PART $1(25$ points$)$: You will demonstrate the use of Principal Component Analysis $($PCA$)$ on Breast Cancer and CIFAR$-10$ datasets. Your demonstration will include the following tasks:

Task $1$ of Part $1$: Data Visualization

Task $2$ of Part $1$ : Speeding Up a Machine Learning $($ML$)$ Algorithm

PART $2$:

$$ Do the following as a continuation of Task $1$ of Part $1$ given above:

Task $1$ of Part $2(25$ points$)$: Modify your code such that

$$ Case $1$: Number of components will be set to $2$

$$ Case $2$: Number of components will be set to $3$

$$ Case $3$: Number of components will be set to $4$

$$ Case $4$: Number of components will be set to $5$

Repeat Task $1$ of Part $1$ for each case given above.

Task $2$ of Part $2(25$ points$)$: For each case given above in Task $1$ of Part $2,$ plot a bar chart to illustrate explained$\_$variance$\_$ratio so that you can display amount of information or variance each principal component holds. Also, add another bar chart to illustrate what percentage of the information is lost in each case. On this chart, each case will correspond to a separate data point.

$$ Do the following as a continuation of Task $2$ of Part $1$ given above:

Task $3$ of Part $2(25$ points$)$: Modify your code such that

$$ Case $1$: PCA will hold $90\%$ of the variance

$$ Case $2$: PCA will hold $80\%$ of the variance

$$ Case $3$: PCA will hold $70\%$ of the variance

$$ Case $4$: PCA will hold $60\%$ of the variance

$$ Case $5$: PCA will hold $50\%$ of the variance

Plot number of components which correspond to the above cases such that each case will be a data point in your plot.

Repeat Task $2$ of Part $1$ for each case given above.