Question

Types of Clusterings. Each of the following parts describes a collection of groups. Describe each of these groups in terms of the characteristics Types of Clusterings. Each of the following parts describes a collection of groups. Describe each of these groups in terms of the characteristics that we applied to sets of clusters. Specifically, classify the groups as to what Types of Clusterings. Each of the following parts describes a collection of groups. Describe each of these groups in terms of the characteristics that we applied to sets of clusters. Specifically, classify the groups as to whether they are her they are that we applied to sets of clusters. Specifically, classify the groups as to whether they are

        - 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

Partitional clustering (or partitioning clustering) are clustering methods used to classify observations, within a data set, into multiple groups based on their similarity.

The Hierarchical clustering [or hierarchical cluster analysis (HCA)] method is an alternative approach to partitional clustering for grouping objects based on their similarity.

Case-1:The objects are the students in a class. There are groups for each official grade students received for the class.

partitional, non-overlapping, crisp, complete.

Here the students will be partitioned into clusters with separate category to each no student having two grades.

Case 2: The objects are cities. There are groups of cities corresponding to various locations, namely, county (local region), state or province, and country.

hierarchical, overlapping, fuzzy, incomplete.

The country will come first, then state and county. Further there will be overlapping and it will be fuzzy as there may not be clearly defined demarcated boundaries. Moreover there may be independent entities hence it is incomplete.

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.

partitional, non-overlapping, crisp, complete.

The students will be classified based on the scores, each student will have a unique score with crisp marks. Moreover all the students will be classified.