Spatial-spectral classification (SSC) has become a trend for hyperspectral image (HSI) classification. However, most SSC methods mainly consider local information, so that some correlations may not be effectively discovered when they appear in regions that are not contiguous. Although many SSC methods can acquire spatial-contextual characteristics via spatial filtering, they lack the ability to consider correlations in non-Euclidean spaces. To address the aforementioned issues, we develop a new semisupervised HSI classification approach based on normalized spectral clustering with kernel-based learning (NSCKL), which can aggregate local-to-global correlations to achieve a distinguishable embedding to improve HSI classification performance. In this work, we propose a normalized spectral clustering (NSC) scheme that can learn new features under a manifold assumption. Specifically, we first design a kernel-based iterative filter (KIF) to establish vertices of the undirected graph, aiming to assign initial connections to the nodes associated with pixels. The NSC first gathers local correlations in the Euclidean space and then captures global correlations in the manifold. Even though homogeneous pixels are distributed in noncontiguous regions, our NSC can still aggregate correlations to generate new (clustered) features. Finally, the clustered features and a kernel-based extreme learning machine (KELM) are employed to achieve the semisupervised classification. The effectiveness of our NSCKL is evaluated by using several HSIs. When compared with other state-of-the-art (SOTA) classification approaches, our newly proposed NSCKL demonstrates very competitive performance. The codes will be available at https://github.com/yuanchaosu/TCYB-nsckl.