# Improvement of ID3 Algorithm Based on Simplified Information Entropy and Coordination Degree
## 1 Introduction  
Large amount of data that includes a lot of potential and valuable information is stored in a database. If a wealth of hidden information can be extracted from the database, more potential value will be created. Faced with the challenge of the above issue, data mining [1; 2] technologies came into being and showed strong vitality. Data mining includes several important technologies such as classification [3], clustering [4], regression [5], etc. The classification mining technology, among data mining technologies, is becoming a most active and mature research direction allowing for successful applications. Classification mining [6] can be applied to discover useful information from large amounts of data stored in a large number of fields such as hospital, stock, banking, etc. For example, it is important for a hospital to accurately predict the length of stay (LOS), and Ref. [7] showed that the classification mining technology was not only beneficial to solve limited bed resources, but was also helpful for the hospital staff to implement better planning and management of hospital resources. In Ref. [8], in order to easily acquire stock returns in the stock market, different classifiers were used in the stock market prediction, and the prediction accuracy was commonly satisfied. Ref. [9] used two types of classifier ensembles to predict stock returns. The problem of bank note recognition is very important for bank staff. Ref. [10] presented neuro-classifiers to address the big problem. Ref. [11] presented the ANN classification approach, which could be used to detect early warning signals of potential failures for banking sectors. The decision tree methods [12; 13], the neural network methods [14] and the statistical methods [15; 16] are common classification algorithms used by researchers in the field of classification mining. A large amount of decision tree algorithms such as Iterative Dichotomizer 3 (ID3) [17], C4.5 [18], and Classification And Regression Tree (CART) [19] are used in different fields. Most decision tree methods are developed from the ID3 method. For example, the C4.5 method [20] presented an optimal attribution selection standard (gain ratio) [21] instead of the optimal attribution selection standard (information gain) in ID3; The CART method took the Gini index [22] as the selection standard of the optimal attribution. Although many advantages are acquired from these improved decision tree methods, there is also much room for improvement. The ID3 algorithm is used as a general classification function, and it has many advantages, such as understandable decision rules and the intuitive model. Nevertheless, ID3 also has some disadvantages, for example: (1) there exists a problem of multi-value bias in the process of attribute selection [23], but the attribution that has more values is not always optimal; (2) it is not easy to calculate information entropy [24; 25] by using logarithmic algorithms, which costs a lot of time; and (3) the tree size is difficult to control [26], and the tree with a big size requires many long classification rules. In order to solve the problems above, an optimized scheme is proposed here based on the ID3 method. First of all, in order to solve the defect of multi-value bias brought by the information gain equation in ID3, C4.5 selected gain ratio instead of the information gain equation, but this method included a lot of logarithmic operations, which will affect the whole performance. This paper presents a novel method by directly adding different weights for the information gain equation of every candidate attribution, and this way not only makes the selection of the optimal attribute more reasonable, but also has a small effect on the running speed. Secondly, as we all know, in two equivalent formulas (e.g., the logarithmic expression and the four arithmetic operation), the computation speed of the logarithmic expression is slower than that of the four arithmetic operations that only include add, subtract, multiply and divide [27].