Cluster Analysis: Advanced Concepts and Algorithms

For sparse data, discuss why considering only the presence of non-zero values might give a more accurate view of the objects than considering the actual magnitudes of values. When would such an approach not be desirable?
Describe the change in the time complexity of K-means as the number of clusters to be found increases.
Discuss the advantages and disadvantages of treating clustering as an optimization problem. Among other factors, consider efficiency, non-determinism, and whether an optimization-based approach captures all types of clusterings that are of interest.
What is the time and space complexity of fuzzy c-means? Of SOM? How do these complexities compare to those of K-means?
Explain the difference between likelihood and probability.
Give an example of a set of clusters in which merging based on the closeness of clusters leads to a more natural set of clusters than merging based on the strength of the connection (interconnectedness) of clusters.