Chapter 5

1. Hard clustering is based on fixed assignments; hence, a sample x_i will always belong to a single cluster. Conversely, soft clustering returns a degree vector whose elements represent the membership level, with respect to each cluster (for example, (0.1, 0.7, 0.05, 0.15)).
2. No; fuzzy c-means is an extension of k-means, and it's not particularly suitable for non-convex geometries. However, the soft assignments allow for evaluating the influence of neighboring clusters.
3. The main assumption is that the dataset has been drawn from a distribution that can be efficiently approximated with the weighted sum of a number of Gaussian distributions.
4. It means that the first model has a number of parameters that is the double of the second one.
5. The second one, because it can achieve the same result with fewer parameters.
6. Because we want to employ such a model for the auto-selection...