propose a viable improvement to the manifold regularization model and validate its superiority through experiments., Comment: 20 pages, 24figures

A series of 5,7-dihydroxyflavanone derivatives were efficiently synthesized. Their antimicrobial efficacy on Gram-negative, Gram-positive bacteria and yeast were evaluated. Among these compounds, most of the halogenated derivatives exhibited the best antimicrobial activity against Gram-positive bacteria, the yeast Saccharomyces cerevisiae, and the Gram-negative bacterium Vibrio cholerae. The cytotoxicities of these compounds were low as evaluated on HepG2 cells using a cell viability assay. This study suggests that halogenated flavanones might represent promising pharmacological candidates for further drug development.