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CS 3262 - Final Exam - Fall 2023

from google.colab import drive

drive.mount('/content/drive')

Mounted at /content/drive

Welcome to your final exam!

Logistics:

  Open book/open note/no internet

  You are not allowed to discuss the exam with each other

  All questions about the exam will come to me, through email. Do not send any public messages to me, or each other about the exam.

   If there are any clarifications required, I will post them on brightspace and update this document.

A note on the kinds of answers I expect: As is our style on HW and in class, many of these questions are open ended and are not asking you to  repeat what you've read or heard in class. On the contrary, if I read my own words (or a texts) I will mark that down! I expect you to demonstrate your original thoughts. Almost none of these questions require 3-word answers (some do though, those should be clear by the question!).

Having said that, I also don't want you to start just typing out vocabulary words that we've used in class.

Tip: If you feel you can't answer a question, skip it and come back. Sometimes reading the entire thing will help clarify the individual parts. If all else fails, I will award partial credit for effort, and a clear explanation of what you're confused about and why.

Try and explain your confusion!

Changelog

Note: This is version 1, updated on 2023-12-11

   Notebook Setup

# imports

import numpy as np

import matplotlib.pyplot as plt

colors = plt.rcParams["axes.prop_cycle"].by_key()["color"]

import seaborn as sns

import pandas as pd

import sklearn as sk

# styling additions

from IPython.display import HTML

style = '''

<style>

div.info{

padding: 15px;

border: 1px solid transparent;

border-left: 5px solid #dfb5b4;

border-color: transparent;

margin-bottom: 10px;

border-radius: 4px;

background-color: #fcf8e3;

border-color: #faebcc;

}

hr{

border: 1px solid;

border-radius: 5px;

}

</style>'''

HTML(style)

NameError                                 Traceback (most recent call last)

<ipython-input-15-9950d8cf5234> in <cell line: 5>()

3

4 fig,axes = plt.subplots(1,1,dpi=300)

----> 5 clfviz(rf, X, y, ax=axes,

6        # show classification regions not probabilities

7        show=[ 'instances', 'boundaries', 'misclassified'],

NameError: name 'clfviz' is not defined

SEARCH STACK OVERFLOW

#### approach 2:

fig,axes = plt.subplots(1,1,dpi=300)

decision_boundaries(rf, X, y, ax=axes,

# show classification regions not probabilities

show=[ 'instances', 'boundaries', 'misclassified'],

feature_names=[ 'proline', 'flavanoid'])

Double-click (or enter) to edit

  BONUS B1 - PCA

For this bonus problem, run PCA on the full wine dataset we imported above! (meaning you don't have to split your data into trainig and test)

from sklearn.decomposition import PCA

Note: I have intentionally not given you a code example for this problem! Try reading the sklearn documentation and use what we currently know to see how to specify a PCA yourself!

from sklearn.decomposition import PCA

from sklearn.datasets import load_wine

import pandas as pd

wine = load_wine()

X = wine.data

pca = PCA(n_components=2)

X_pca = pca.fit_transform(X)

pca_df = pd.DataFrame(data=X_pca, columns=[ 'PC1', 'PC2'])

print(pca_df)

	PC1	PC2
0	318.562979	21.492131
1	303.097420	-5.364718
2	438.061133	-6.537309
3	733.240139	0.192729
4	-11.571428	18.489995

..               ...            ...

173	-6.980211	-4.541137
174	3.131605	2.335191
175	88.458074	18.776285
176	93.456242	18.670819
177	-186.943190	-0.213331

[178 rows x 2 columns]

  Pause-and-Ponder: Comment below on the quality of the ¦t! How did PCA do on this dataset? Give a good answer here!

PC1 outperforms PC2

  Pause-and-Ponder: Explain what exactly PCA is doing to our dataset. How is it different than linear regression? Comment below!

PCA is a method used to condense the information contained in a dataset with many variables into a smaller set of new variables, known as principal components. These components are ranked such that each subsequent component has the highest possible variance under the

constraint that it is orthogonal to the preceding components.

In contrast to PCA, Linear Regression is a predictive technique that requires both input and output variables. It attempts to predict the value of a dependent variable, based on one or more independent variables, by ¦tting a linear equation to observed data.

Key distinctions between the two methods include:

  PCA operates without guidance from an output variable, aiming to simplify the data structure through variance. It is a technique for feature extraction and dimensionality reduction.

  Linear Regression works under supervision, employing a target output to shape its predictions. It is a method for understanding the relationship between inputs and outputs within the dataset.

  Bonus B2 - KMeans

For this problem run a K-Means on the result of your PCA dimensionality reduced data for the following:

  2 components

  5 components

  10 components

And give the three plots!

Note: I have intentionally not given you a code example for this problem! Try reading the sklearn documentation and use what we currently know to see how to specify a KMeans yourself!

from sklearn.decomposition import PCA

from sklearn.cluster import KMeans

from sklearn.datasets import load_wine

import matplotlib.pyplot as plt

import pandas as pd

# 2 components

wine = load_wine()

X = wine.data

pca_2 = PCA(n_components=2)

X_pca_2 = pca_2.fit_transform(X)

kmeans_2 = KMeans(n_clusters=3, random_state=42)

clusters_2 = kmeans_2.fit_predict(X_pca_2)

plt.figure(figsize=(8, 6))

plt.scatter(X_pca_2[:, 0], X_pca_2[:, 1], c=clusters_2)

plt.title( 'K-Means with 2 PCA Components')

plt.xlabel( 'PC1')

plt.ylabel( 'PC2')

plt.show()