CS 422 – Data Mining Homework 1 solved


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1 Recitation Exercises
These excercises are to be found in: Introduction to Data Mining, 2nd
Edition by Pang-Ning Tan, Michael Steinbach, Anuj Karpatne, Vipin Kumar.
1.1 Chapter 1
Exercises: 1
1.2 Chapter 2
Exercises: 2,7,15,16,17,18,19
2 Practicum Problems
These problems will primarily reference the lecture materials and the examples
given in class using Python. It is suggested that a Jupyter/IPython notebook
be used for the programmatic components.
2.1 Problem 1
Load the titanic sample dataset from the Seaborn library into Python using a Pandas dataframe, and visualize the dataset. Create a distribution plot
(histogram) of survival conditional on age and gender – what is the basic relationship between these variables using just visual inspection? Do the results
make sense? Why?
2.2 Problem 2
Load the auto-mpg sample dataset from the UCI Machine Learning Repository
(auto-mpg.data) into Python using a Pandas dataframe. The horsepower
feature has a few missing values with a ? – replace these with a NaN from
NumPy, and calculate summary statistics for each numerical column (Hint:
Use an Imputer from Scikit). Replace the missing values with the overall mean,
median, and mode (Hint: Pandas makes this easy) – and calculate the variance
of the feature. What imputation results in the lowest variance? Why? Is there
a different method of imputing values that would match the distribution more
accurately? Describe your method.
Prof. Panchal:
Wed. 6:45PM-9:35PM
CS 422 – Data Mining Spring 2021:
All Sections
January 31, 2021 Homework 1
February 14, 2021
2.3 Problem 3
Load the iris sample dataset into Python using a Pandas dataframe. Perform
a PCA using the Scikit Decomposition component, and provide the percentage
of variance explained by each of the Principal Components. Compare this to
the percentage of variance explained by each of the original features. What do
you observe?
2.4 Problem 4
Use Matplotlib to plot a projection of each feature onto the 1st Principal Component from the above problem against vs. the original feature itself. Which
pair of features show a closer relationship to PC1 vs. the others? Why? (Hint:
Think in terms of cosine distance/the angle θ). Calculate the correlation coefficient between the pair of features you have selected and their projections onto
PC1 – do the result agree with the visual inspection?
2.5 Problem 5
Calculate the total variance of the original features and the total variance of
the four eigenvectors from the above problem. What can you say about the
corresponding values? If we wished to capture > 95% of the variance of the
original data, how many principal components would we be selecting? How
does this number correspond to the number of dimensions we are reducing our
features to?
Prof. Panchal:
Wed. 6:45PM-9:35PM
CS 422 – Data Mining Spring 2021:
All Sections