  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.
