Data Clustering

Question 1

What is K-means Clustering?

Answer 1

When we seek to partition observations into a pre-specified number of clusters

Question 2

What does good K-means clustering look like?

Answer 2

When the observations are partitioned enough to which the total within-cluster variation, summed over all the K-clusters is as small as possible

Question 3

How do we define the total within-cluster variation?

Answer 3

The sum of all the pairwise squared Euclidian distances between the observations in the kth cluster divided by the total number of observations in the kth cluster

Question 4

What is Hierarchical Clustering?

Answer 4

When we don’t know in advance how many clusters we want, so we end up in a tree-like figure called a dendrogram, allowing us to view at once the clustering obtained for each possible number of clusters, from 1 to “n”

Question 5

What is a dendrogram?

Answer 5

Starts from leaves and combine clusters up to trunk

Question 6

What does each leaf in a dendrogram represent?

Answer 6

One of the observations

Question 7

What does the height of a fusion of two observations indicate?

Answer 7

The dissimilarity between two observations

Question 8

Will observations fused at the bottom be similar or different?

Answer 8

Similar

Question 9

Will observations fused at the top be similar or different?

Answer 9

Different

Question 10

What does the height of the whole dendrogram represent?

Answer 10

The height of the dendrogram represents the number of clusters possible

Question 11

What does the cut in the dendrogram represent?

Answer 11

The number of clusters chosen

Question 12

What is correlation-based distance?

Answer 12

Two observations to be similar if their features are highly correlated even though their Euclidean distance could be far apart. Focuses on the shapes of the observation profiles rather than the magnitudes.

Question 13

When can hierarchical clustering be worse than K-means?

Answer 13

When the true number of clusters is not nested within each other all the time, which if we go by the assumption that it is, we can yield unrealistic and inaccurate results

Question 14

Difference between K-means and hierarchical clustering?

Answer 14

We have a pre-specified number of clusters for K-means, but for hierarchical we must create a dendrogram to figure out how many clusters we want

Question 15

Steps of K-means Clustering Algorithm:

Answer 15

1. Randomly assign a number, from 1 to K, to each of the observations. These serve as initial cluster assignments
2. Iterate until the cluster assignments stop changing
   - For each of the K clusters, compute the cluster centroid
   - Assign each observation to the cluster whose centroid is the closest (where closest is defined using Euclidian distance)

Question 16

What is the purpose of the elbow method and how do we identify?

Answer 16

To determine the optimal number of clusters based on the sum of squares of many random clusters and we identify by picking the the major change in slope.

Question 17

Difference between a dendrogram and decision tree

Answer 17

Dendrograms are unsupervised while decision trees are supervised

Question 18

What is complete linkage?

Answer 18

Shows maximal inter-cluster dissimilarity, so we compute all the pairwise dissimilarities between observations in all the clusters and record the largest of these similarities

Question 19

What is single linkage?

Answer 19

Shows minimal inter-cluster dissimilarity, so we compute all the pairwise dissimilarities between observations in all the clusters and record the smallest of these similarities

Question 20

What is average linkage?

Answer 20

Shows mean inter-cluster dissimilarity, so we compute all the pairwise dissimilarities between observations in all the clusters and record the average of these similarities

Question 21

What is centroid linkage?

Answer 21

Dissimilarity between centroids for each cluster

Question 22

What two linkages are the most preferred and why?

Answer 22

Complete and average linkage because they yield more balanced dendrograms

Question 23

What two linkages are the least preferred and why?

Answer 23

• Single because it can result in extended trailing clusters in which single observations are fused one at a time
• Centroid because it can result in undesirable inversions which means the two clusters are fused at a height below either of the individual clusters in the dendrogram

Question 24

Describe the 3 main decisions that need to be made when performing hierarchical clustering:

Answer 24

• The dissimilarity measure being used to determine the dissimilarity between observations
• The linkage being used to expand the application of dissimilarity from individual observations to clusters of them
• Placement of the horizontal cut in the dendrogram to determine the number of clusters

Question 25

Why is scaling important?

Answer 25

When looking at observations, there might be one variable that’s having more of an effect than the other which can make the EDA less informative overall, so we need to scale each variable by its standard deviation to minimize the dissimilarities and make sure each variable has equal value and not a skewed effect on the data

Question 26

Why are clustering methods not the most appropriate?

Answer 26

Does not consider or adjust for the presence of outliers so clusters may be heavily distorted

Question 27

What are two ways of using clustering right?

Answer 27

- Perform clustering with a different set of parameters, to track what patterns constantly emerge - Cluster subsets of the data to get a sense of robustness of the clusters obtained