Computers in Biology and Medicine 32 (2002) 99–109 www.elsevier.com/locate/compbiomed Perceptron error surface analysis: a case study in breast cancer diagnosis  Mia K. Markey a; b; * , Joseph Y. Lo a; b , Rene Vargas-Voracek b , Georgia D. Tourassi b , Carey E. Floyd Jr. a; b a Department of Biomedical Engineering, Duke University, Durham, NC 27708, USA b Digital Imaging Research Division, Department of Radiology, Duke University, Medical Center, Box 3302, Durham, NC 27710, USA Received 3 August 2001; accepted 30 October 2001 Abstract Perceptrons are typically trained to minimize mean square error (MSE). In computer-aided diagnosis (CAD), model performance is usually evaluated according to other more clinically relevant measures. The purpose of this study was to investigate the relationship between MSE and the area (A z ) under the receiver operating characteristic (ROC) curve and the high-sensitivity partial ROC area ( 0:90 A ′ z ). A perceptron was used to predict lesion malignancy based on two mammographic ndings and patient age. For each performance measure, the error surface in weight space was visualized. Comparison of the surfaces indicated that minimizing MSE tended to maximize A z , but not 0:90 A ′ z . ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Computer-aided diagnosis; Perceptron; Neural network; Breast cancer; Error surface 1. Introduction While mammography is very sensitive at detecting breast cancer, its specicity is low. Only 15 –34% of non-palpable, mammographically suspicious lesions are found to be malignant at biopsy [1,2]. The excessive number of benign breast biopsies raises the overall cost of mammographic screening to society [3] and results in emotional and physical burden to the patients. One goal of  This work was supported in part by USPHS grant number R29-CA75547 awarded by the National Cancer Institute, Whitaker Foundation grant number RG 97-0322, Susan G. Komen Breast Cancer Foundation grant number 9803, and USAMRMC grants number DAMD 17-96-1-6226 and DAMD 17-94-J-4371 awarded by the US Army. * Corresponding author. Department of Radiology, Duke University Medical Center, Box 3302, Durham, NC 27710, USA. Tel.: +1-919-684-7751; fax: +1-919-684-7122. E-mail address: markey@duke.edu (M.K. Markey). 0010-4825/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII:S0010-4825(01)00035-X