Week 13: More advanced Methods - Cluster Analysis

Question 1

What is an exploratory data analysis tool for organizing observed data into meaningful clusters, based on combinations of variables?

Answer 1

Cluster analysis

Question 2

Example of When to look at grouping (cluster) patterns:

Answer 2

1. A PT practitioner would like to group patients according to their attributes in order to better treat them with personalized care plan
2. A PT practitioner would like to classify patients based on their individual health records in order to develop specific management strategies that are appropriate to the patients

Question 3

Hierarchical clustering -

Answer 3

• a set of nested clusters organized using a hierarchical tree
• the clustering is mapped into a hierarchy basing its grouping on the inter-cluster similarities or dissimilarities

Question 4

Non-hierarchical clustering -

Answer 4

• a group of individuals into non-overlapping subsets (clusters) such that each object is in exactly one cluster
• Divide a dataset of n individuals into m clusters

Question 5

What is the most commonly used non-hierarchical technique?

Answer 5

K-mean clustering

Question 6

What are 3 types of clustering techniques?

Answer 6

1. Hierarchical clustering
2. K-mean clustering
3. Two-step clustering

Question 7

Bottom-up or agglomerative hierarchical clustering -

Answer 7

starts with one single piece of datum and then merge it with others to form larger groups

Question 8

Top-down or divisive hierarchical clustering -

Answer 8

starts with all in one group and then partition the data step by step using a flat clustering algorithm

Question 9

Agglomerative hierarchical clustering procedure:

Answer 9

Step 1: Assign each item to a cluster
Step 2: Find the closest (most similar) pair of clusters and merge them into a single cluster, so that now you have one cluster less
Step 3: Compute distances (similarities) between the new cluster and each of the old clusters
Step 4: Repeat steps 2 and 3 until all items are clustered into a single cluster of the original sample size

Question 10

3 Limitations of hierarchical clustering:

1. Arbitrary decisions

Answer 10

• necessary to specify both the distance metric and the linkage criteria without any strong theoretical basis for such decisions

Question 11

3 Limitations of hierarchical clustering:

2. Data types

Answer 11

• works well with continuous data

Question 12

3 Limitations of hierarchical clustering:

3. Misinterpretation of dendrogram

Answer 12

• selecting the number of clusters using dendrogram may mislead

Question 13

K-mean clustering -

Answer 13

clustering algorithm where data is classified into K number of clusters this is the most widely used clustering method each individual data is mapped into the cluster with its nearest mean

Question 14

Procedure for k-mean clustering:

Answer 14

Step 1: Select K points as the initial centroids
Step 2: Assign points to different centroids based on proximity
Step 3: Re-evaluate the centroid of each group
Step 4: Repeat Steps 2 and 3 until the best solutions emerges (the centers are stable)

Question 15

Limitations of k-mean clustering:

Answer 15

• K-mean is subjective
  1. The researcher chooses the number of clusters
  2. More Ks (number of clusters), shorter distance from the centroid
  3. As an extreme scenario:
• When every data point is a centroid, the distance is zero.
• But it is useless
  4. What is the optimal K?

Question 16

What is two-step clustering?

Answer 16

hybrid approach where we run pre-clustering first and then run hierarchical methods (this is why it has this name)

Question 17

What 3 features differentiate two-step clustering from traditional clustering techniques?

Answer 17

1. the ability to create clusters based on both categorical and continuous variables
2. automatic selection of the number of clusters
3. the ability to analyze large data set efficiently

Question 18

Procedure of two-step clustering:

Answer 18

Step 1: A sequential approach is used to pre-cluster the cases by condensing the variables (pre-clustering)
Step 2: The pre-clusters are statistically merged into the desired number of clusters (clustering)

Question 19

What 2 limitations can two-step clustering overcome?

Answer 19

1. It can take both continuous and categorical data
2. There is no need to enter the number of clusters a priority because it uses indexes of fit (AIC or BIC) to compare each cluster solution to determine which number of cluster is best

Question 20

Cluster quality validation index :

Silhouette coefficient -

Answer 20

it measures how well an individual data is clustered and it estimates the average distance between clusters

Question 21

Cluster quality validation index :

Silhouette plot -

Answer 21

it displays a measure of how close each point in one cluster is to points in the neighboring cluster

Question 22

Interpretation with Silhouette coefficient:

Large Silhouette coefficient value of almost 1 -

Answer 22

very well clustered

Question 23

Interpretation with Silhouette coefficient:

negative Silhouette coefficient value -

Answer 23

probably placed in the wrong cluster

Question 24

Interpretation with Silhouette coefficient:

small Silhouette coefficient value of around 0 -

Answer 24

lies between two clusters

Question 25

Silhouette value of 0.5-1 =

Answer 25

Good

Question 26

Silhouette value of .2-.5 =

Answer 26

Fair

Question 27

Silhouette value of -1 to .2 =

Answer 27

Poor

Question 28

application of cluster analysis involves what?

Answer 28

grouping similar cases into homogenous groups (called clusters) when the grouping is not previously known

Question 29

With hierarchical clustering -

Answer 29

the clustering is mapped into a hierarchy basing its grouping on the inter-cluster similarities or dissimilarities

Question 30

With k-mean clustering -

Answer 30

data is classified into K number of clusters mapping each individual data into the cluster with its nearest mean

Question 31

With two-step clustering -

Answer 31

a sequential approach is first used to pre-cluster the cases, and second the pre-clusters are statistically merged into the desired number of clusters

Question 32

Why might Two step clustering may be a better choice over hierarchical or k-mean?

Answer 32

the two step clustering can work with categorical data and it is not bound to an arbitrary choice of the number of clusters