K-Means clustering is one of the simplest and widely used unsupervised machine learning algorithms. K-means algorithm identifies the k number of centroids and then it will allocate every data point to the nearest cluster while keeping the centroid as small as possible.

Hierarchical clustering treats each data as a singleton cluster and successively merges clusters until all points have been merged into a single remaining cluster. In single link clustering, if dn the distance of the two clusters merged in step n, and G(n) is the graph that links all data points with a distance of at most dn. Then, the clusters after step n are the connected components of G(n).

Now we will look at how descriptive data mining for financial level is carried out. I will be explaining in detail the steps and methods used for both RapidMiner and Pyhton. For descriptive me and my group decided to do clustering by using K-Means and Agglomerative Clustering (Single Link).

Before proceeding to steps on descriptive data mining, I will show the features we used for financial target.

The features selected are Age, Martial status, Level of education, Socio economic, Salary, self-rate health, financial well being and Leveldistress.

Optimal K-value

To find the optimum k value we used three different methods which are Elbow method, Silhouette method and Davies Bouldin method.

Step 1: Select features using this code

x1 = data.iloc[:, [0, 1, 2, 3, 4, 6, 7, 11]].values

Based on the three different methods, we can conclude that the optimum k value is 6. All Elbow method, Silhouette score and Davies Bouldin score show the best k value is 6.

Python

K-Means

Step 1: Import Library

from sklearn.cluster import KMeans

from sklearn.cluster import AgglomerativeClustering

from sklearn.metrics import silhouette_score

from sklearn.metrics import davies_bouldin_score

from numpy import unique

from numpy import where

import matplotlib.pyplot as plt

import seaborn as sns

Step 2: Create six clusters using K-Means

#For this clustering, we choose 6 clusters

#K-Means

kmeans6 = KMeans(n_clusters=6)

y_kmeans6 = kmeans6.fit_predict(x1)

centroids = kmeans6.cluster_centers_

# insert into predicted table

frame = pd.DataFrame(x1)

frame['cluster'] = y_kmeans6

Step 3: Calculate number of values in each cluster

# to calculate how many are in each cluster

frame['cluster'].value_counts()

Below is the result:

3 371

1 339

5 210

4 150

0 115

2 29

Name: cluster, dtype: int64

Step 4: Visualize the cluster

#visualizing clustering

#in this one, each column has the code, for example ,

#we wanted to see realtionship between AGE index 0 and SALARY index 4

plt.figure(figsize=(7, 5))

plt.scatter(x1[:,0], x1[:,4],c=y_kmeans6, cmap='rainbow')

plt.xlabel('AGE')

plt.ylabel('SALARY')

plt.show()

Agglomerative Clustering

Step 1: Import Library

# import hierarchical clustering libraries

from sklearn.cluster import AgglomerativeClustering

Step 2: Create a dendrogram

from scipy.cluster.hierarchy import linkage, dendrogram

#create a dendogram

Z = linkage(x1, 'single')

fig = plt.figure(figsize=(20, 10))

plt.title("Dendrograms (Single-linkage)")

dn = dendrogram(Z)

plt.show()

From the dendrogram, it is unclear to find the k-value since one tree is bigger than the other. Thus, we decided to use k=6 as suggested by Elbow method, Silhouette score and Davies Bouldin score to visualize the clusters later on.

Step 3: Create six cluster for agglomerative clustering

# create clusters

agglo2 = AgglomerativeClustering(n_clusters=6, affinity = 'euclidean', linkage = 'single')

# save clusters for chart

y_agglo2 = agglo2.fit_predict(x1)

The number of cluster is 6. For the affinity or metruc used to computer the linkage, we used euclidean while linkage criterion is set to single.

Step 4: Calculate how many values in each cluster

# insert into predicted table

frame = pd.DataFrame(x1)

frame['cluster'] = y_agglo2

# to calculate how many are in each cluster

frame['cluster'].value_counts()

4 1185

2 14

5 7

1 4

3 2

0 2

Name: cluster, dtype: int64

Step 5: Visualize the clusters

#visualizing clustering

#in this one, each column has the code, for example ,

#we wanted to see realtionship between AGE index 0 and SALARY index 4

plt.figure(figsize=(7, 5))

plt.scatter(x1[:,0], x1[:,4],c=y_agglo2, cmap='rainbow')

plt.xlabel('AGE')

plt.ylabel('SALARY')

plt.show()

RapidMiner

Now we will look at clustering using RapidMiner.

K-Means

Step 1: Retrieve data

The first operator is used to retrieve data that will be used for the clustering.

Step 3: Include the Nominal to Numerical operator

The reason we used this operator is because the data for Leveldistress is nominal so we need to use this operator to convert the nominal data to numerical. After that only we can continue with the clustering since K-Means requires numerical data.

Step 4: Create clusters

To create clusters, we used the Clustering operator (K-Means). The number of clusters was set to 6 since the optimum k-value is 6 after calculating using the three different methods as stated previously which are Elbow method, Silhouette score and Davies Bouldin score. As for measure type, we are using Euclidean.

Step 5: Calculate the performance and visualize the clusters

We used the performance to calculate the clusters performance by using Davies Bouldin Score. The criterion was set to average within centroid since we are doing K-Means and we maximize the result. This is because if we do not maximize the result, the result will be in negative. Since we are going to observe Davies Bouldin Score, we decided to make the result positive. Meanwhile, to visualize the clusters, we used the cluster model visualizer operator.

Agglomerative Clustering

Step 1: Retrieve data

First we retrieved dataset that will be used for this agglomerative clustering by using the Retrieve operator as shown below.

Step 3: Create the clusters

To create the clusters, we are using the Clustering (Agglomerative Clustering) operator. The mode was set to SingleLink since we decided to do single link agglomerative. The measures types was set to MixedMeasures because Leveldistress is nominal and not munerical. Lastly, for measurement we used MixedEuclideanDistance.