Perceptron error surface analysis: a case study in breast cancer diagnosis

Area of Science:

• Machine Learning in Medical Imaging
• Computer-Aided Diagnosis (CAD)
• Receiver Operating Characteristic (ROC) Analysis

Background:

• Perceptrons are commonly trained using mean square error (MSE).
• Clinical performance evaluation in computer-aided diagnosis (CAD) often relies on measures beyond MSE.
• The relationship between MSE and clinically relevant performance metrics requires further investigation.

Purpose of the Study:

• To investigate the relationship between mean square error (MSE) and key performance metrics in a perceptron model.
• To compare the impact of minimizing MSE on the area under the ROC curve (A(z)) and the high-sensitivity partial ROC area ((0.90)A'(z)).

Main Methods:

• A perceptron model was developed to predict lesion malignancy.
• Input features included two mammographic findings and patient age.
• Error surfaces in weight space were visualized for MSE, A(z), and (0.90)A'(z) to compare optimization landscapes.

Main Results:

• Minimizing MSE during perceptron training showed a tendency to maximize the area under the ROC curve (A(z)).
• However, minimizing MSE did not consistently maximize the high-sensitivity partial ROC area ((0.90)A'(z)).
• Visualizations revealed different error surface topographies for each performance measure.

Conclusions:

• Standard MSE minimization in perceptron training may not be optimal for all clinical performance measures in CAD.
• Alternative or combined training strategies might be necessary to optimize metrics like high-sensitivity partial ROC area.
• Further research is needed to align model training objectives with specific clinical evaluation criteria for improved CAD systems.