Rule extraction by a structural learning of neural networks

在从连续值输入中提取规则时，均方输出误差和规则复杂度之间的平衡是很重要的。AIC等信息标准代表了这种权衡。在带遗忘的结构学习（SLF）中，遗忘量由最小化AIC决定，但单靠SLF不能产生适当复杂度的规则。为了克服这个困难，训练了各种复杂程度的神经网络。这里，复杂度由每个隐藏单元的最大传入连接数定义。从这些中，具有最小AIC的一个被选择为最佳。由于隐藏单元的输出是二进制的，由于学习与隐藏单元澄清，传入的连接权重，每个隐藏单元确定相应的判别超平面。这些超平面的逻辑组合提供了规则。此外，与机器学习中流行的C4.5相比。并与KT met进行了比较 ...更多信息 傅立叶提出的方法。C4.5和KT方法只能产生每项只有一个属性的规则。另一方面，所提出的方法可以产生各种复杂度的规则。第一个任务是将一个二维平面分成两类。在这种情况下，每个术语只有一个属性的规则不是自然的表示。C4.5生成了许多简单的规则，但所提出的方法可以用6个规则和两个属性来解释所有数据。第二项任务是将鸢尾花分为3类：刚毛鸢尾、杂色鸢尾和处女鸢尾。三个规则最多3个属性可以解释150个样本中的148个。第三个任务是诊断甲状腺功能分为3类：正常，低和高功能。在这种情况下，最多具有2个属性的4个规则可以解释所有215个样本。对于连续输入和离散输入的规则提取以及连续输入和输出的规则提取，由于其固有的困难，目前还没有得到令人满意的结果。这些问题留待进一步研究。少

In extracting rules from continuous valued inputs, the balance between mean square output error and the complexity of rules is important. Information criteria such as AIC represents this trade-off. In a structural learning with forgetting (SLF), the amount of forgetting is determined by minimizing AIC.However, SLF alone cannot produce rules of appropriate complexity. To overcome this difficulty, neural networks of various degrees of, complexity are trained. The degree of complexity, here, is defined by the maximum number of incoming connections to each hidden unit. From among these, the one with the smallest AIC is selected as optimal. Since outputs of hidden units are binary owing to the learning with hidden units clarification, incoming connection weights to each hidden unit determine the corresponding discriminating hyperplane. A logical combination of these hyperplanes provides rules. Furthermore, comparison with C4.5 popular in machine learning. Also comparison is made with KT met … More hod proposed by Fu. C4.5 and KT method can only produce rules with only one attribute at each term. On the other hand, the proposed method can produce rules of various complexities.The first task is to divide a two-dimensional plane into two categories. In this case, rules with only one attribute at each term is not a natural representation. C4.5 generates many simple rules, but the proposed method can explain all data by 6 rules with two attributes. The second task is the classification of irises into 3 categories : setosa, versicolor, and virginica. Three rules with at most 3 attributes can explain 148 samples out of 150. The third task is the diagnosis of thyroid functioning into 3 classes : normal, hypo and hyper functioning. In this case 4 rules with at most 2 attributes can explain all 215 samples. Furthermore, the number of classification errors is smaller than those by C4.5 and KT method.Concerning rule extraction from both continuous and discrete inputs and that from continuous inputs and outputs, satisfactory results are not yet obtained due to inherent difficlty. These are left for further study. Less