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

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

This is the worst (of many) plays. It’s either... a moving screen, or a steal that leads to a 4-on-2 fast break. Instead, it turned into 3 points for the Knicks.show more

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.show more

The Brava Race to a Thousand Galxe Quest is... now live! 1/2 Join the quest and be one of the winners to get a share of the 1,000 $USDC Prize Pool! Start collecting Brava points and get exclusive Discord roles that entitle you to future rewards within the Brava ecosystem.show more

Q: Many Republicans felt the first 28-point plan was... too favorable to Russia. Have you changed it? Trump: That was just a map, not a plan. It was a concept. And from there they’re taking each one of the 28 points and then you get down to 22 points. A lot of them resolved. 2/show more

(🧵1/3) The largest groups receiving British Citizenships are Sub-Saharan... Africans & South Asians (graph below). Who is granting these citizenships and why? Both denaturalisation & deportation are crucial to prevent the Native British becoming a minority in our own homeland.show more

The largest Decentralized Knowledge Graph (DKG) provides a powerful... substrate to tackle #AI hallucinations, bias & model collapse. The NEW ChatDKG.ai allows you to supercharge your AI solution with data always on $trac(k)🔎 It's as easy as 1-2-3! 👉show more

It’s Friday, WatchX Fam! 🎉 Few hours to our... Gartic Game Hangout! 🎨 Join for laughs, chaos & a chance to win some WatchX Points 💎 🕕 2 PM UTC | 📍 Discord Gartic Channel 🏆 Last week’s Top 3: 🥇 @behemoth4174 — 2000 WatchX Points 🥈 Niyi ❖,❖ — 1500 WatchX Points 🥉 str8aaas — 1000 WatchX Points Thanks to all for bringing the energy! 🔥show more

The incident that led to Bolton Wanderers going 2-1... up vs Leyton Orient A corner comes into the box and it’s alleged that Azeem Abdulai handles the ball 😳 Referee points to the spot! Harsh or definitely a penalty?🤔 #bwfc #LOFC #OneOrientshow more

After EATING FROZEN RAW LIVER and bone marrow, I... was truly accepted by these local Buryats. Descendants from the Mongolian steppe nomads, they would eat this (and still do!) while travelling vast distances on horseback. It was a bit like tartar, nicer than the cooked stuff. I’m just glad they didn’t make me try any other local delicacies, that was enough for one day!show more

3 games to go. 3 cup finals. Win all... 3 and we win the league. Simple as that. First up … Wealdstone (H). We haven’t been convincing for a while now. But, now’s the time for us to step up with a huge performance and a big 3 points. Let’s do it together, Up The Dale!👊💙 #RAFCshow more

The Brava Galxe Quest is now live! 1/2 Join... the Quest to earn points and unlock the exclusive Initiator Badge on Discord, entitling you to future rewards within the Brava ecosystem. Also, 10 lucky participants will share a 250 $USDC prize pool.show more

Today SciPhi is open-sourcing Triplex, a SOTA LLM for... knowledge graph construction. Triplex is so small that it can be used with SciPhi's R2R to build knowledge graphs directly from your laptop. Triplex outperforms few-shot prompted gpt-4o at 1/60th the inference cost.show more

This guy built a visual scanner that reads 468... points on his face and 42 points on his hands from a regular webcam and turns them into a cloud of thousands of particles right between his palms. Inside, MediaPipe and TouchDesigner are linked: the first captures hands and face from the webcam with high accuracy, the second turns those coordinates into a live plane and feeds it into a POP system that instantly generates a swarm of particles in the shape of a head. No studio, no render farmer, no VR headset. Just a laptop, a webcam, and 1 TouchDesigner session. And traditional VJ studios keep teams of 5 people on a setup with lighting, custom hardware, and commercial plugins, while his expenses are only a TouchDesigner subscription and a regular USB camera. One laptop runs MediaPipe and TouchDesigner simultaneously, holds the camera stream at 60 FPS without drops, and in parallel processes 468 face points + 21 points on each hand. The camera captures frame after frame, MediaPipe in real time sends TouchDesigner the finger coordinates and face geometry, and the POP operator inside the engine translates those numbers into thousands of particle points with colors from bright pink to gold. This setup immediately defines the role of the tool and the limits of its autonomy. It knows where the fingertips are at every moment of the frame. It knows how to read the face geometry at any angle to the camera. It knows how to draw a swarm of particles between them with the right color and contour. → MediaPipe pulls 468 points from the face and 21 points from each hand, 60 times per second → TouchDesigner receives those coordinates, builds a virtual rectangle between the fingertips, and feeds it into the POP system → POP generates thousands of particle points in the shape of a head, coloring them in a gradient from bright pink to gold → The HUD layer adds green corners and a blue neon frame, styling the image like an AR interface → All layers assemble into 1 real-time frame that projects back onto the video in the camera window → The final image is recorded to a file or broadcast to a projector for a live installation And only when the guy spreads his hands wider does the plane between the palms stretch; brings them together, it narrows. Otherwise the system runs on its own. And when he moves from his home room to a concert hall, the same laptop with the same webcam launches the same TouchDesigner session in just 5 minutes, without reconfiguration, without a new team, and without a single line of new code. In his work setup there is no studio of his own and no team for assembly. On the desk sits a laptop with a webcam, on top run MediaPipe and TouchDesigner with POP operators, and the same setup through a USB camera moves to any concert without a new configuration. Out of everything I have seen this year, this is the cleanest Creative Coding setup on 1 laptop: 0 render farms, 0 studio lighting, and between them 3 libraries, thousands of particle points, and 1 webcam.show more

What Happens When Prime Numbers Enter The Complex Plane?... Prime numbers live on the number line. Gaussian primes live on the complex lattice. Instead of looking only at numbers like 2, 3, 5, 7, we look at points z = a + bi, where a and b are integers. The key quantity is the norm: N(a+bi) = a² + b². This norm decides which lattice points behave like primes. For points away from the axes, a+bi is a Gaussian prime when a² + b² is an ordinary prime. On the axes, the rule changes. A point is prime only when the nonzero coordinate is an ordinary prime of the form p ≡ 3 mod 4. And the prime 2 is special: 2 = (1+i)(1−i). That is why the animation grows as a structured prime landscape. Off-axis primes appear in symmetric families. Axis primes survive only in the 4k+3 class. The norm-2 points glow as the ramified prime. The result is a square lattice where prime numbers stop looking like isolated dots and start behaving like geometry. #PrimeNumbers #NumberTheory #GaussianIntegers #ComplexPlane #Mathematics #Matheliriumshow more

🪂 Airdrop Checklist: 💰 Raised: $51M Towns is a... decentralized group chat app where you can vibe, build, and earn ✨How to earn Towns points 👇 1️⃣ Sign up & login 2️⃣Join a Town: Find a Town and start chatting, here is mine: 3️⃣Create your Town : Hit "+" in the left bar > Customize > Share your Town in the comments 4️⃣Add ETH: Profile > Wallet > Add a few bucks ($2-3 is enough) 5️⃣Earn Points: Tap the Beaver 🦫 daily and approve (small fee) Chat. Earn. Repeat 🔁 Like + RT the post 🫡❤️show more