k-d Tree

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Usage notes


In this exercise we build the first branch of a k-d searching tree for the following 6 points in
(We use Maple notation.)

X = [[-4,3],[-2,2],[5,5],[7,3],[4,-4],[5,-6]]







a)

Write a small Maple program in the Maple frontend or in your local Maple to compute the covariance matrix and copy the values of below:
(Write exact values using fractions)

___________________
___________________
___________________
___________________






b)

Using the Maple command Eigenvals compute the eigenvalues of the covariance matrix

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___________________

(To get an example to see how to use Eigenvals type ?Eigenvals in Maple)






c)

Which eigenvalue do we choose to split the points in two groups?











d)

With the command Eigenvals used in b) you can also compute the eigenvectors. Write down the eigenvector corresponding to the eigenvalue chosen in c) normalized to 1 (use exact values; in Maple the square root is computed with the command sqrt(), use it)

___________________ ___________________
or ___________________ ___________________






e)

Now you can write down the equation of the straight line splitting the points. (The splitting line is given by , where is the eigenvector, and is a threshold. Computing is equivalent to finding the median of )

y = ___________________






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