The SHIP Advantage

Most algorithms run from scratch every time you change a parameter. SHIP is different.

⚡

Instant Re-Clustering

Perform the expensive distance calculation only once to build a similarity tree. After that, finding solutions for any number of clusters (k) or changing objective functions is effectively instantaneous.

🔭

True Exploration

Don't settle for the first result. Effortlessly switch between different mathematical "lenses"—from density-based connectivity to variance-based compactness—to find the structure that matters.

🧩

Unifies Algorithms

SHIP unifies distinct methods. By adjusting the tree type and power parameter, you can replicate the behavior of DBSCAN, k-Means, and Single-Linkage clustering within one consistent framework.

📐

Guaranteed Optimality

Within the constructed ultrametric space, SHIP provides provably optimal solutions for center-based objectives. This removes the approximation errors and initialization bias (like k-Means seeds) found in heuristics.

The 3 Steps of SHIP: Similarity → Hierarchy → Partition

The similarity structure is computed once. A hierarchy is derived from it for the chosen power. A partition is cut from that hierarchy. Only the first step is expensive.

1

Similarity (The Map)

The similarity structure of the data is computed once as a Similarity Tree (an ultrametric). The tree type decides what "similar" means: density connectivity or spatial proximity.

This is the only computationally expensive step. We translate pairwise distances into a hierarchical tree (an Ultrametric). Different tree types capture different aspects of the data: DCTree captures density-connectivity (like DBSCAN), while CoverTree or KDTree capture spatial proximity.

Tree Types determine the "Map"

Select a tree type to see how it connects data points:

DCTree: Builds density-based connections, great for complex shapes.

Key Tree Types

DCTree (Density-Connectivity)

The most powerful option for complex data. It connects points based on local density, unifying concepts from DBSCAN and Spectral Clustering.

CoverTree / BallTree

Spatial partitioning trees. Good for high-dimensional data and identifying compact, spherical clusters.

2

Hierarchy (The Lens)

A cluster hierarchy is derived from the similarity tree for the chosen power (the objective, e.g. k-median at 1, k-means at 2). Changing the power derives a new hierarchy instantly.

From the single Similarity Tree, we can instantly derive different hierarchies by changing the Power Parameter (z). This parameter controls how we penalize distances. Low values prioritize connectivity (chain-like clusters), while high values prioritize compactness (round clusters).

Power Parameter controls Compactness

Adjust the power to change the clustering objective:

2 (Balanced)4 (Tight)6 (Very Tight)
Power = 2: Standard k-Means objective. Balanced compactness.

Objective Functions

Power ≈ 0 (k-Center)

Minimizes the maximum distance. Great for finding connected components and continuous shapes.

Power = 1 (k-Median)

Minimizes the sum of distances. Robust average, less sensitive to outliers than k-means.

Power = 2 (k-Means)

Minimizes squared distances. The standard for finding compact, spherical clusters.

3

Partition (The Solution)

A partition is cut from the hierarchy: pick a number of clusters k, or let a selection criterion (elbow, silhouette, stability, ...) choose the cut.

A hierarchy contains every possible clustering from 1 to N clusters. The Partition step "cuts" this hierarchy. You can cut manually (selecting K) or use smart algorithms that analyze the cost curve to find the mathematical "sweet spot" or the most stable structures.

Smart Partitioning

How do we decide where to cut the tree?

K Method: You specify exactly 3 clusters - direct control.

Partition Strategies

Elbow Method

Automatically finds the "knee" in the cost curve—the point of diminishing returns.

Stability

Finds clusters that persist over a wide range of scales (similar to HDBSCAN). Robust against noise.

Manual K

Precision control. Because SHIP is fast, you can scroll through K=2 to K=50 in seconds to see how the data breaks down.

How to Read an Icicle Plot

Top-Down The top bar is the whole dataset. Lower bars are sub-clusters.
Width = Size The wider the bar, the more data points are in that cluster.
Color Indicates cluster membership in the current partition.
Structure Immediately see if clusters are balanced or if one dominates.

Icicle Plot vs. Dendrogram

The Icicle plot is more space-efficient for showing cluster proportions:

Icicle Plot
Clear view of cluster proportions
Dendrogram
Classic view of merge distances
Compare how the same hierarchical data looks in both visualization types
💡
Pro Tip: Use the Icicle plot to spot imbalanced clustering. If you see one huge bar and many tiny slivers, your algorithm might be chaining noise points instead of finding groups.

Ready to Explore?

Jump right in. No code required.