Abstract: Concept lattice,the core data structure in FCA(Formal Concept Analysis)，has been widely used in machine learning and data mining. In its applications, building concept lattice is very important, for which an efficient algorithm CMCG based on concept matrix was put forward. The algorithm started from the top node of the lattice, generated all subnodes for each node using the rank of the concept matrix's attributes,completed the link between the subnodes and their parent, and generated the Hasse graph. The validity of the algorithm was proved in theory. In the end, the pseudo code of CMCG algorithm was given and that performance of CMCG is superior in time to lattice algorithm was proved by experiments.

Key words: Concept lattice, Concept matrix, Rank of matrix, Formal concept analysis, Hasse graph