Chapter 3

1. No; in a convex set, given two points, the segment connecting them always lies inside the set.
2. Considering the radial structure of the dataset, the RBF kernel can generally solve the problem.
3. With ε=1.0, many points are not density-reachable. When the radius of the balls is reduced, we should expect more noisy points.
4. No; k-medoids can employ any metric.
5. No; DBSCAN is not sensitive to the geometry, and can manage any kind of cluster structure.
6. We have shown that the performance of mini-batch K-means is slightly worse than k-means. Therefore, the answer is yes. It's possible to save memory by using a batch algorithm.
7. Considering that the variance of the noise is σ²=0.005 → σ ≈ 0.07, which is about 14 times smaller than the cluster standard deviation, we cannot expect such a large number of new assignments (80%) in a stable clustering...