Data Mining Clustering

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https://www.dropbox.com/s/4oze9kxwbzpgvw8/Clustering_Part1.mp4?dl=0

Watch the video and answer the question.

Imagine a Clustering problem where the educational researchers would like to find clusters of students (group of students) who have similar correlation patterns when it comes to correlation of their GPA vs Income of their parents. And you are hired as the Data Scientist to do this job. 

What kind of Objective Function would you design?

Why?

Please use your own reasoning and explain in details.