worksheet_10.ipynb

Kernel: R

Worksheet 10 - Clustering

Lecture and Tutorial Learning Goals:

After completing this week's lecture and tutorial work, you will be able to:

• Describe a case where clustering would be an appropriate tool, and what insight it would bring from the data.

• Explain the k-means clustering algorithm.

• Interpret the output of a k-means cluster analysis.

• Perform k-means clustering in R using k-means

• Visualize the output of k-means clustering in R using a coloured scatter plot

• Identify when it is necessary to scale variables before clustering and do this using R

• Use the elbow method to choose the number of clusters for k-means

• Describe advantages, limitations and assumptions of the kmeans clustering algorithm.

### Run this cell before continuing.
library(tidyverse)
library(forcats)
library(repr)
library(broom)
source('tests_worksheet_10.R')
source("cleanup_worksheet_10.R")

Question 0.0 Multiple Choice:
{points: 1}

In which of the following scenarios would clustering methods likely be appropriate?

A. Identifying sub-groups of houses according to their house type, value, and geographical location

B. Predicting whether a given user will click on an ad on a website

C. Segmenting customers based on their preferences to target advertising

D. Both A. and B.

E. Both A. and C.

Assign your answer to an object called answer0.0. Your answer should be a single upper-case character surrounded by quotes.

# your code here
fail() # No Answer - remove if you provide an answer

test_0.0()

Question 0.1 Multiple Choice:
{points: 1}

Which step in the description of the Kmeans algorithm below is incorrect?

0. Choose the number of clusters

1. Randomly assign each of the points to one of the clusters

2. Calculate the position for the cluster centre (centroid) for each of the clusters (this is the middle of the points in the cluster, as measured by straight-line distance)

3. Re-assign each of the points to the cluster who's centroid is furthest from that point

4. Repeat steps 1 - 2 until the cluster centroids don't change very much between iterations

Assign your answer to an object called answer0.1. Your answer should be a single numerical character surrounded by quotes.

# your code here
fail() # No Answer - remove if you provide an answer

test_0.1()

Hoppy Craft Beer

Craft beer is a strong market in Canada and the US, and is expanding to other countries as well. If you wanted to get into the craft beer brewing market, you might want to better understand the product landscape. One popular craft beer product is hopped craft beer. Breweries create/label many different kinds of hopped craft beer, but how many different kinds of hopped craft beer are there really when you look at the chemical properties instead of the human labels?

We will start to look at the question by looking at a craft beer data set from Kaggle. In this data set, we will use the alcoholic content by volume (abv column) and the International bittering units (ibu column) as variables to try to cluster the beers.

Question 1.0
{points: 1}

Read in the beers.csv data and assign it to an object called beer. The data is located within the worksheet_10/data/ folder.

Assign your dataframe answer to an object called beer.

# your code here
fail() # No Answer - remove if you provide an answer
head(beer)

test_1.0()

Question 1.1
{points: 1}

Let's start by visualizing the variables we are going to use in our cluster analysis as a scatter plot. Put ibu on the horizontal axis, and abv on the vertical axis. Name the plot object beer_eda.

Remember to follow the best visualization practices, including adding human-readable labels to your plot.

# your code here
fail() # No Answer - remove if you provide an answer
beer_eda

test_1.1()

Question 1.2
{points: 1}

We need to clean this data a bit. Specifically, we need to remove the rows where ibu is NA, and select only the columns we are interested in clustering, which are ibu and abv.

Assign your answer to an object named clean_beer.

# your code here
fail() # No Answer - remove if you provide an answer
head(clean_beer)

test_1.2()

Question 1.3.1
{points: 1}

Why do we need to scale the variables when using k-means clustering?

A. k-means uses the Euclidean distance to compute how similar data points are to each cluster centre

B. k-means is an iterative algorithm

C. Some variables might be more important for prediction than others

D. To make sure their mean is 0

Assign your answer to an object named answer1.3.1. Make sure your answer is a single upper-case character surrounded by quotes.

# your code here
fail() # No Answer - remove if you provide an answer

test_1.3.1()

Question 1.3.2
{points: 1}

Let's do that scaling now. Recall that we used the preProcess function for scaling when doing classification and regression. This is because we needed to be able to split train and test data, compute a standardization on just training data, and apply the standardization to both train and test data.

But in clustering, there is no train/test split. So let's use the much simpler scale function in R. scale takes in a column of a dataframe and outputs the standardized version of it. We can therefore apply scale to all variables in the cleaned data frame using the map_df function.

Assign your answer to an object named scaled_beer. Use the scaffolding provided.

# ... <- ... %>% 
#    map_df(...)

# your code here
fail() # No Answer - remove if you provide an answer
head(scaled_beer)

test_1.3.2()

Question 1.4
{points: 1}

From our exploratory data visualization, 2 seems like a reasonable number of clusters. Use the kmeans function with centers = 2 to perform clustering with this choice of K.

Assign your model to an object named beer_cluster_k2. Note that since k-means uses a random initialization, we need to set the seed again; don't change the value!

# DON'T CHANGE THE SEED VALUE!
set.seed(1234)

# ... <- kmeans(..., centers = 2)
# your code here
fail() # No Answer - remove if you provide an answer
beer_cluster_k2

test_1.4()

Question 1.5
{points: 1}

Use the augment function from the broom package to get the cluster assignment for each point in the scaled_beer data frame.

