Traumatic brain injury (TBI) is a major public health problem worldwide. Intracranial bleedings represents the most serious complication of TBI and need to be surgically evacuated promptly to save lives and mitigate injury. Microwave technology (MWT) is promising as a complement to computed tomography (CT) to be used in road and air ambulances for early detection of intracranial bleedings. In this study, we perform numerical simulations to investigate if a classification algorithm based on singular value decomposition can distinguish between bleedings at different positions adjacent to the skull bone for a similar but simplified problem. The classification accuracy is 94-100% for all classes, a result that encourages us to pursue our efforts with MWT for more realistic scenarios. This indicates that MWT has potential for localizing a detected bleeding, which would increase the diagnostic value of this technique.