Analysis on the Input Sets

The sets of input patterns that the network separates at the hidden units are determined using the methods descibed above in Section 3.2.3.

We are interested in finding the commonalities that the network recognized to put certain inputs together. For this reason we look for the following features in a given input pattern set:

Unary features

occur when an input has a constant value for all the patterns in the set. In order to observe unary features we display mean values together with the standard deviation of each input in the set.

Binary features

occur when two inputs take same or exactly opposite values for all pattens in the set. In order to observe binary features we display the correlation coefficients of all pairs of inputs in a set.

The above mentioned features are displayed in graph form in a separate display for each set that has been distinguished. The tool AnalyzeInputSets.m   is used in order to generate this display which is described in Section 4.2.3. Each display looks like the Figure 7.

  

Figure 7: Analyzing input sets for the banding analysis.

The display is composed of the following two parts.

1.

The part above gives information about the unary features, i.e. the mean and standard deviation of each input represented with a diamond shape. The x-axis increases with the number of inputs to the network and each diamond has a fixed width. The y-axis stands for the value of the inputs. The vertical position of the middle of a diamond shows the mean value of the corresponding input. The vertical length of the diamond shows the standard deviation of the input.

Therefore if the diamond is slim the mean value is more reliable, e.g. the inputs 1,4 and 5 all have mean value of 1 without any deviation in Figure 7. On the other hands the inputs 2,3 and 6 have large deviations and their mean values are between 0 and 1. We are more interested in crisp mean values centered at the values 0 or 1 for easier interpretation of the input attributes.

2.

The part below gives a correlation matrix showing the correlation coefficients of all pairs of inputs in the network for the specified set of input patterns. The meaning of the color codes used in the matrix has been given at the bottom of the display. Comparing color codes one can see if highly positive or negative correlaions are observed for the set being analyzed.

In the Figure 7 there is a perfect positive correlation for the input pair 6 and 2. The other insignificant correlations exist for pairs (6, 3) and (2, 3).