
| Features        | Neural Network   |       |      |      |        |         |         |        |
|-----------------|------------------|-------|------|------|--------|---------|---------|--------|
| Data Set        | Cases            | Class | Cont | Disc | Inputs | Outputs | Hiddens | Epochs |
| breast-cancer-w | 699              | 2     | 9    | -    | 9      | 1       | 5       | 20     |
| credit-a        | 690              | 2     | 6    | 9    | 47     | 1       | 10      | 35     |
| credit-g        | 1000             | 2     | 7    | 13   | 63     | 1       | 10      | 30     |
| diabetes        | 768              | 2     | 9    | -    | 8      | 1       | 5       | 30     |
| glass           | 214              | 6     | 9    | -    | 9      | 6       | 10      | 80     |
| heart-cleveland | 303              | 2     | 8    | 5    | 13     | 1       | 5       | 40     |
| hepatitis       | 155              | 2     | 6    | 13   | 32     | 1       | 10      | 60     |
| house-votes-84  | 435              | 2     | -    | 16   | 16     | 1       | 5       | 40     |
| hypo            | 3772             | 5     | 7    | 22   | 55     | 5       | 15      | 40     |
| ionosphere      | 351              | 2     | 34   | -    | 34     | 1       | 10      | 40     |
| iris            | 159              | 3     | 4    | -    | 4      | 3       | 5       | 80     |
| kr-vs-kp        | 3196             | 2     | -    | 36   | 74     | 1       | 15      | 20     |
| labor           | 57               | 2     | 8    | 8    | 29     | 1       | 10      | 80     |
| letter          | 20000            | 26    | 16   | -    | 16     | 26      | 40      | 30     |
| promoters-936   | 936              | 2     | -    | 57   | 228    | 1       | 20      | 30     |
| ribosome-bind   | 1877             | 2     | -    | 49   | 196    | 1       | 20      | 35     |
| satellite       | 6435             | 6     | 36   | -    | 36     | 6       | 15      | 30     |
| segmentation    | 2310             | 7     | 19   | -    | 19     | 7       | 15      | 20     |
| sick            | 3772             | 2     | 7    | 22   | 55     | 1       | 10      | 40     |
| sonar           | 208              | 2     | 60   | -    | 60     | 1       | 10      | 60     |
| soybean         | 683              | 19    | -    | 35   | 134    | 19      | 25      | 40     |
| splice          | 3190             | 3     | -    | 60   | 240    | 2       | 25      | 30     |
| vehicle         | 846              | 4     | 18   | -    | 18     | 4       | 10      | 40     |

Table 1: Summary of the data sets used in this paper. Shown are **the number of examples in**
the data set; the number of output classes; the number of continuous and discrete input features; the number of input, output, and hidden units used in the neural networks tested; and how many epochs each neural network was **trained.**

## 3.3 Data Set Error Rates

Table 2 shows test-set error rates for the data sets described in Table 1 for five neural network methods and four decision tree methods. (In Tables 4 and 5 we show these error rates as well as the standard deviation for each of these values.) Along with the test-set errors for Bagging, Arcing, and Ada-boosting, we include the test-set **error rate for a single neuralnetwork and a single decision-tree classifier. We also report results for a simple (baseline)**
neural-network ensemble approach - creating an ensemble of **networks where each network** varies only by randomly initializing the weights of the network. We include these results in certain comparisons to demonstrate their similarity to Bagging. One obvious conclusion drawn from the results is that each ensemble method appears to reduce the error rate for almost all of the data sets, and in many cases this reduction is large. In fact, the twotailed sign test indicates that every ensemble method is significantly better than its single