Assign your answer to an object named tidy_beer_cluster_k2.

# ... <- augment(..., ...)
# your code here
fail() # No Answer - remove if you provide an answer
head(tidy_beer_cluster_k2)

test_1.5()

Question 1.6
{points: 1}

Create a scatter plot of abv on the y-axis versus ibu on the x-axis (using the data in tidy_beer_cluster_k2) where the points are labelled by their cluster assignment. Name the plot object tidy_beer_cluster_k2_plot.

# your code here
fail() # No Answer - remove if you provide an answer
tidy_beer_cluster_k2_plot

test_1.6()

Question 1.7.1 Multiple Choice:
{points: 1}

We do not know, however, that two clusters (K = 2) is the best choice for this data set. What can we do to choose the best K?

A. Perform cross-validation for a variety of possible Ks. Choose the one where within-cluster sum of squares distance starts to decrease less.

B. Perform cross-validation for a variety of possible Ks. Choose the one where the within-cluster sum of squares distance starts to decrease more.

C. Perform clustering for a variety of possible Ks. Choose the one where within-cluster sum of squares distance starts to decrease less.

D. Perform clustering for a variety of possible Ks. Choose the one where the within-cluster sum of squares distance starts to decrease more.

Assign your answer to an object called answer1.7.1. Make sure it is a single upper-case character surrounded by quotes.

# your code here
fail() # No Answer - remove if you provide an answer

test_1.7.1()

Question 1.7.2
{points: 1}

Use the glance function from the broom library to get the model-level statistics for the clustering we just performed, including total within-cluster sum of squares.

Assign your answer to an object named beer_cluster_k2_model_stats.

Note: Do not pass tidy_beer_cluster_k2 into the glance function. This will cause the R kernel to crash.

# your code here
fail() # No Answer - remove if you provide an answer
beer_cluster_k2_model_stats

test_1.7.2()

Question 1.8
{points: 1}

Let's now choose the best K for this clustering problem. To do this we need to create a data frame (or a tibble, this time it doesn't matter) with a column named k, where we vary K from 1 to 10.

Assign your answer to an object named beer_ks.

# your code here
fail() # No Answer - remove if you provide an answer
beer_ks

test_1.8()

Question 1.9
{points: 1}

Next we use mutate to create a new column named models, where we use map to apply the kmeans function to our scaled_beer data set for each of the K's.

Assign your answer to an object named beer_clustering.

# ... <- ... %>%
    # mutate(models = map(k, ~kmeans(..., .x)))

# your code here
fail() # No Answer - remove if you provide an answer
glimpse(beer_clustering)

test_1.9()

Question 2.0
{points: 1}

Next we use mutate again to create a new column called model_statistics where we use map to apply the glance function to each of our models (in the models column) to get the model-level statistics (this is where we can get the value for total within sum of squares that we use to choose K).

Assign your answer to an object named beer_model_stats.

# ... <- ... %>% 
    # mutate(... = map(models, ...))

# your code here
fail() # No Answer - remove if you provide an answer
glimpse(beer_model_stats)

test_2.0()

Question 2.1
{points: 1}

Now we use the unnest function to expand the data frames in the model_statistics column so that we can access the values for total within sum of squares as a column.

Assign your answer to an object named beer_clustering_unnested.

# ... <- ... %>% unnest(model_statistics)
# your code here
fail() # No Answer - remove if you provide an answer
glimpse(beer_clustering_unnested)

test_2.1()

Question 2.2
{points: 1}

We now have the the values for total within-cluster sum of squares for each model in a column (tot.withinss). Let's use it to create a line plot of total within-cluster sum of squares versus k, so that we can choose the best number of clusters to use.

Assign your plot to an object called choose_beer_k. Total within-cluster sum of squares should be on the y-axis and K should be on the x-axis. Remember to follow the best visualization practices, including adding human-readable labels to your plot.

# your code here
fail() # No Answer - remove if you provide an answer
choose_beer_k

test_2.2()

Question 2.3
{points: 1}

From the plot above, which K should we choose?

Assign your answer to an object called answer2.3. Make sure your answer is a single numerical character surrounded by quotation marks.

# your code here
fail() # No Answer - remove if you provide an answer

test_2.3()

Question 2.4
(optional - not graded)

In your own words, explain why we chose the K we chose above.

DOUBLE CLICK TO EDIT THIS CELL AND REPLACE THIS TEXT WITH YOUR ANSWER.

Question 2.5
(optional - not graded)

What can we conclude from our analysis? How many different types of hoppy craft beer are there in this data set using the two variables we have? Do you think our analysis might change if we added additional variables? Why/why not?

DOUBLE CLICK TO EDIT THIS CELL AND REPLACE THIS TEXT WITH YOUR ANSWER.

Question 2.6
(optional - not graded)

Visually verify that 2 clusters is the "best" choice for K for this analysis. Do this by plotting the cluster assignments for the points for each K (each should be its own scatter plot).

DOUBLE CLICK TO EDIT THIS CELL AND REPLACE THIS TEXT WITH YOUR ANSWER.