Clustering

Comparing Clustering Algorithms

K-Means (Partition Clustering): This algorithm divides data into a pre-specified number of non-overlapping clusters (k). It works by assigning each point to the nearest centroid and then re-calculating the centroid based on the mean of those points. It is fast and efficient but assumes clusters are spherical, requires you to know k in advance, and is highly sensitive to outliers.

Hierarchical Clustering: This method builds a tree of clusters (a dendrogram) either bottom-up (agglomerative) or top-down (divisive). It does not require you to pre-specify the number of clusters, as you can "cut" the tree at any height to form your desired groups. It's great for visualizing data structure but is computationally expensive for very large datasets.

DBSCAN (Density-Based Clustering): Unlike K-Means, DBSCAN groups points based on density (how closely packed they are). It can discover clusters of arbitrary shapes and automatically identifies outliers (noise) rather than forcing them into a cluster. It does not require specifying the number of clusters in advance, but it can struggle with datasets where clusters have varying densities.

Original mixed dataset with labels:

Quantitative-only dataset with labels removed:

After applying PCA to reduce the dataset to 3 dimensions, 97.85% of the original variance was retained. 

The Silhouette Method shows that k=2 yields the highest score (0.575), followed by k=3 (0.496) and k=4 (0.470). So, we will plot k=2, 3, 4 

K-Means applied to k=2, 3, 4. The data points are colored by their true, original labels (Region), while the black 'X' marks the K-Means algorithm's calculated centroids. At k=2, the algorithm broadly separates the successful reformers (Baltics) from the rest of the bloc. 

Hierarchical Clustering using the Ward linkage method. Comparing this to K-Means, the dendrogram confirms the strong grouping of the Baltic states (Estonia, Latvia, Lithuania) which form a distinct, distant branch from the rest of the post-Soviet states. 

DBSCAN results. Because our dataset is small (15 countries) and tightly correlated, DBSCAN groups the majority of the countries into a single main cluster (Cluster 0) and identifies Estonia as an outlier/noise point (-1) due to its uniquely high economic trajectory. This differs from K-Means, which forced Estonia into a defined group. 

Furthermore, the DBSCAN algorithm was particularly insightful. Rather than grouping Estonia with other nations, it flagged Estonia as "noise" (an outlier). In the context of our research, this "noise" actually represents the most successful post-Soviet economic transition, highlighting how Estonia's massive GDP growth broke the standard pattern followed by the other 14 republics.

Conclusions:
Applying clustering algorithms to the economic data of post-Soviet states revealed distinct, naturally occurring geopolitical groups without needing the original labels. The K-Means and Hierarchical clustering clearly isolated the Baltic states (Estonia, Latvia, Lithuania) from the rest of the former Soviet Union. This perfectly aligns with our topic's hypothesis: the Baltics, which aggressively demilitarized and reformed to join Western markets, had an economic trajectory so unique that machine learning algorithms treat them as an entirely separate cluster from Eastern Europe, the Caucasus, and Central Asia.

Link to code used