In this paper, the well-known competitive clustering algorithm (CA) is revisited and reformulated from a point of view of entropy minimization. That is, the second term of the objective function in CA can be seen as quadratic or second-order entropy. Along this novel explanation, two generalized competitive clustering algorithms inspired by Renyi entropy and Shannon entropy, i.e. RECA and SECA, are respectively proposed in this paper.Simulation results show that CA requires a large number of initial clusters to obtain the right number of clusters, while RECA and SECA require small and moderate number of initial clusters respectively. Also the iteration steps in RECA and SECA are less than that of CA.Further CA and RECA are generalized to CA-p and RECA-p by using the p-order entropy and Renyi's p-order entropy in CA and RECA respectively. Simulation results show that the value of phas a great impact on the performance of CA-p, whereas it has little in uence on that of RECA-p.