Observations

The purpose of a back propagation training algorithm is for the neural network to determine the importance of given inputs without interference from the programmer. Interestingly enough, every neural network found a significant degree of relevance to each attribute. Each network learned a little differently, just as every human learns differently but an underlying theme of taking all input into account emerged. Below is a sample graph of weightings from a commercial network trial:

Input Description
 Clump Thickness Assesses if cells are mono- or multi-layered.
 Uniformity of Cell Size Evaluates the consistency in size of the cells in the sample.
 Uniformity of Cell Shape Estimates the equality of cell shapes and identifies marginal variances.
 Marginal Adhesion Quantifies how much cells on the outdside of the epithelial tend to stick together.
 Single Epithelial Cell Size Relates to cell uniformity, determines if epithelial cells are significantly enlarged.
 Bare Nuclei Calculates the proportion of the number of cells not surrounded by cytoplasm to those that are.
 Bland Chromatin  Rates the uniform "texture" of the nucleus in a range from fine to coarse.
 Normal Nucleoli Determines whether the nucleoli are small and barely visible or larger, more visible, and more plentiful.
 Mitoses Describes the level of mitotic (cell reproduction) activity.

Below is a sample graph of the neural learning pattern. Neural networks learn just like humans. Therefore, at first the programs act like elementary school kids trying to diagnose breast cancer—they get almost all of the detections incorrect. As the neural networks run through training examples, they begin to detect patterns. By the end of training, the neural network is a seasoned physician and usually diagnoses over 90% of the tumors correctly.


A key decision point for whether this network is viable is what its optimal success could be.  When all samples were included, the network achieves 100% predictive success, demonstrating the network could adjust to handle the complexity of information and outliers if it had full data.  With trials run across multiple test sample sizes, the pattern is clearly observed in the following chart.  Success rate is trending up and the inconclusive rate trends down as you increase the sample size.  Please note the scale of this chart suggests the increase is tenths of a percent for the last 300 samples; however, the trend is clear and those tenths of a percent could correctly diagnose 2 extra people for every 1,000 that are tested.


One anomaly in the chart is that the success rate actually increases early in the cycle before decreasing.  After careful analysis, it was determined that this was caused because the inconclusive rate was so high.  In essence, the network was able to predict the obvious choices and simply identified everything else as inconclusive.  The test really wouldn't be useful if 20% of the population returned inconclusive results.