Question

- hierarchical or partitional - overlapping or non-overlapping - fuzzy or crisp - complete or incomplete Note: Each part should be labeled with four characteristics, e.g., partitional, overlapping, crisp, and incomplete. Also, if you feel there may be some ambiguity about what characteristics a grouping has, provide a short justification of your answer. Case 1: The objects are the students in a class. There are groups for each official grade students received for the class. Case 2: The objects are cities. There are groups of cities corresponding to various locations, namely, county (local region), state or province, and country. Case 3: The objects are the applicants to a college. Each applicant is assigned a score from 0 to 10 indicating the likelihood/desirability of their admission. Even before any decisions have been made, the admissions personnel view the students as belonging to two groups: those that will be accepted and those that will be rejected.

Answer 1

In Case 1: K- Means Clustering can be done in this case.

In Case 2: Given that objects are cities, I think hierarchical clustering  can be used since clusters can be made based on the locations distance.

In Case 3: Roughly the idea is division of students into two sets and definitely according to the question a student whose application is accepted will fall in one group(accepted) and the others in another group. Clearly a student cannot fall in both the groups. So overlapping is not possible. Since Partitional clustering is all about division of set of data objects into non-overlapping subsets. So I think this is apt.