Three-way concept analysis is a very important topic in the field of artificial intelligence. The biggest advantage of this theory is that it can study “attributes that are commonly possessed” and “attributes that are commonly not possessed” of the objects in the formal context at the same time. It is well known that the new formal context generated by attribute clustering has a strong connection with the original formal context， and there is a close internal connection between the original three-way concepts and the new three-way concepts obtained by attribute clustering. Therefore， the comparative study and analysis of three-way concepts under attribute clustering were carried out. Firstly， the concepts of pessimistic， optimistic and general attribute clusterings were proposed on the basis of attribute clustering， and the relationship among these three concepts was studied. Moreover， the difference between the original three-way concepts and the new ones was studied by comparing the clustering process with the formal process of three-way concepts. Furthermore， two minimum constraint indexes were put forward from the perspective of object-oriented and attribute-oriented respectively， and the influence of attribute clustering on three-way concept lattice was explored. The above results further enrich the theory of three-way concept analysis and provide feasible ideas for the field of visual data processing.