By making use of compressive mapping and isomorphic mapping in the kernel extension of graph embedding, this paper proves that the essence of kernel extension of graph embedding (KGE) is KPCA (kernel principal component analysis) plus all kinds of linear dimension reduction approaches interpreted in a linear extension of graph embedding (LGE). Based on the theory framework, a combined framework, which takes advantage of the discriminant feature in both null and non-null spaces, is developed. Furthermore, every kernel dimensionality reduction algorithm has its own corresponding combined algorithm. The experimental results from ORL, Yale, FERET and PIE face databases show that the proposed methods are better than the original methods in terms of recognition rate.