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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
Machine Learning: unsupervised classifiers
for a divorce dataset
Paula Robles López
Universidad Politécnica de Madrid (UPM)
7-12-2022
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 1 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
1 Introduction
2 Hierarchical clustering
3 Nonhierarchical clustering
4 Feature importances
5 External validation
6 Conclusions
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 2 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
1 Introduction
2 Hierarchical clustering
3 Nonhierarchical clustering
4 Feature importances
5 External validation
6 Conclusions
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 3 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
Problem overview:
1 Goal: to group the data observations into k clusters
according to their similarities
2 Data for 84 divorced and 86 married people from Turkey.
Balanced classes. "UNKNOWN
3 54 ordinal features and 170 total records.
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 4 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
PCA
We will be performing a PCA for a better cluster visualization:
→ 170 objects in a 54-dimensional space
→ Dimensionality reduction to a 2-dimensional space
→ The PCs explain +80% of the initial data variance
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 5 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
PCA
Our first step, 170 data points projected onto the first two PC:
" We do not know the real labels, we have no prior knowledge
of the groupings.
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 6 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
1 Introduction
2 Hierarchical clustering
3 Nonhierarchical clustering
4 Feature importances
5 External validation
6 Conclusions
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 7 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
We will be performing agglomerative clustering, but first we need
to find the k value.
→ We need internal validation measures like a dendrogram of the
tree-like groupings according to the clustering.
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 8 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
→ We also have the silhoutte scores.
k = 2, silhouette score = 0.809
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 9 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
k = 3, silhouette score = 0.726
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 10 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
k = 4, silhouette score = 0.479
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 11 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
k = 2 is the optimal number of cluster according to the silhouette
scores!
→ The Calinski index also says so.
Higher values → the clusters are dense and well separated
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 12 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
Clustering results!
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 13 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
1 Introduction
2 Hierarchical clustering
3 Nonhierarchical clustering
Partitional clustering
Probabilistic clustering
4 Feature importances
5 External validation
6 Conclusions
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 14 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
1 Introduction
2 Hierarchical clustering
3 Nonhierarchical clustering
Partitional clustering
Probabilistic clustering
4 Feature importances
5 External validation
6 Conclusions
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 15 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
We will be performing K-Means clustering, but first we need to
find the k value.
→ We need internal validation measures like the elbow method of
the SSE against the number of clusters.
k = 2 is the elbow point.
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 16 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
→ We also have the silhoutte scores.
k = 2, silhouette score = 0.809
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 17 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
k = 3, silhouette score = 0.724
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 18 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
k = 4, silhouette score = 0.493
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 19 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
k = 2 is the optimal number of cluster according to the silhouette
scores!
→ The Calinski index also says so.
Higher values → the clusters are dense and well separated
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 20 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
Clustering results!
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 21 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
1 Introduction
2 Hierarchical clustering
3 Nonhierarchical clustering
Partitional clustering
Probabilistic clustering
4 Feature importances
5 External validation
6 Conclusions
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 22 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
We will be performing Gaussian Mixture clustering, but first we
need to find the k value.
→ We need internal validation measures like the BIC score to
choose the best fitting model among the candidates.
k = 3 is the lowest point.
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 23 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
→ We also have the silhoutte scores.
k = 2, silhouette score = 0.809
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 24 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
k = 3, silhouette score = 0.715
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 25 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
k = 4, silhouette score = 0.466
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 26 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
. .. .. .
Conclusions
k = 2 is the optimal number of cluster according to the silhouette
scores!
→ The Calinski index also says so.
Higher values → the clusters are dense and well separated
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 27 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
Clustering results!
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 28 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
1 Introduction
2 Hierarchical clustering
3 Nonhierarchical clustering
4 Feature importances
5 External validation
6 Conclusions
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 29 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
We can use the Random Forest classifier to know more about
the clustering.
→ New categorical variable: the K-Means cluster assignation.
→ We compute this variable as the class label.
→ We train a Random Forest classifier and extract the most
important features.
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 30 / 36

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Introduction
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Hierarchical clustering
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
→ Shared values, overall happiness and knowledge about the
partner’s inner and outer world.
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 31 / 36

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Introduction
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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
1 Introduction
2 Hierarchical clustering
3 Nonhierarchical clustering
4 Feature importances
5 External validation
6 Conclusions
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 32 / 36

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External validation
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Conclusions
External information can be used to validate the clusterings. Here,
we use the class label to calculate how similar our cluster results
are to reality.
→ For this: Adjusted Rand Index (ARI).
Close to one → almost perfect match!
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 33 / 36

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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
1 Introduction
2 Hierarchical clustering
3 Nonhierarchical clustering
4 Feature importances
5 External validation
6 Conclusions
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 34 / 36

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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
Conclusions:
1 The silhouette plots and the Calinski index suggest k = 2 for
all the clusterings.
2 All the clustering methods give the same output → our results
are reasonably reliable.
3 We can use PCA to improve efficiency and get equally good
clustering results!
4 The feature importances extraction proves that there are more
core-like issues and fundamental incompantibilities than
expected, which could be related to the data source (Turkey).
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 35 / 36

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Nonhierarchical clustering
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Feature importances
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External validation
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Conclusions
Thank you.
Paula Robles López Universidad Politécnica de Madrid (UPM)
Machine Learning: unsupervised classifiers 36 / 36