# Pattern Classification Based on RBF Networks with Self-Constructing Clustering and Hybrid Learning
## 6 Experimental Results
### Experiment 1--Single-Label Data Sets  
In this experiment, we would like to show the performance of single-label classification of different methods. Average accuracy (AACC), macro-averaged recall (MAREC), macro-averaged precision (MAPRE), and macro-averaged F-measure (MAFM) are adopted metrics for performance evaluation [57]. For category \(i\), \(1\leq i\leq m\), let TP\({}_{i}\), FP\({}_{i}\), FN\({}_{i}\), TN\({}_{i}\) are the number of true positives, false positives, and true negatives, respectively. AACC, MAREC, MAPRE, and MAFM are defined as  
\[\text{AACC}=\frac{\sum_{i=1}^{m}\frac{\text{TP}_{i}+\text{TN}_{i}}{\text{TP}_ {i}+\text{TP}_{i}+\text{TN}_{i}+\text{TN}_{i}}}{m}\]  
\[\text{MAREC}=\frac{\sum_{i=1}^{m}\frac{\text{TP}_{i}}{\text{TP}_{i}+\text{TN} _{i}}}{m}\]  
\[\text{MAPRE}=\frac{\sum_{i=1}^{m}\frac{\text{TP}_{i}}{\text{TP}_{i}+\text{TP }_{i}}}{m}\]  
\[\text{MAFM}=\frac{2\text{MAREC}\times\text{MAPRE}}{\text{MAREC}+\text{MAPRE}}\]  
Clearly, higher values of the above metrics indicate a better classification. Several benchmark data sets are used in this experiment. Table 1 lists the characteristics of these data sets. For example, the dataset \"Liver Disorders\" contains 345 patterns, and each patterns has 7 features. There are two categories involved in the dataset. Note that cardinality denotes the average number of categories each pattern belongs to. Since each pattern belongs to one and only one category, the cardinality of the dataset is 1.000. The data sets of Table 1 are taken from the repository of the machine learning database at the University of California at Irvine (UCI) [58]. Tables 2 and 3 shows the testing AACC and MMFM, respectively, obtained by different methods, including LinearSVC [59], SVC-rbf (Support Vector Classifier with RBF kernel), SVM [11], NN (Neural Network) [60], RBF [22], and RBF-ISCC for the data sets in Table 1. SVC-rbf, support vector classification with RBF kernel, is implemented based on _libsvm_[61] and using one-vs.-rest scheme for classification. LinearSVC, Linear support vector classification, is similar to SVC with linear kernel, but implemented in terms of _liblinear_[59] rather than _libsvm_. We also used one-vs.-rest scheme \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Data Set** & **\# Features** & **\# Categories** & **\# Patterns** & **Cardinality** \\ \hline Liver Disorders & 7 & 2 & 345 & 1.000 \\ Heart & 13 & 2 & 270 & 1.000 \\ Ionosphere & 34 & 2 & 351 & 1.000 \\ Sonar & 60 & 2 & 208 & 1.000 \\ Iris & 4 & 3 & 150 & 1.000 \\ Lung Cancer & 56 & 3 & 32 & 1.000 \\ Soybean & 35 & 4 & 47 & 1.000 \\ Glass & 9 & 6 & 214 & 1.000 \\ Ecoli & 8 & 8 & 336 & 1.000 \\ Yeast-SL & 8 & 10 & 1484 & 1.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Single-label data sets for experiments. for classification for LinearSVC. SVM is a support vector machine based on the MATLAB toolbox ([[http://www.mathworks.com](http://www.mathworks.com)]([http://www.mathworks.com](http://www.mathworks.com))). NN is a three-layer neural network, using the hyperbolic tangent sigmoid transfer function (tanh) in the hidden layer. NN optimizes the log-loss function using LBFGS (Limited-memory BFGS) [60], which is a BFGS (Broyden-Fletcher-Goldfarb-Shanno) based optimizer in the family of quasi-Newton methods. The codes of LinearSVC, SVC-rbf, and NN are downloaded from the scikit-learn library ([[http://scikit-learn.org](http://scikit-learn.org)]([http://scikit-learn.org](http://scikit-learn.org))) [62,63]. RBF is a radial basis function network downloaded from the website [[http://neupy.com/apidocs](http://neupy.com/apidocs)]([http://neupy.com/apidocs](http://neupy.com/apidocs)). In the tables, the best performance for each data set is boldfaced. The average matric values obtained by each method are shown in the bottom line of Tables 2 and 3. Note that RBFISCC performs best, having the highest average AACC, 87.72% and the highest average MAFM, 77.96%. In particular, RBF-ISCC gets the highest AACC and MAFM for 8 and 5, respectively, out of 10 data sets.