In order to monitor nonlinear processes, kernel principal component analysis (KPCA) has become a popular technique. Nevertheless, KPCA suffers from two major disadvantages. First, the underlying manifold structure of data is not considered in process modeling. Second, the selection of kernel function and kernel parameters is always problematic. To avoid such deficiencies, an integrating method of manifolding learning and Gaussian process is proposed in this paper, which extends the utilization of maximum variance unfolding (MVU) to online process monitoring and fault isolation. The proposed method is named as extendable MVU (EMVU), whose effectiveness is verified by the case studies on the benchmark Tennessee Eastman (TE) process.