
| Dataset       | #Samples   | stacking   | arcing   | bagging   |
|---------------|------------|------------|----------|-----------|
| Wave form     | 10.2       |            |          |           |
| Glass         | 12.9       |            |          |           |
| Ionosphere    | 1.5        |            |          |           |
| Soybean       | ±1.1       |            |          |           |
| Breast Cancer | 10.8       |            |          |           |
| Diabetes      | 1.2        |            |          |           |

The results on six datasets are given in Table and indicate that the three methods are very competitive 4  Stacking performs better than both arcing and bagging in three datasets Waveform Soybean and Breast Cancer and is better than arcing but worse than bagging in the Diabetes dataset  Note that stacking performs very poorly on Glass and Ionosphere two small real world datasets This is not surprising because cross validation inevitably produces poor estimates for small datasets

## 4.2 Discussion

Like bagging stacking is ideal for parallel computation The construction of ea level model proceeds independently  no communication with the other modeling processes being ncessary Arcing and bagging require a considerable number of member models because they rely on varying the data distribution to get a diverse set of models from a single learning algorithm  Using a level   generalizer  stacking can work with only two or three level models Suppose the computation time required for a learning algorithm is C  and arcing or bagging needs h models The learning time required is T a    hC  Suppose stacking requires g models and each model employs J fold cross validation  Assuming that time C is needed to derive each of the g level   models and the level   model  the learning time for stacking is T s C  For the results given in Table      h g J
and a thus J
C and T s     C  However in practice the learning time required for the level T a and level   generalizers may be different Users of stacking have a free choice of level    models   They may either be derived from a single learning algorithm  or from a variety of different algorithms  The example in Section uses different types of learning algorithms  while bag-stacking  stacking  bagged models Ting Witten uses data variation to obtain a diverse set of models from a single learning algorithm In the former case performance may vary substantially between the level models for example NB performs very poorly in the Vowel and Euthyroid datasets to compared to the other two models  see Table Stacking copes well with this situation The performance variation among the member models in bagging is rather small because they are derived from the same learning algorithm using bootstrap samples  Section