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DS 303 Homework 8

Instructions: Homework is to be submitted on Canvas by the deadline stated above. Please
clearly print your name and student ID number on your HW.
Show your work (including calculations) to receive full credit. Please work hard to make your
submission as readable as you possibly can – this means no raw R output or code (unless
it is asked for specifically or needed for clarity).
Code should be submitted with your homework as a separate file (for example, a
.R file, text file, Word file, or .Rmd are all acceptable). You should mark sections of the
code that correspond to different homework problems using comments (e.g. ##### Problem 1
#####).
Problem 1: MNIST handwritten digit database
Load the handwritten digits (MNIST) dataset into R using the R scripts we went over in class.
a. Randomly select 3000 observations from the training set and randomly select 100 observations
from the test set. Implement KNN classification. Report the following:
– Carry out 10-fold cross-validation on the training set to determine the optimal K. Try
K = 1, 5, 7, 9. What is the optimal K?
– Use this optimal K to implement KNN classification on the test set. Report your
confusion matrix and misclassification error rate on the test set.
b. Try to implement LDA on the MNIST dataset. What kind of error message do you obtain? Do
some searching and explain what this error message means. Hint: check var(train$x[,1]).
c. Try to implement multinomial logistic regression on the MNIST dataset. What kind of error
message do you obtain?
d. Discuss how this dataset highlights some of the advantages of using KNN for classification.
Problem 2: Fashion MNIST
Many people consider the handwritten digits database to be far too easy for classifiers these days.
More challenging datasets have appeared as new benchmarks. One example is the fashion MNIST
dataset: https://github.com/zalandoresearch/fashion-mnist. Read up on the documentation for
this dataset. Then, just like we did with the handwritten digits database, download the training
and test set for this data. Load it into R using the same R scripts used in Problem 1.
a. Produce plots of the first 5 observations in the training set. What do you see?
b. Repeat Problem 1(a) for this dataset. How do your confusion matrices and misclassification
error rates compare?
DS 303: Homework 8 1 Fall 2021