New approaches are proposed for complex industrial process monitoring and fault diagnosis based on kernel independent component analysis (KICA) and sparse support vector machine (SVM). The KICA method is a two-phase algorithm: whitened kernel principal component analysis (KPCA). The data are firstly mapped into high-dimensional feature subspace. Then, the ICA algorithm seeks the projection directions in the KPCA whitened space. Performance monitoring is implemented through constructing the statistical index and control limit in the feature space. If the statistical indexes exceed the predefined control limit, a fault may have occurred. Then, the nonlinear score vectors are calculated and fed into the sparse SVM to identify the faults. The proposed method is applied to the simulation of Tennessee Eastman (TE) chemical process. The simulation results show that the proposed method can identify various types of faults accurately and rapidly.