Bias Learning Rule (learncon) :: Self-Organizing and Learn. Vector Quant. Nets (Neural Network Toolbox)

Neural Network Toolbox

Bias Learning Rule (learncon)

One of the limitations of competitive networks is that some neurons may not always get allocated. In other words, some neuron weight vectors may start out far from any input vectors and never win the competition, no matter how long the training is continued. The result is that their weights do not get to learn and they never win. These unfortunate neurons, referred to as dead neurons, never perform a useful function.

To stop this from happening, biases are used to give neurons that only win the competition rarely (if ever) an advantage over neurons that win often. A positive bias, added to the negative distance, makes a distant neuron more likely to win.

To do this job a running average of neuron outputs is kept. It is equivalent to the percentages of times each output is 1. This average is used to update the biases with the learning function learncon so that the biases of frequently active neurons will get smaller, and biases of infrequently active neurons will get larger.

The learning rates for learncon are typically set an order of magnitude or more smaller than for learnk. Doing this helps make sure that the running average is accurate.

The result is that biases of neurons that haven't responded very frequently will increase versus biases of neurons that have responded frequently. As the biases of infrequently active neurons increase, the input space to which that neuron responds increases. As that input space increases, the infrequently active neuron responds and moves toward more input vectors. Eventually the neuron will respond to an equal number of vectors as other neurons.

This has two good effects. First, if a neuron never wins a competition because its weights are far from any of the input vectors, its bias will eventually get large enough so that it will be able to win. When this happens, it will move toward some group of input vectors. Once the neuron's weights have moved into a group of input vectors and the neuron is winning consistently, its bias will decrease to 0. Thus, the problem of dead neurons is resolved.

The second advantage of biases is that they force each neuron to classify roughly the same percentage of input vectors. Thus, if a region of the input space is associated with a larger number of input vectors than another region, the more densely filled region will attract more neurons and be classified into smaller subsections.

Kohonen Learning Rule (learnk) Training