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Describe singular value decomposition and principal component analysis. Here is a potentially useful compare and contrast describing the two methods of dimensional reduction. Since we don't have to implement these two components, describing what they are and that we understand them is crucial.

The objective of this part is to understand how PCA works, the connection between SVD and PCA, and the application of PCA to dimensionality reduction. You are required to pick a dataset that’s big and interesting to demonstrate your understanding of PCA. Make sure you give us the background of your data and tell me what you can conclude from the PCA results.

Apart from the wiki, some good places to start would be:

• A tutorial on PCA
• Math stackexchange's intuitive relationship between SVD & PCA
• SVD & PCA - Madsen04

Discuss any insights on the problem and algorithm (efficiency, modularity,
generalizability, stability, etc.).

We're not required to implement these methods ourselves, but can choose from an awesome and convenient, hopefully heavily document, third party library that does it all for us! Some options include:

• LAPACK in particular is supposed to have incredibly high efficiency
• Boost's uBLAS
• Eigen
• redsvd
• Armadillo

I'm sure there are others, but these were the first and most promising search results. From my understanding, most if not all of these build off of BLAS. Though why go lower level when high level already exists?

Theorize how long the implementation of SVD and PCA will take and the expected size reduction, and compare this against the empirical results from the testing metrics. Discuss the differences and create lovely, colorful charts that are not of the type scatterplot.