Model construction

A custom module was built to classify samples using two layers of models: (i) three linear kernel support vector machine (SVM) models: a malignant versus healthy model (MH model), a malignant versus benign model (MB model), and a benign versus healthy model (BH model). Each model searches for a hyperplane with maximal distances from both two pre-defined training classes. Like all linear classifiers, the decision function is presented as fx=wTx+b, where w = [ w₁, w₂, …, w_k ]T is the weight vector and b represents the distance of the hyperplane from the origin. (ii) A multinomial logistic regression model: for each sample, the output from the MH, MB, and BH models was fed into a multinomial logistic regression model to obtain a cancer/benign/healthy assignment as a final prediction. Both layers were trained by the stochastic gradient descent (SGD) algorithm, and the performance of the training set was assessed by iterated 5-fold cross-validation. During the independent validation phase, the model with locked parameters was applied directly to the blind samples and the clinical information was not released until all analyses were completed.