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 distancesshow more

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

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.show more

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.show more

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. 1/3show more

using the same color names, comparing different dimensionality reduction... algorithms (pca, tsne and umap):show more

Need the git graph in a remote project? Support... lands next Zednesday.show more

Conditional independence of entries of Gaussian vectors defines a... graph associated to the inverse of the covariance (precision matrix). Graphical Lasso estimates a sparse graph by l^1 penalizing the maximum likelihood estimator.show more

Another excellent, interactive visual explainer for math and algorithms... - using game dev concepts, is Don't forget to check the chapters on Graph Theory!show more

Without touching a single piece of land, it's possible... to sail from Alaska to India in a completely straight line. More precisely, along a geodesic, or a curve that constitutes the shortest path (arc) between two points on a surface, like a spheroid.show more

The Cucker-Smale system of ODEs is the simplest model... of particles exhibiting flocking behaviors. Diffusion of speeds is governed by a Laplacian on the fully connected graph of points.show more

AN ENGINEER SOLVED A PROBLEM NOBODY IN THE COMPANY... COULD FULLY MAP ON THEIR OWN The problem wasn't a missing tool, it was that every process touched three other processes nobody had written down. He wired dozens of agents into one shared graph instead of documenting each department's workflow by hand. Each agent owned one process, reading its own logs while writing every dependency it found straight into the shared structure. Within days, the graph surfaced a connection between two departments that had been quietly blocking each other for over a year. The company adopted the graph as its live map of operations, and it hasn't stopped finding new connections since. See what the graph found in the first 48 hours below👇show more

Italy moving from a more positional 4-3-3, characterised by... automatisms and large distances during deep build-up, towards a more relational model with shorter distances in higher areas of the pitch.show more

Released: major updates to the network dashboard, including a... new live graph and a leaderboard. It is time to run a node and earn points. This network currently runs the world’s most advanced incentivized system for any AI network, and it is also the largest in the world.show more

Oldies but goldies: Felipe Cucker, Steve Smale, The Mathematics... of Emergence, 2007. Defines a simple model of particles exhibiting flocking behaviors. Diffusion of speeds is governed by a Laplacian on the fully connected graph of points.show more

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 ↓show more

Big time performance by Jalen Brown. 33 points in... a win over Brookfield Central. Six points and game-tying assist in final three minutes to push the game to regulation. Six more points in overtime including the go-ahead 3-pointer. And a congrats from the #Badgers.show more

That was A Massive 3 points. UP THE VILLA