Question

Customer	Age	Female	Income	Married	Children	Loan	Mortgage
A	29	0	12623.4	1	1	1	0
B	25	0	23818.6	1	0	0	0
C	40	1	31473.9	0	2	0	1
D	48	0	20268	1	0	0	0
E	65	0	51417	1	2	0	0
F	59	1	30971.8	1	3	1	1
G	61	1	47025	0	2	1	1
H	30	1	9672.25	1	0	1	0
I	31	1	15976.3	1	0	1	0
J	29	0	14711.8	1	0	0	1

Know Thy Customer (KTC) is a financial consulting company that provides personalized financial advice to its clients. As a basis for developing this tailored advising, KTC would like to segment its customers into several representative groups based on key characteristics. Peyton Blake, the director of KTC’s fledging analytics division, plans to establish the set of representative customer profiles based on 600 customer records in the file KnowThyCustomer. Each customer record contains data on age, gender, annual income, marital status, number of children, whether the customer has a car loan, and whether the customer has a home mortgage. KTC’s market research staff has determined that these seven characteristics should form the basis of the customer clustering.

The data contains both categorical variables (Female, Married, Car, and Mortgage) and numerical variables (Age, Income, and Children).

1. Using matching coefficient to compute dissimilarity between observations (hints: consider only the categorical/binary variables Female, Married, Loan, and Mortgage.)

2. Using hierarchical clustering method in analyzing the selected data set (hints: consider only the numerical variables; normalize the values of variables – calculating z-scores before you conduct the cluster analysis)

3. For the selected data set, apply k-means clustering with using Age, Income, and Children as variables. Normalize the values of the input variables. This will generate a total of two clusters. Describe these two clusters of clients according to their “average” characteristics.

4. For Question 3, set k = 3, i.e., three clusters and rerun the cluster analysis. Compare the clustering results (k = 2 vs. k = 3) and discuss, in your opinion, which method is better while describing customers’ average charteristics and designing marketing segmentation.

5. Applying appropriate data visualization tool(s) while illustrating your analysis results.

Answer 1

Question:

Using hierarchical clustering method in analyzing the selected data set (hints: consider only the numerical variables; normalize the values of variables – calculating z-scores before you conduct the cluster analysis)

Answer:

Cluster Analysis of Observations: Age, Income, Children

Standardized Variables, Euclidean Distance, Complete Linkage

Amalgamation Steps

At each step in the amalgamation process, view the clusters that are formed and examine their similarity and distance levels. The higher the similarity level, the more similar the observations are in each cluster. The lower the distance level, the closer the observations are in each cluster.

Ideally, the clusters should have a relatively high similarity level and a relatively low distance level. However, you must balance that goal with having a reasonable and practical number of clusters.

Key Results: Similarity level, Distance level

In these results, the data contain a total of 10 observations. In step 1, two clusters (observations 9 and 10 in the worksheet) are joined to form a new cluster. This step creates 9 clusters in the data, with a similarity level of 96.1429 and a distance level of 0.15756. Although the similarity level is high and the distance level is low, the number of clusters is too high to be useful. At each subsequent step, as new clusters are formed, the similarity level decreases and the distance level increases. At the final step, all the observations are joined into a single cluster.

Step	Number of clusters	Similarity level	Distance level	Clusters joined	New cluster	Number of obs. in new cluster
1	9	96.1429	0.15756	9	10	9	2
2	8	90.1496	0.40238	5	7	5	2
3	7	89.1278	0.44413	8	9	8	3
4	6	77.8102	0.90645	1	8	1	4
5	5	70.7584	1.19451	1	2	1	5
6	4	62.9473	1.51359	3	6	3	2
7	3	60.7288	1.60422	1	4	1	6
8	2	47.5129	2.14409	3	5	3	4
9	1	0.0000	4.08498	1	3	1	10

Final Partition

	Number of observations	Within cluster sum of squares	Average distance from centroid	Maximum distance from centroid
Cluster1	6	2.66623	0.585548	1.09268
Cluster2	4	3.76429	0.943228	1.24289

Cluster Centroids

Variable	Cluster1	Cluster2	Grand centroid
Age	-0.633492	0.95024	-0.0000000
Income	-0.670189	1.00528	0.0000000
Children	-0.721688	1.08253	0.0000000

