graph-based approaches have been successful in unsupervised and semi-supervised learning. in this paper, we focus on the real-world applications where the same instance can be represented by multiple heterogeneous features. the key point of utilizing the graph-based knowledge to deal with this kind of data is to reasonably integrate the different representations and obtain the most consistent manifold with the real data distributions. in this paper, we propose a novel framework via the reformulation of the standard spectral learning model, which can be used for multiview clustering and semisupervised tasks. unlike other methods in the literature, the proposed methods can learn an optimal weight for each graph automatically without introducing an additive parameter as previous methods do. furthermore, our objective under semisupervised learning is convex and the global optimal result will be obtained. extensive empirical results on different real-world data sets demonstrate that the proposed methods achieve comparable performance with the state-of-the-art approaches and can be used more practically.