Traditional matrix-based dimensional reduction methods, e.g., two-dimensional principal component analysis (2DPCA) and two-dimensional singular value decomposition (2DSVD), minimize mean square errors (MSE), which is sensitive to outliers. To overcome this problem, in this paper we propose a new robust 2DSVD method based on the kernel mean $p$ power error loss (KMPE-2DSVD). Different from the MSE and the correntropy based ones which are second order statistics based measurements, the KMPE-2DSVD is based on the non-second order statistics in the kernel space, and thus is more flexible in controlling the representation error. Experimental results show that the proposed method significantly improves the accuracy of facial image clustering.