You have a large number of x-ray images of the lung. After some segmenta- tion process, you obtain a distinct feature vector v = {v1, v2, v3 } for each segmented feature that consists of v₁: radiological density; v2: Radiological density variance; v3: outline irregularity. You plan to use k-means cluster- ing to assign each feature to one of the three classes A (alveolar tissue), B (benign nodule), and C (malignant nodule). a. Explain the k-means clustering algorithm in general, and explain how you can make each feature vector v become a member of one class A, B, or C. b. Assume that alveolar tissue has a low radiological density, and nod- ules can be recognized by their higher radiological density. The three classes can be approximately described through Alveolar tissue: Low and fairly homogeneous density, wide spread of irregularity Benign nodules: High density with high density variance, but low shape irregularity • Malignant nodules: High density with high density variance and high shape irregularity In the orthogonal space of {v1, v2, v3 } provided in Figure 6, sketch where you would expect to find most of the members of the three classes (for example, as three clouds). How does this information help you select the initial class centroids? V1A (density) (shape irreg.) V3 (density var.) v2