A Two-Parameter Fractional Tsallis Decision Tree

• Published in: Entropy (Basel, Switzerland) Vol. 24; no. 5; p. 572
• Main Authors: De la Cruz-García, Jazmín S, Bory-Reyes, Juan, Ramirez-Arellano, Aldo
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 19.04.2022; MDPI
• Subjects: Algorithms; Classification; complex networks; Data mining; Decision trees; Entropy; Entropy (Information theory); Gini index; Parameter sensitivity; two-parameter Tsallis entropy; Gini index; complex networks; two-parameter Tsallis entropy; decision trees
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e24050572

Decision trees are decision support data mining tools that create, as the name suggests, a tree-like model. The classical C4.5 decision tree, based on the Shannon entropy, is a simple algorithm to calculate the gain ratio and then split the attributes based on this entropy measure. Tsallis and Renyi entropies (instead of Shannon) can be employed to generate a decision tree with better results. In practice, the entropic index parameter of these entropies is tuned to outperform the classical decision trees. However, this process is carried out by testing a range of values for a given database, which is time-consuming and unfeasible for massive data. This paper introduces a decision tree based on a two-parameter fractional Tsallis entropy. We propose a constructionist approach to the representation of databases as complex networks that enable us an efficient computation of the parameters of this entropy using the box-covering algorithm and renormalization of the complex network. The experimental results support the conclusion that the two-parameter fractional Tsallis entropy is a more sensitive measure than parametric Renyi, Tsallis, and Gini index precedents for a decision tree classifier.