Principle:Rapidsai Cuml Clustering Algorithm Configuration
| Knowledge Sources | |
|---|---|
| Domains | Machine_Learning, Clustering |
| Last Updated | 2026-02-08 00:00 GMT |
Overview
Clustering algorithm configuration is the process of selecting and parameterizing the appropriate clustering strategy -- centroid-based, density-based, or hierarchical density-based -- to match the geometric and statistical properties of a dataset.
Description
Different clustering algorithms embody fundamentally different assumptions about the structure of data. Proper configuration requires understanding these assumptions and choosing hyperparameters accordingly:
Centroid-Based Clustering (KMeans): Assumes clusters are convex, roughly spherical, and of similar size. The primary hyperparameters are:
- n_clusters (k): The number of clusters to find. Must be specified in advance.
- init: The initialization strategy for centroids (e.g., scalable k-means++, random). Good initialization reduces the risk of convergence to poor local optima.
- n_init: Number of independent runs with different initializations. The run with lowest inertia is selected.
- max_iter: Maximum number of Lloyd's iterations before stopping.
- tol: Convergence tolerance on centroid movement.
Density-Based Clustering (DBSCAN): Assumes clusters are regions of high point density separated by regions of low density. No assumption about cluster shape or count is needed. Key hyperparameters are:
- eps (epsilon): The maximum distance between two points for them to be considered neighbors. This defines the neighborhood radius.
- min_samples: The minimum number of points within eps-distance required for a point to be a core point and form a dense region.
- metric: The distance metric used for neighbor queries (euclidean, cosine, precomputed).
- algorithm: The nearest-neighbor search method (brute force, random ball cover).
Hierarchical Density-Based Clustering (HDBSCAN): Extends DBSCAN by building a hierarchy of clusterings across all density levels, then extracting the most persistent clusters. Key hyperparameters are:
- min_cluster_size: The smallest number of points that can constitute a cluster. Controls the granularity of detected clusters.
- min_samples: Controls how conservative the clustering is; higher values make the algorithm more robust to noise but may merge small clusters.
- cluster_selection_method: Either 'eom' (Excess of Mass) for variable-density clusters or 'leaf' for fine-grained clusters.
- cluster_selection_epsilon: A distance threshold below which clusters are not split, enabling DBSCAN-like behavior at a given scale.
- alpha: A scaling parameter for the mutual reachability distance.
Usage
Algorithm configuration should be performed when:
- Starting a new clustering task and the data geometry is known or hypothesized.
- Tuning hyperparameters after initial exploratory runs.
- Switching between algorithms to compare results (e.g., KMeans for speed vs. HDBSCAN for robustness to noise and varying density).
Theoretical Basis
KMeans Configuration Theory: KMeans minimizes the within-cluster sum of squares (WCSS, also called inertia):
J = sum_{i=1}^{k} sum_{x in C_i} ||x - mu_i||^2
where mu_i is the centroid of cluster C_i. The choice of k directly determines the partitioning granularity. The k-means++ initialization samples initial centroids with probability proportional to squared distance from existing centroids, provably achieving an O(log k) approximation to the optimal WCSS.
DBSCAN Configuration Theory: DBSCAN defines clusters through the concepts of core points, directly reachable points, and density-connected points. A point p is a core point if |N_eps(p)| >= min_samples, where N_eps(p) is the set of points within distance eps of p. The eps parameter acts as a spatial resolution dial: too small and clusters fragment, too large and distinct clusters merge. The min_samples parameter controls noise tolerance.
HDBSCAN Configuration Theory: HDBSCAN constructs a mutual reachability graph where the distance between points x and y is:
d_mreach(x, y) = max(core_dist(x), core_dist(y), d(x, y))
where core_dist(x) is the distance from x to its min_samples-th nearest neighbor. A minimum spanning tree of this graph is built, then a condensed cluster tree is extracted. The cluster_selection_method ('eom' or 'leaf') determines how flat clusters are extracted from the hierarchy.