What interesting option could I explore to create the tiers within the 3 clusters (e.g. RFM quantile separation, classification algorithms)?
I'm late for this party but after generating synthetic data (with a bit challengeing nature not separted sample groups) with 3 main clusters as OP asked:
- cluster 0,
- cluster 1,
- and cluster 2
Then applying PCA to get the top 2 PCA: PCA Component 1 and PCA Component 2 with the main explained variance of info overall features. 
I have explored 2 proposed or potential solutions for micro clustering desired available main clusters
cluster_to_micro = 0 # Target one of the clusters cluster_to_micro = 1 cluster_to_micro = 2
for proof of concept (PoC) and detail study of sued models performance for micro-clustering of potential sub-clusters. Please see the results:
import numpy as np import pandas as pd import matplotlib.pyplot as plt from sklearn.datasets import make_blobs from sklearn.decomposition import PCA from sklearn.cluster import KMeans from scipy.cluster.hierarchy import linkage, fcluster # Step 1: Generate synthetic data n_customers = 5000 n_features = 30 #X, y_true = make_blobs(n_samples=n_customers, centers=5, n_features=n_features, random_state=42) X, y_true = make_blobs(n_samples=n_customers, centers=5, # 5 centers for clearer substructure n_features=n_features, cluster_std=[2.0, 2.5, 1.5, 1.0, 1.8], # Variable cluster spread random_state=42) df = pd.DataFrame(X, columns=[f"feature_{i}" for i in range(n_features)]) df['TrueCluster'] = y_true # Assign true cluster labels for reference # Step 2: Apply PCA for dimensionality reduction pca = PCA(n_components=2) # Reduce to 2 components for visualization X_pca = pca.fit_transform(X) # Step 3: Apply KMeans to identify initial clusters kmeans = KMeans(n_clusters=3, random_state=42) # 3 clusters at the top level cluster_labels = kmeans.fit_predict(X_pca) df['predicted_Cluster'] = cluster_labels # Avoid data leakage by using a separate name def visualize_micro_clustering(cluster_to_micro, X_pca, cluster_labels, df): # Focus on the target cluster (drop 'predicted_Cluster' for computations) target_cluster_data = df[df['predicted_Cluster'] == cluster_to_micro].drop(columns=['predicted_Cluster']) # Apply PCA to target cluster # Instead of dropping rows with NaNs, Impute NaNs with column means or 0 before applying PCA # target_cluster_pca = PCA(n_components=2).fit_transform(target_cluster_data.iloc[:, :-1].dropna()) # Drop rows with NaNs # Explicitly handle NaNs (replace with 0 in this example) target_cluster_data_imputed = target_cluster_data.iloc[:, :-1].fillna(0) target_cluster_pca = PCA(n_components=2).fit_transform(target_cluster_data_imputed) # Apply KMeans for micro-clustering kmeans_micro = KMeans(n_clusters=2, random_state=42) df.loc[df['predicted_Cluster'] == cluster_to_micro, 'KMeansCluster'] = kmeans_micro.fit_predict(target_cluster_pca) # Apply Hierarchical clustering for micro-clustering linkage_matrix = linkage(target_cluster_pca, method='ward') df.loc[df['predicted_Cluster'] == cluster_to_micro, 'HierarchicalCluster'] = fcluster(linkage_matrix, t=2, criterion='maxclust') # Visualization plt.figure(figsize=(18, 6)) # Main data clustering plt.subplot(1, 3, 1) main_colors = ['red', 'blue', 'green'] for main_cluster in range(3): main_subset = X_pca[cluster_labels == main_cluster] plt.scatter(main_subset[:, 0], main_subset[:, 1], alpha=0.6, label=f"Main Cluster {main_cluster}", color=main_colors[main_cluster]) plt.title(f"Main Data Clustering (KMeans)") plt.xlabel("PCA Component 1") plt.ylabel("PCA Component 2") plt.legend() # KMeans-based micro-clustering in target cluster plt.subplot(1, 3, 2) kmeans_colors = ['orange', 'purple'] for kmeans_cluster in [0, 1]: kmeans_subset = target_cluster_pca[df.loc[df['predicted_Cluster'] == cluster_to_micro, 'KMeansCluster'] == kmeans_cluster] plt.scatter(kmeans_subset[:, 0], kmeans_subset[:, 1], alpha=0.6, label=f"KMeans Micro-Cluster {kmeans_cluster}", color=kmeans_colors[kmeans_cluster]) plt.title(f"KMeans Micro-Clustering in Target Cluster {cluster_to_micro} (PCA)") plt.xlabel("PCA Component 1") plt.ylabel("PCA Component 2") plt.legend() # Hierarchical-based micro-clustering in target cluster plt.subplot(1, 3, 3) hierarchical_colors = ['cyan', 'magenta'] for hierarchical_cluster in [1, 2]: hierarchical_subset = target_cluster_pca[df.loc[df['predicted_Cluster'] == cluster_to_micro, 'HierarchicalCluster'] == hierarchical_cluster] plt.scatter(hierarchical_subset[:, 0], hierarchical_subset[:, 1], alpha=0.6, label=f"Hierarchical Micro-Cluster {hierarchical_cluster}", color=hierarchical_colors[hierarchical_cluster - 1]) plt.title(f"Hierarchical Micro-Clustering in Target Cluster {cluster_to_micro} (PCA)") plt.xlabel("PCA Component 1") plt.ylabel("PCA Component 2") plt.legend() plt.tight_layout() plt.show() # Generate visualizations for all three clusters for cluster_to_micro in [0, 1, 2]: visualize_micro_clustering(cluster_to_micro, X_pca, cluster_labels, df)
later you can apply from sklearn.metrics import silhouette_score, calinski_harabasz_score, davies_bouldin_score which performance was better to micro-cluster of potential sub-clusters witin main clusters better:
- sub-cluster 0
- sub-cluster 1
Hope this answer provides you possible options for your real data.
