In order to accurately diagnose the faulty parts of the rolling bearing under different operating conditions, the KJADE (Kernel Function Joint Approximate Diagonalization of Eigenmatrices) algorithm is proposed to reduce the dimensionality of the high-dimensional feature data. Then, the VNWOA (Von Neumann Topology Whale Optimization Algorithm) is used to optimize the LSSVM (Least Squares Support Vector Machine) method to diagnose the fault type of the rolling bearing. The VNWOA algorithm is used to optimize the regularization parameters and kernel parameters of LSSVM. The low-dimensional nonlinear features contained in the multidomain feature set are extracted by KJADE and compared with the results of PCA, LDA, KPCA, and JADE methods. Finally, VNWOA-LSSVM is used to identify bearing faults and compare them with LSSVM, GA-LSSVM, PSO-LSSVM, and WOA-LSSVM. The results show that the recognition rate of fault diagnosis is up to 98.67% by using VNWOA-LSSVM. The method based on KJADE and VNWOA-LSSVM can diagnose and identify fault signals more effectively and has higher classification accuracy.