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Manifold Explorer

Interactive dimensionality reduction — watch PCA, t-SNE & UMAP unfold step by step

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Numeric columns will be used as features. The last non-numeric column will be used as labels.

Data Preview

Select or upload a dataset to begin exploring.

PCA Controls

1 Center
2 Covariance
3 Eigenvectors
4 Project
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PCA Projection

PCA finds the directions of maximum variance in your data. Each step reveals a principal component — an axis along which data varies the most.

t-SNE Controls

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How t-SNE Works

t-SNE models pairwise similarities as probabilities. In high-D, nearby points have high probability; far points have low. It then arranges points in 2D to match these probabilities, using gradient descent to minimize their divergence.

t-SNE Embedding

UMAP Controls

15
0.10
300
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How UMAP Works

UMAP builds a fuzzy topological representation of data in high dimensions, then optimizes a low-dimensional layout to have the closest possible equivalent fuzzy structure. It preserves both local and global structure.

UMAP Embedding

Does My Data Live on a Manifold?

Run automated diagnostics to determine whether dimensionality reduction is appropriate for your dataset.

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The Manifold Hypothesis & Complexity Economics

Connecting dimensionality reduction to Eric Beinhocker's The Origin of Wealth complexity economics framework.

Core insight: Just as high-dimensional data often lies on a lower-dimensional manifold, market dynamics and strategic options — seemingly infinite — often inhabit a lower-dimensional "strategy space" shaped by a few key driving forces.
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Fitness Landscapes

Beinhocker describes businesses navigating rugged fitness landscapes. Dimensionality reduction reveals the true dimensionality of your competitive landscape — how many independent factors actually drive success. If PCA shows 90% variance in 2-3 components, your strategic space is simpler than it appears.

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Deductive Tinkering

Rather than predicting the future, Beinhocker advocates exploring the adjacent possible through many small experiments. Manifold structure tells you where to tinker: along the manifold surface where variation matters, not orthogonal to it where changes are noise.

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Business Plan Populations

In complexity economics, firms maintain populations of business plans competing for resources. t-SNE/UMAP reveal the clusters and gaps in your strategy portfolio — are your plans diverse enough to cover the landscape, or dangerously concentrated?

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When Reduction Works

If your data lives on a manifold, it means latent structure governs apparent complexity. For business: customer segments, market dynamics, and operational metrics that look independent may be driven by a few hidden factors. Finding them is the key to strategy.

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When Reduction Fails

If the diagnostic says “no manifold,” your domain may be genuinely high-dimensional — like early-stage markets with no established structure. In Beinhocker's terms, the fitness landscape is so rugged that no simple map captures it. You need more data or a different framing.

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Practical Application

Step 1: Gather your key business metrics (customer data, operational KPIs, market signals).
Step 2: Run them through this explorer.
Step 3: If a manifold exists, the principal components ARE your strategic dimensions.
Step 4: Use cluster structure to identify strategic positions and white space.

Your Data & Strategy

Load a dataset and run the diagnostic to see strategy insights tailored to your data.