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CSE4334/5334 Data Mining Assignment 1 solution

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CSE4334/5334 Data Mining Assignment 1

What to turn in:
1. Your submission should include your complete code base in an archive file (zip, tar.gz) and q1/,
q2/, and so on), and a very very clear README describing how to run it.
2. A brief report (typed up, submit as a PDF file, NO handwritten scanned copies) describing what you solved, implemented and known failure cases.
3. Submit your entire code and report to Blackboard.
Notes from instructor:
• Start early!

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CSE4334/5334 Data Mining Assignment 1

What to turn in:
1. Your submission should include your complete code base in an archive file (zip, tar.gz) and q1/,
q2/, and so on), and a very very clear README describing how to run it.
2. A brief report (typed up, submit as a PDF file, NO handwritten scanned copies) describing what you solved, implemented and known failure cases.
3. Submit your entire code and report to Blackboard.
Notes from instructor:
• Start early!
• You may ask the TA or instructor for suggestions, and discuss the problem with others (minimally).
But all parts of the submitted code must be your own.
• Use Matlab or Python for your implementation.
• Make sure that the TA can easily run the code by plugging in our test data.
Problem 1
(k-means, 40pts) Generate 2 sets of 2-D Gaussian random data, each set containing 500 samples using
parameters below.
µ1 = [1, 0], µ2 = [0, 1.5], Σ1 =
?
0.9 0.4
0.4 0.9
?
, Σ2 =
?
0.9 0.4
0.4 0.9
?
(1)
1. (20pts) Write a function cluster = mykmeans(X, k, c) that clusters data X ∈ R
n×p
(n number of
objects and p number of attributes) into k clusters. The c here is the initial centers, although this is
usually not necessary, we will need it to test your function. Terminate the iteration when the `2-norm
between a previous center and an updated center is ≤ 0.001 or the number of iteration reaches 10000.
2. (10pts) Apply your code to the data generated above with k = 2 and initial centers c1 = (10, 10) and
c2 = (−10, −10). In your report, report the centers found for each cluster. How many iterations did it
take? Show a scatter plot of the data and the centers of clusters found.
3. (10pts) Apply your code to the data generated above with k = 4 and initial centers c1 = (10, 10) and
c2 = (−10, −10), c3 = (10, −10) and c4 = (−10, 10). In your report, report the centers found for each
cluster. How many iterations did it take? Show a scatter plot of the data and the centers of clusters
found.
Problem 2
(Non-parameteric density estimation 60pts)
1. (30pts) Write a function [p, x] = mykde(X,h) that performs kernel density estimation on X with
bandwidth h. It should return the estimated density p(x) and its domain x where you estimated the
p(x) for X in 1-D and 2-D.

2. (10pts) Generate N = 1000 Gaussian random data with µ1 = 5 and σ1 = 1. Test your function mykde
on this data with h = {.1, 1, 5, 10}. In your report, report the histogram of X along with the figures of
estimated densities.
3. (10pts) Generate N = 1000 Gaussian random data with µ1 = 5 and σ1 = 1 and another Gaussian
random data with µ2 = 0 and σ2 = 0.2. Test your function mykde on this data with h = {.1, 1, 5, 10}.
In your report, report the histogram of X along with the figures of estimated densities.
4. (10pts) Generate 2 sets of 2-D Gaussian random data with N1 = 500 and N2 = 500 using the following
parameters:
µ1 = [1, 0], µ2 = [0, 1.5], Σ1 =
?
0.9 0.4
0.4 0.9
?
, Σ2 =
?
0.9 0.4
0.4 0.9
?
. (2)
Test your function mykde on this data with h = {.1, 1, 5, 10}. In your report, report figures of estimated
densities.