This paper proposes a multiclass semisupervised learning algorithm by using kernel spectral clustering (KSC) as a core model. A regularized KSC is formulated to estimate the class memberships of data points in a semisupervised setting using the one-versus-all strategy while both labeled and unlabeled data points are present in the learning process. The propagation of the labels to a large amount of unlabeled data points is achieved by adding the regularization terms to the cost function of the KSC formulation. In other words, imposing the regularization term enforces certain desired memberships. The model is then obtained by solving a linear system in the dual. Furthermore, the optimal embedding dimension is designed for semisupervised clustering. This plays a key role when one deals with a large number of clusters.