As the training set size grows, the training examples tend to be more representative of the population of observations in a given domain. Therefore, the default rule accuracy tends to be higher as the training set size grows. For example, on the lenses domain, the default rule accuracy has an obvious increasing trend as the size of training set increases.
However, the training set size is not the only element that influences default rule accuracy. As displayed in Table 5, the default rule accuracy is higher for the 10% sized lenses data than that for the 10% sized iris data, although 10% lenses training set is much smaller than 10% iris data. This is related to the class distribution among the training examples. For the lenses data, most (62.5%) of the included examples are in the ``No Contact Lenses'' class. Since both the training and testing data are taken randomly from the whole data set, the default rule has captured the ``No Contact Lenses'' class and would give correct classification for many of the testing observations. Similarly, for the glass data, the default rule has captured the dominant class (i.e., the ``Window Glass'' class which includes 76.2% of the prelabeled examples) and gives correct classifications for most of the testing observations.
In contrast, for the iris data, the training observations are evenly distributed among the three classes. The default rule only predicts one of the three equiprobable classes. When the testing observations are also evenly distributed among the three classes, the default rule gives roughly 33.3% accuracy. It can be even worse if most of the testing examples are in one of the classes not captured by the default rule. This explains why the default rule performs better for 10% sized lenses data than for 10% sized iris data. A similar observation can be made regarding the soybean domain, where classes are roughly evenly distributed.
From the above analysis, we know that training set size and the class distribution among the training examples influence the default rule coverage and its accuracy. These two elements in turn influence the performance of the learner as a whole.
Jing Lin