Decision Tree Based on Shannon, Rényi and Tsallis Entropies for Intrusion Tolerant Systems

This paper describes a comparative study of the use of Shannon, Renyi and Tsallis entropies for designing Decision Tree, with goal to find more efficient alternatives applied to Intrusion Tolerant Systems. Decision Tree has been used in classification model problems related to intrusion detection in networks, presenting good results. A very used decision tree is the C4.5 one that applies the Shannon entropy in order to choose the attributes that better divide data intoclasses. However, other ways to measure entropy, e.g., Tsallis and Renyi entropy, may be applied aiming at guaranteeing better generalization related to split criteria. Experimental results demonstrate that Tsallis and Renyi entropy can be used to construct more compact and efficient decision trees compared with Shannon entropy and these models can to provide more accurate intrusion tolerante systems.