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1) You have a sample of 100 rocks and for each you are measuring different characteristic...

1) You have a sample of 100 rocks and for each you are measuring different characteristic y (e.g. mass, volume, mineral composition, compressibility, etc). Overall there are 20 different characteristics that you measure.

a) How will you determine what characteristics actually matter for your sample (you care about those that provide most of information about the sample)?

b) Show the input matrix (data) you would use for PCA and show how to calculate the covariance matrix C. c

) What is the dimension (number of elements) of each eigenvector and what is the total number of modes you would get by PCA?

d) How would you decide on how many modes to keep?

f) How many rows and column does the score (PC) matrix have?

e) How would you determine what is the most 'generic' rock in your sample?

math   Statistics-And-Probability   
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