Accurately representing data is a fundamental problem in many pattern recognition and computational intelligence applications. In this chapter, a robust constrained concept factorization (RCCF) method is proposed. RCCF allows the extraction of important information, while simultaneously utilizing prior information when it is available, and is noise invariant. To guarantee data samples share the identical cluster and obtain similar representation in the new laten space, the proposed method uses a constraint matrix that is embodied into the rudimentary concept factorization model. The L -norm is used for both the reconstruction function and the regularization, which allows the proposed model to be insensitive to outliers. Furthermore, the L -norm regularization assists in the selection of useful information with joint sparsity. An elegant and efficient iterative updating scheme is also introduced with convergence and correctness analysis. Experimental results on commonly used databases in pattern recognition and computational intelligence demonstrate the effectiveness of RCCF.