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.

Traditional K$-$means has a number of limitations$,$ such as sensitivity to outliers and difficulty in handling clusters of different sizes and densities, or with non$-$globular shapes. Comment on the ability of fuzzy c$-$means to handle these situations.

Explain the difference between likeliho$$d and probability.