In this work we examine, for the first time, the use of classification algorithms for early-stage tumor detection with an experimental time-domain microwave breast screening system. The experimental system contains a 16-element antenna array, and testing is done on breast phantoms that mimic breast tissue dielectric properties. We obtain experimental data from multiple breast phantoms with two possible tumor locations. In this work, we investigate a method for detecting the tumors within the breast but without the usual complexity inherent to image-generation methods, and confirm its feasibility on experimental data. The proposed method uses machine learning techniques, namely Support Vector Machines (SVM) and Linear Discriminant Analysis (LDA), to determine whether the current breast being scanned is tumor-free. Our results show that both SVM and LDA methods have promise as algorithms supporting early breast cancer microwave screening.