Big Data Analysis

Academic Year $2023-2024$

We have access to a database on different consumers according to $5$ attributes.

$\backslash$table$[[$Consumer$,\backslash$table$[[$Average$],[$Spending$]],$Revenue,Height,Weight,Age$],[1,100,1500,165,64,22],[2,78,3200,175,70,35],[3,210,2500,167,60,25],[4,50,2000,176,76,57],[5,140,1600,167,65,21],[6,98,2700,178,82,38]]$

Question $1$: Calculate the centroid of these data.

Question $2$: Calculate the Euclidean distance between Consumer $1$ and the centroid.

Question $3$: Calculate the Manhattan distance between Consumer $1$ and the centroid.

Question $4$: Calculate the Euclidean and Manhattan distances between Consumer $4$ and the centroid.

Question $5$: Will you say that Consumer $1$ is better represented by the centroid compared to consumer $4?$

Question $6$: You want to create two clusters on this dataset. The centroid of the first cluster is given by $C1=(80$;$2500$;$170$;$70$;$45).$ The centroid of the second cluster is given by C$2$ ; $2300$; $169$; $65$; $38).$ To which cluster $($C$1$ or C$2)$ consumer $3$ will be affected? Answer using the Euclidean distance.

Question $7$: How would you describe the difference between clusters $1$ and $2?$

Question $8$: How does software usually choose to initialize centroid? Could it be a problem for clustering results $($explain$)?$

Question $9$: Why combining PCA and K$-$means algorithms can increase the quality of the clustering?

Question $10$: Why the combination of PCA and K$-$means improve the visualization of the clustering?

Question $11$: Describe in practice how to combine PCA and K$-$means.

$1$