Lab 06 Problem 1: k-means

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Lab 06
For this homework, provide a single rendered R Markdown file in pdf
format on crowdmark for the problems (you may render the R Markdown
file to html, and then convert the html file to pdf using the print function
on your web browser). Indicate your student number on the markdown file
before the first section header, and make a section for each lettered part
of each problem (i.e., ‘# Problem 1a)’, ‘# Problem 1b)’, ‘# Problem
2a)’ etc.). Provide in the markdown the final version of all of the code you
wrote for this homework, and make sure long lines of code are wrapped in
the rendered pdf. If your Markdown file involves examining a large dataset,
do not print the entire dataset to the markdown file in the steps of your
solution (instead, suppress the output, or only show a small section of the
data as an example). If you do the bonus problem, provide it as a separate
R Markdown file in pdf format on crowdmark.
Problem 1: k-means
a) Write a function called my.dist2. This function should take two data
frames, the first with N rows and the second with K rows. Both of
the data frames should have the same column names (i.e., they should
both be D dimensional). This function should return a matrix with
N rows and K columns such that the i, j-th element is the Euclidean
distance between the i-th row of the first data frame and the j-th row
of the second data frame. (So, this function should operate the same
way as the function dist2 from the package flexclust.)
(2 points)
b) Write your own implementation of the k-means without using any
libraries and without using the R function kmeans, as a function called
my.kmeans. It should work for datasets of arbitrary dimension D, and
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STAT240 Spring 2023 SFU Due March 10th 5PM PST
should return the centroids and the cluster assignments of the last
iteration of the algorithm. You may work from the code from the slides
for Week 08 (but extend from 2 dimensions to arbitrary dimension,
and use your own my.dist2 function). For stopping condition, have
your function take two parameters (in addition to a parameter for the
data): 1) A maximum number of iterations such that if the number
of iterations reaches this maximum number, the iterations stop, 2) A
threshold such that if the all Euclidean distances between the centroids
before an iteration and after an iteration is less than this threshold,
the iterations stop. Set reasonable default values for these parameters.
Provide your code, and write a one paragraph help for your function,
indicating the names of the parameters, and the nature of the return
(4 points)
d) Create a simulated dataset by hand with k`1 clusters using the Calm
Code page (the link is in the Week 08 slides). Set k to be the last digit
of your student number. Run both my.kmeans and kmeans on the
data. Make scatter plots with the results. In at most a few sentences:
Are the results for the two methods the same? Why or why not?
(4 points)
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