The recent surge of interests in cognitive assessment has led to developments of novel statistical models for diagnostic classification. Central to many such models is the well-known "Q"-matrix, which specifies the item-attribute relationships. This article proposes a data-driven approach to identification of the "Q"-matrix and estimation of related model parameters. A key ingredient is a flexible "T"-matrix that relates the "Q"-matrix to response patterns. The flexibility of the "T"-matrix allows the construction of a natural criterion function as well as a computationally amenable algorithm. Simulations results are presented to demonstrate usefulness and applicability of the proposed method. Extension to handling of the "Q"-matrix with partial information is presented. The proposed method also provides a platform on which important statistical issues, such as hypothesis testing and model selection, may be formally addressed. (Contains 4 tables and 2 figures.)