Scott asks . . .
Dear Ask a Data Miner,
I am using SPSS Clementine 12. The Neural Network node in Clementine allows users to choose from six different training methods for building neural network models:
• Quick. This method uses rules of thumb and characteristics of the data to choose an appropriate shape (topology) for the network.
• Dynamic. This method creates an initial topology but modifies the topology by adding and/or removing hidden units as training progresses.
• Multiple. This method creates several networks of different topologies (the exact number depends on the training data). These networks are then trained in a pseudo-parallel fashion. At the end of training, the model with the lowest RMS error is presented as the final model.
• Prune. This method starts with a large network and removes (prunes) the weakest units in the hidden and input layers as training proceeds. This method is usually slow, but it often yields better results than other methods.
• RBFN. The radial basis function network (RBFN) uses a technique similar to k-means clustering to partition the data based on values of the target field.
• Exhaustive prune. This method is related to the Prune method. It starts with a large network and prunes the weakest units in the hidden and input layers as training proceeds. With Exhaustive Prune, network training parameters are chosen to ensure a very thorough search of the space of possible models to find the best one. This method is usually the slowest, but it often yields the best results. Note that this method can take a long time to train, especially with large datasets.
Which is your preferred training method? How about for a lot of data - (a high number of cases AND a high number of input variables)? How about for a relatively small amount of data?
Our general attitude with respect to fancy algorithms is that they provide incremental value. However, focusing on data usually provides more scope for improving results. This is particularly true of neural networks, because stable neural networks should have few inputs.
Before addressing your question, there are a few things that you should keep in mind when using neural networks:
(1) Standardize all the inputs (that is, subtract the average and divide by the standard deviation). This puts all numeric inputs into a particular range.
(2) Avoid categorical inputs! These should be replaced by appropriate numeric descriptors. Neural network tools, such as Clementine, handle categorical inputs using something called n-1 coding, which converts one variable into many flag variables, which, in turn, multiplies the number of weights in the network that need to be optimized.
(3) Avoid variables that are highly collinear. These cause "multidimensional ridges" in the space of neural network weights, which can confuse the training algorithms.
To return to your question in more detail. Try out lots of the different approaches to determine which is best! There is no rule that says that you have to decide on one approach initially and stick with it. To test the approaches use a separate partition of the data to see which works best.
For instance, the Quick method is probably very useful in getting results back in a reasonable amount of time. Examine the topology, though, to see if it makes sense (no hidden units or too many hidden units). Most of the others are all about adding or removing units, which can be valuable. However, always test the methods on a test set that is not used for training. The topology of the network may depend on the training set, so that provides an opportunity for overfitting.
These methods are focusing more on the topology than on the input parameters. If the prune method really does remove inputs, then that would be powerful functionality. For the methods that are comparing results, ensure that the results are compared on a validation set, separate from the test set used to calculate the weights. It can be easy to overfit neural networks, particularly as the number of weights increases.
A comment about the radial basis function approach. Make sure that Clementine is using normalized radial basis functions. Standard neural networks use an s-shaped function that starts low and goes high (or vice versa), meaning that the area under the curve is unbounded. RBFs start low, go high, and then go low again, meaning that the area under the curve is finite. Normalizing the RBFs ensures that the basis functions do not get too small.
My personal favorite approach to neural networks these days is to use principal components as inputs into the network. To work effectively, this requires some background in principal components to choose the right number as inputs into the network.