结合Copula理论与贝叶斯决策理论的分类算法

Classification algorithm based on Copula theory and Bayesian decision theory

传统的贝叶斯决策分类算法易受类条件概率密度函数估计的影响,可能会对分类结果造成干扰。对此本文提出来一种改进的贝叶斯决策分类算法,即Bayesian-Copula判别分类器(BCDC)。该方法无需对类条件概率密度函数的形式进行假设,而是将Copula理论和核密度估计相结合进行函数构建,利用核密度估计平滑特征的概率分布,概率积分变换将特征的累计概率分布转化为均匀分布,Copula函数构建2个类别的边缘累积分布之间的相关性。随后,用极大似然估计方法确定Copula函数的参数,贝叶斯信息准则(BIC)用于选择最合适的Copula函数。通过生物电信号的仿真实验进行模型验证,结果表明相比传统的概率模型,提出的分类算法在分类精度和AUC两个性能指标上表现较好,鲁棒性更强,说明了BCDC模型充分利用Copula理论和核密度估计的优点,提高了估计的准确性和灵活性。

Traditional Bayesian decision classification algorithm is easily affected by the estimation of class-conditional probability densities,a fact that may result in incorrect classification results. Therefore,this paper proposes an improved classification algorithm based on Bayesian decision,i. e.,Bayesian-Copula Discriminant Classifier（ BCDC）. This method constructs class-conditional probability densities by combining Copula theory and kernel density estimation instead of making assumptions on the form of class-conditional probability densities. Kernel density estimation is used to smooth the probability distribution of each feature. By performing probability integral transform,continuous distribution is converted to random variables having a uniform distribution. Then,Copula functions are used to construct the dependency structure between these probability distributions for two categories. Moreover,the maximum likelihood estimation is applied to determine the parameters of Copula functions,and two wellfitted Copula functions for two categories are selected based on Bayesian information criterion. The BCDC method was validated with experimental datasets of physiological signals. The obtained results showed that the proposed method outperforms other traditional methods in terms of classification accuracy and AUC as well as robustness. Moreover,it takes full advantage of Copula theory and kernel density estimation and improves the accuracy and flexibility of the estimation.