Manifold Assumptionis a common assumption in semi-supervised learning, and the other is the clustering assumption.

The manifold assumption states that examples with similar properties are usually in small local neighborhoods and therefore have similar labels, which reflects the local smoothness of the decision function.

Different from the clustering hypothesis that focuses on the overall characteristics, the manifold hypothesis focuses more on the local characteristics of the model.

Under this assumption, the purpose of a large number of unlabeled examples is to make the data space more compact, which helps to more accurately characterize the characteristics of local areas and enable the decision function to better fit the data.