Matrix Factorization based methods, e.g., the Concept Factorization (CF) and Nonnegative Matrix Factorization (NMF), have been proved to be efficient and effective for data clustering tasks. In recent years, various graph extensions of CF and NMF have been proposed to explore intrinsic geometrical structure of data for the purpose of better clustering performance. However, many methods build the affinity matrix used in the manifold structure directly based on the input data. Therefore, the clustering results are highly sensitive to the input data. To further improve the clustering performance, we propose a novel manifold concept factorization model with adaptive neighbor structure to learn a better affinity matrix and clustering indicator matrix at the same time. Technically, the proposed model constructs the affinity matrix by assigning the adaptive and optimal neighbors to each point based on the local distance of the learned new representation of the original data with itself as a dictionary. Our experimental results present superior performance over the state-of-the-art alternatives on numerous datasets.