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Many dimensionality reduction algorithms share a few central principles. 1. Construct a graph that captures the data's local structure 2. Measure "geodesic" distances between points using the graph 3. Project the points to a lower dimension while preserving these distances

Alec Helbling

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88,874 Aufrufe • vor 9 Monaten •via X (Twitter)

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Laplacian eigenmaps perform non-linear dimensionality reduction ("manifold learning") by embedding data points using the eigenvectors of a graph Laplacian as coordinates.

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Oldies but goldies: M. Belkin, P. Niyogi, Laplacian Eigenmaps for Dimensionality Reduction and Data Representation, 2003. Non-linear dimensionality reduction by embedding data points using the eigenvectors of a graph Laplacian as coordinates.

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I wrote this fun interactive article explaining Isomap, a classic non-linear dimensionality reduction technique. Isomap captures the local similarity structure of data through a graph and computes an embedding that preserves this structure. Check it out! Link below.

I wrote this fun interactive article explaining Isomap, a classic non-linear dimensionality reduction technique. Isomap captures the local similarity structure of data through a graph and computes an embedding that preserves this structure. Check it out! Link below.

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In the data manifold, the shortest path between two points is a geodesic that pass through high density regions of data. Just like mass curves the space geometry, data also curves the space. In the example below we can see a geodesic being optimized between two points. 1/3

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A TEAM JUST DEPLOYED 15 AUTONOMOUS LOOP AGENTS FROM A SINGLE PROMPT USING APPLIED GRAPH ENGINEERING Most developers still manually hardcode multi agent systems, writing separate logic for every individual task. Graph engineering changes this by using a central topological map to spin up all 15 nodes simultaneously. A single 200 word input generates the architecture, routing 120 unique pathways between agents instantly. Instead of failing under conflicting instructions, these loop agents self correct via continuous state sharing. Managing a 15 node mesh requires high token throughput, making this dependent on strict low-] latency API tiers. See exactly how this automated multi agent graph architecture actually operates in real time ↓

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Back in 2014, 17-year old Jalen Brunson already understood the value of making the right play finding the balance between being a scorer and playmaker. 39 points, 12 assists, 1 turnover for the 2-time all-star in a crucial Game 5 to put the Knicks up 3-1 on Boston.

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