Peterson Leif E, Coleman Matthew A
Baylor College of Medicine, Houston, Texas 77030 USA.
Int J Approx Reason. 2008 Jan;47(1):17-36. doi: 10.1016/j.ijar.2007.03.006.
Receiver operating characteristic (ROC) curves were generated to obtain classification area under the curve (AUC) as a function of feature standardization, fuzzification, and sample size from nine large sets of cancer-related DNA microarrays. Classifiers used included k nearest neighbor (kNN), näive Bayes classifier (NBC), linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), learning vector quantization (LVQ1), logistic regression (LOG), polytomous logistic regression (PLOG), artificial neural networks (ANN), particle swarm optimization (PSO), constricted particle swarm optimization (CPSO), kernel regression (RBF), radial basis function networks (RBFN), gradient descent support vector machines (SVMGD), and least squares support vector machines (SVMLS). For each data set, AUC was determined for a number of combinations of sample size, total sum[-log(p)] of feature t-tests, with and without feature standardization and with (fuzzy) and without (crisp) fuzzification of features. Altogether, a total of 2,123,530 classification runs were made. At the greatest level of sample size, ANN resulted in a fitted AUC of 90%, while PSO resulted in the lowest fitted AUC of 72.1%. AUC values derived from 4NN were the most dependent on sample size, while PSO was the least. ANN depended the most on total statistical significance of features used based on sum[-log(p)], whereas PSO was the least dependent. Standardization of features increased AUC by 8.1% for PSO and -0.2% for QDA, while fuzzification increased AUC by 9.4% for PSO and reduced AUC by 3.8% for QDA. AUC determination in planned microarray experiments without standardization and fuzzification of features will benefit the most if CPSO is used for lower levels of feature significance (i.e., sum[-log(p)] ~ 50) and ANN is used for greater levels of significance (i.e., sum[-log(p)] ~ 500). When only standardization of features is performed, studies are likely to benefit most by using CPSO for low levels of feature statistical significance and LVQ1 for greater levels of significance. Studies involving only fuzzification of features should employ LVQ1 because of the substantial gain in AUC observed and low expense of LVQ1. Lastly, PSO resulted in significantly greater levels of AUC (89.5% average) when feature standardization and fuzzification were performed. In consideration of the data sets used and factors influencing AUC which were investigated, if low-expense computation is desired then LVQ1 is recommended. However, if computational expense is of less concern, then PSO or CPSO is recommended.
生成了受试者工作特征（ROC）曲线，以获取曲线下分类面积（AUC），该面积是九个大型癌症相关DNA微阵列的特征标准化、模糊化和样本量的函数。所使用的分类器包括k近邻（kNN）、朴素贝叶斯分类器（NBC）、线性判别分析（LDA）、二次判别分析（QDA）、学习向量量化（LVQ1）、逻辑回归（LOG）、多分类逻辑回归（PLOG）、人工神经网络（ANN）、粒子群优化（PSO）、收缩粒子群优化（CPSO）、核回归（RBF）、径向基函数网络（RBFN）、梯度下降支持向量机（SVMGD）和最小二乘支持向量机（SVMLS）。对于每个数据集，针对样本量、特征t检验的总和[-log(p)]的多种组合，在有和没有特征标准化以及有（模糊）和没有（清晰）特征模糊化的情况下确定AUC。总共进行了2,123,530次分类运行。在最大样本量水平下，ANN得出的拟合AUC为90%，而PSO得出的拟合AUC最低，为72.1%。源自4NN的AUC值对样本量的依赖性最大，而PSO的依赖性最小。ANN对基于总和[-log(p)]使用的特征的总统计显著性依赖性最大，而PSO的依赖性最小。特征标准化使PSO的AUC提高了8.1%，使QDA的AUC降低了0.2%，而模糊化使PSO的AUC提高了9.4%，使QDA的AUC降低了3.8%。如果在没有特征标准化和模糊化的计划微阵列实验中确定AUC，那么对于较低水平的特征显著性（即总和[-log(p)]50）使用CPSO，对于较高水平的显著性（即总和[-log(p)]500）使用ANN将最有益。当仅进行特征标准化时，对于低水平的特征统计显著性使用CPSO，对于较高水平的显著性使用LVQ1，研究可能会受益最大。仅涉及特征模糊化的研究应采用LVQ1，因为观察到AUC有显著提高且LVQ1成本较低。最后，当进行特征标准化和模糊化时，PSO得出的AUC水平显著更高（平均89.5%）。考虑到所使用的数据集以及所研究的影响AUC的因素，如果希望进行低成本计算，则推荐使用LVQ1。然而，如果对计算成本不太关注，则推荐使用PSO或CPSO。
