L9 Cluster Analysis

Question 1

What is the main difference between factor and cluster analysis?

Answer 1

In the factor analysis we want to find factors of items.
In the cluster analysis we want to find clusters of objects.

Question 2

What is the goal of the cluster analysis?

Answer 2

Find clusters such that within a cluster the objects are as similar as possible (internal homogeneity) while at the same time the clusters are as distinct as possible (external heterogeneity)

Question 3

Two ways of qunatifying similarity

Answer 3

Distance and correlation

Question 4

Two types of distance measure

Answer 4

Euclidean & city-block distance

–> depends on the case which one to use. (On what you define as similar)

Question 5

What is agglomerative hierarchical clustering?

Answer 5

When you create larger and less clusters

Question 6

What is divisive hierarchical clustering?

Answer 6

When you create more and more clusters out of large ones

Question 7

What is the procedure for derving clusters? In the agglomerative hierarchical approach

Answer 7

Starting point: calculate pairwise similarity between objects (based on distance or correlation)
Step1: Merge those objects with highest similarity (P and Q) into a cluster
Step2: Calculate linkage criterion for the new cluster and the other objects (or clusters)
Step3: Merge those objects and cluster that minimize the linkage criterion
Then repeat steps 2&3 until there is a single cluster

Question 8

What does the coefficient measure in the graph?

Answer 8

It measures the heterogeity index. Heterogeneity increases with a larger coefficient.

Question 9

What are three linkage methods?

Answer 9

Single linkage
Complete linkage
Ward’s method

Question 10

What is single linkage?

Answer 10

You find the nearest neighbor

Question 11

What is complete linkage?

Answer 11

You find the farthest neighbor

Question 12

What is Ward’s method?

Answer 12

Minimize total distance (variance) within a considered cluster.
Most reliable method.
You create a centroid which is the mean value of the hypothetical cluster

Question 13

What are 3 indices for model evaluation? (About how many clusters to retain)

Answer 13

• Within-cluster sum of squares (WSS)
• Information criteria:
• Bayesian information criterion (BIC)
• Akaike information criterion (AIC)

Question 14

How can you minimize within cluster sum of squares?

Answer 14

The smallest WSS is always the max # of clusters available

Question 15

What is the advantage of the Information criteria over WSS?

Answer 15

The BIC and AIC are a trade off between model fit and model complexity

Question 16

Why might the scree plot not be suitable in determining the optimal # clusters?

Answer 16

There might not be a clear elbow. Use the Lowest BIC instead.

Question 17

What does the Silhouette coefficient tell you?

Answer 17

Expresses how clearly the clusters are separated. It measures how similar an object is to its own cluster (cohesion) compared to other clusters (separation).

Question 18

From what till what does the Silhouette coefficient range? What does a high score mean?

Answer 18

Ranges from -1 to 1 (a high positive value indicates that the object is well matched to its own cluster and poorly matched to neighboring clusters)

Question 19

What if many points have a low or negative silhouette coefficient?

Answer 19

Then the clustering configuration may have too many or too few clusters.