Distances Between Cluster Centroids

	Cluster1	Cluster2
Cluster1	0.00000	2.92756
Cluster2	2.92756	0.00000

Dendrogram

In these results, the data contain a total of 10 observations. In step 1, two clusters (observations 9 and 10 in the worksheet) are joined to form a new cluster. This step creates 9 clusters in the data, with a similarity level of 96.1429 and a distance level of 0.15756. Although the similarity level is high and the distance level is low, the number of clusters is too high to be useful. At each subsequent step, as new clusters are formed, the similarity level decreases and the distance level increases. At the final step, all the observations are joined into a single cluster.

Question:

For the selected data set, apply k-means clustering with using Age, Income, and Children as variables. Normalize the values of the input variables. This will generate a total of two clusters. Describe these two clusters of clients according to their “average” characteristics

Answer :

K-means Cluster Analysis: Age, Income, Children

Method

Number of clusters	2
Standardized variables	Yes

Final Partition

	Number of observations	Within cluster sum of squares	Average distance from centroid	Maximum distance from centroid
Cluster1	4	3.764	0.943	1.243
Cluster2	6	2.666	0.586	1.093

Cluster Centroids

Variable	Cluster1	Cluster2	Grand centroid
Age	0.9502	-0.6335	0.0000
Income	1.0053	-0.6702	0.0000
Children	1.0825	-0.7217	0.0000

Distances Between Cluster Centroids

	Cluster1	Cluster2
Cluster1	0.0000	2.9276
Cluster2	2.9276	0.0000

For Question 3, set k = 3, i.e., three clusters and rerun the cluster analysis. Compare the clustering results (k = 2 vs. k = 3) and discuss, in your opinion, which method is better while describing customers’ average charteristics and designing marketing segmentation

K-means Cluster Analysis: Age, Income, Children

Method

Number of clusters	3
Standardized variables	Yes

Final Partition

	Number of observations	Within cluster sum of squares	Average distance from centroid	Maximum distance from centroid
Cluster1	2	0.398	0.446	0.446
Cluster2	4	1.569	0.562	0.970
Cluster3	4	3.764	0.943	1.243

Cluster Centroids

Variable	Cluster1	Cluster2	Cluster3	Grand centroid
Age	-0.7968	-0.5519	0.9502	0.0000
Income	-1.0207	-0.4949	1.0053	0.0000
Children	-0.4330	-0.8660	1.0825	0.0000

Distances Between Cluster Centroids

	Cluster1	Cluster2	Cluster3
Cluster1	0.0000	0.7239	3.0747
Cluster2	0.7239	0.0000	2.8816
Cluster3	3.0747	2.8816	0.0000

Amalgamation Steps

Step	Number of clusters	Similarity level	Distance level	Clusters joined	New cluster	Number of obs. in new cluster
1	9	96.1429	0.15756	9	10	9	2
2	8	90.1496	0.40238	5	7	5	2
3	7	89.1278	0.44413	8	9	8	3
4	6	77.8102	0.90645	1	8	1	4
5	5	70.7584	1.19451	1	2	1	5
6	4	62.9473	1.51359	3	6	3	2
7	3	60.7288	1.60422	1	4	1	6
8	2	47.5129	2.14409	3	5	3	4
9	1	0.0000	4.08498	1	3	1	10

The similarity decreases by more than 13 (from 60.7288 to 47.5129) at steps 7 and 8, when the number of clusters changes from 3 to 2. These results indicate that 3 clusters may be sufficient for the final partition. If this grouping makes intuitive sense, then it is probably a good choice.

This dendrogram was created using a final partition of 3 clusters, which occurs at a similarity level of approximately 60. The first cluster (far left) is composed of two observations (the observations in rows 5 and 7 of the worksheet). The second cluster, directly to the right, is composed of 6 observations (the observations in rows 1,2,4,8,9 and 10 of the worksheet). The third cluster is composed of 2 observations (the observations in rows 3 and 6).If you cut the dendrogram higher, then there would be fewer final clusters, but their similarity level would be lower. If you cut the dendrogram lower, then the similarity level would be higher, but there would be more final clusters.

The method for k=3 is better while describing customers’ average charteristics and designing marketing segmentation.