1. Prediction of Malignancy of Ovarian Tumors Using Least Squares Support Vector Machines C. Lu 1, T. Van Gestel 1, J. A. K. Suykens 1, S. Van Huffel 1, I. Vergote 2, D. Timmerman 2 1 Department of Electrical Engineering, Katholieke Universiteit Leuven, Leuven, Belgium, 2 Department of Obstetrics and Gynecology, University Hospitals Leuven, Leuven, Belgium Email address: chuan.lu@esat.kuleuven.ac.be Demographic, serum marker, color Doppler imaging and morphologic variables 1. Introduction Ovarian masses is a common problem in gynecology. A reliable test for preoperative discrimination between benign and malignant ovarian tumors is of considerable help for clinicians in choosing appropriate treatments for patients. In this work, we develop and evaluate several LS-SVM models within Bayesian evidence framework, to preoperatively predict malignancy of ovarian tumors. The analysis includes exploratory data analysis, optimal input variable selection, parameter estimation, performance evaluation via Receiver Operating Characteristic (ROC) curve analysis. 2. Methods o: benign case x: malignant case Visualizing the correlation between the variables and the relations between the variables and clusters. Biplot of Ovarian Tumor Data Patient Data Unv. Hospitals Leuven 1994~1999 425 records, 25 features 32% malignant Univariate Analysis Preprocessing Multivariate Analysis PCA, Factor analysis Stepwise logistic regression Model Building Bayesian LS-SVM Classifier (RBF, Linear) Logistic Regression Model Evaluation ROC analysis: AUC Cross validation (Hold out, K-fold CV) Descriptive statistics Histograms Input Selection Data Exploration Model Development Procedure of developing models to predict the malignancy of ovarian tumors Bayesian LS-SVM (RBF, Linear) Forward Selection (Max Evidence) LS-SVM Classifier within Bayesian Evidence Framework Level 1: infer w,b Level 2: Infer hyperparameter Level 3: Compare models Positive definite kernel K(.,.) RBF: Linear: Mercer’s theorem Posterior class probability Model evidence Input variable selection Given a certain type of kernel, Performs forward selection  Initial: 0 variables,  Add: variable which gives the greatest increase in the current model evidence at each iteration.  Stop: when the adding of any remaining variable can no longer increase the model evidence. solved in dual space y(x), p(y=1|x,D,H) D train Bayesian LS-SVM Classifier kernel type (rbf/linear) model evidence x  *,  *,  *,  *, , b initial set of {  j } for rbf kernels trainingtest 10 variables were selected using an RBF kernel. l_ca125, pap, sol, colsc3, bilat, meno, asc, shadows, colsc4, irreg Blackbox of Bayesian LS-SVM Classifier 3. Experimental Results RMI: risk of malignancy index = score morph × score meno × CA125 2) Results from randomized cross-validation (30 runs)  Training set : data from the first treated 265 patients  Test set : data from the latest treated 160 patients 1) Results from Temporal validation -- LSSVMrbf -- LSSVMlin -- LR -- RMI ROC curve on test set Performance on Test set Averaged Performance on 30 runs of validations  randomly separating training set (n=265) and test set (n=160)  Stratified, #malignant : #benign ~ 2:1 for each training and test set.  Repeat 30 times Expected ROC curve on validation Goal:  High sensitivity for malignancy low false positive rate.  Providing probability of malignancy for individuals. 4. Conclusions Within the Bayesian evidence framework, the hyperparameter tuning, input variable selection and computation of posterior class probability can be done in a unified way, without the need of selecting additional validation set. A forward input selection procedure which tries to maximize the model evidence can be used to identify the subset of important variables for model building. LS-SVMs have the potential to give reliable preoperative prediction of malignancy of ovarian tumors. Future work LS-SVMs are blackbox models. Hybrid methodology, e.g. combine the Bayesian network with the learning of LS-SVM, might be promising A larger scale validation is needed.  Conditional class probabilities computed using Gaussian distributions  Posterior class probability  The probability of tumor being malignant p(y=+1|x,D,H) will be used for final classification (by thresholding). References 1. C. Lu, T. Van Gestel, J. A. K. Suykens, S. Van Huffel, I. Vergote, D. Timmerman, Prediction of malignancy of ovarian tumors using Least Squares Support Vector Machines, Artificial Intelligence in Medicine, vol. 28, no. 3, Jul. 2003, pp. 281-306. 2. J.A.K. Suykens, T. Van Gestel, J. De Brabanter, B. De Moor, J. Vandewalle. Least Squares Support Vector Machines. World Scientific, Singapore: 2002.