Setosa

Anything from Setosa [0] is really good. It contains interactive, animated illustrations of several Machine Learning ideas. I _loved_ reading papers from Distill Pub [1] as they contained interactive diagrams. My most favorite one so far is the thread on Differentiable Self-organizing Systems [2]. I liked the lizard example very much as it is interactive, and lizards grow lost organs back. I think this is funny. [0]: https://setosa.io [1]: https://distill.pub [2]: https://distill.pub/2020/selforg/

A little parasitic! It is horrendously parasitic. Here are some other great maths visualisations for understanding. http://setosa.io/#/

what about http://setosa.io/ ? many excellent visualizations there

Great visualization (as the rest from http://setosa.io , go have a look)!! I wonder, though: I learnt OLS as standard math / symbolic logic; but, if kids and students learnt from these visualization, would they be better off, or worse off? Because, at least for me, it is difficult to reason about this and other visual math examples (whereas there are others that are great as demonstrations, as the integer proof in http://www.catonmat.net/blog/visual-math-friday/ , this one, regarding OLS, confuses me). It probably depends a lot on each person. Out of curiosity, does this particular example give you insights? Which ones? How?

I really recommend this explorable explanation: https://setosa.io/ev/ordinary-least-squares-regression/ And for actual gradient descent code, here is an older example of mine in PyTorch: https://github.com/stared/thinking-in-tensors-writing-in-pytorch/blob/…

This is from one of the authors of Explained Visually, which has a ton of great visual explanations: https://setosa.io/ev/

I would love someone like gwern [0] to write an analysis of how Mathematics articles on Wikipedia start off being understandable by most and then get lapped into a submicron finish that only reflects an insular subset of folks. These mathematical nuggets sit like hard grains in mud (sorry wikipedia) that only mathematicians can understand. And in so doing, they slowly bootstrap themselves so far away from any grounding context that it is incredibly difficult for anyone to _learn_ mathematics from reading wikipedia articles. There are groups doing great things like Setosa [1], nLab [2] and for concepts, Simplicable [3] [0] https://www.gwern.net/ [1] https://setosa.io/ev/ [2] https://ncatlab.org/nlab/show/HomePage [3] https://simplicable.com/new/communication

Excellent explanation! I find this visualization really helpful when I need to explain PCA: http://setosa.io/ev/principal-component-analysis/

Here is an excellent place to start: http://setosa.io/ev/markov-chains/

I looked up the Victor Powell visualization they cite and it's quite a bit more in-depth then the version they have: http://setosa.io/conditional/ But seriously, all of these interactive visualizations are amazing. I wish they had this kind of stuff when I was an undergrad. I remember trying to plot the beta distribution for different alpha and beta parameters in MATLAB trying to get an intuition for it; just dragging the sliders around on the prior and watching it update as each data point comes in is a million times more accessible.

When I was in grad school I made these to explain concepts from traffic theory: http://setosa.io/blog/2014/09/02/gridlock/ http://setosa.io/bus/ These were major efforts and I don't recommend building out anything similar while pursuing a master's. But control theory does lend itself to simulation well, so I would use jupyter notebooks to present little annotated simulations with code. Print out plots of the state space at intervals for example. I also highly recommend the graphing calculator desmos.com.

Here are a couple of other Markov Chain articles that are worthwhile: http://setosa.io/ev/markov-chains/ https://towardsdatascience.com/a-zero-math-introduction-to-markov-chai…

I love light rail, not the bus: http://setosa.io/bus/ https://en.wikipedia.org/wiki/Bus_bunching

Setosa (http://setosa.io/) hosts some impressive interactive visualizations as well.

This site/group also did a fantastic visualization on gridlock vs. bottlenecks: http://setosa.io/blog/2014/09/02/gridlock/

Absolutely agree with this. Another nice illustration of how when arrival rate is greater than departure rate we get overflowing queues: http://setosa.io/blog/2014/09/02/gridlock/index.html

http://setosa.io/bus/ is my favorite demonstration of this.

I thought it was interesting the same technique (convolution) was used in two different applications: photoshop/gimp for image filters and in convolutional neural networks (CNNs). What is the purpose of convolution in CNNs? the setosa interactive says convolution is "a technique for determining the most important portions of an image" the hubel and wiesel experiment showed "there is a topographical map in the visual cortex that represents the visual field, where nearby cells process information from nearby visual fields. Moreover, their work determined that neurons in the visual cortex are arranged in a precise architecture. Cells with similar functions are organized into columns, tiny computational machines that relay information to a higher region of the brain, where a visual image is formed" I'm interested in David Marr's work, about to order Vision: A Computational Investigation into the Human Representation and Processing of Visual Information, his level of analysis approach is interesting. I think he did work on edge detection, which must of been involved some kind of convolution/filter This setosa interactive is great, and actually references the gimp documentation http://setosa.io/ev/image-kernels/ An image kernel is a small matrix used to apply effects like the ones you might find in Photoshop or Gimp, such as blurring, sharpening, outlining or embossing. They're also used in machine learning for 'feature extraction', a technique for determining the most…

Eigenvalues and eigenvectors are one of those things that pop up in a million places because they're so useful, but to recognize where they may be useful you need intuition as to what they're doing. One of my biggest hurdles learning linear algebra was getting that intuition. This "standard way of explaining scientific things" never built that intuition for me, only forced the mechanics of the computation into pencilized muscle memory. Don't get me wrong, you need that muscle memory in practice. But without the intuition, your muscle memory is always going to be inferior to a couple commands in matlab. Stuff like this visualization builds the intuitive knowledge -- you see, you explore, you wiggle a few things and see what happens when you go in and out of the sweet spot. Play (and simulation) is an extremely effective way to build intuition, and one I'd love to see more. These guys are doing an awesome job at these kinds of simulations -- their markov chain one was fantastic too http://setosa.io/ev/markov-chains/

Related - Gridlock vs Bottleneck Simulator: https://setosa.io/blog/2014/09/02/gridlock/

http://setosa.io/bus/ it's harder than it seems, pure incompetence seems a little unfair.

Tough one, I'd have to say: 45% http://setosa.io/ev/markov-chains/ 30% https://en.wikipedia.org/wiki/Markov_chain 25% Youtube

I just read this today. You may find it helpful. http://setosa.io/ev/principal-component-analysis/

Yes, that's exactly how the author of the article is explaining it (including the picture). I was just commenting that it was good that, the author took time to explain this. And those kinds of nuances/counter examples are not always available in explanatory dynamic visualization tools (such as the ones referenced in the comments here [1] ). To be clear, I am not arguing against dynamic visualizations. These are very nice, very very helpful, and very time consuming to build and present on a website. I am just suggesting that showing negative examples is a complimentary, and powerful explanation technique. [1] http://setosa.io/ev/eigenvectors-and-eigenvalues/

Reminds me of http://setosa.io/ev/eigenvectors-and-eigenvalues/

On a tangental note, another HN user posted another visualisation a few months back which I quite enjoyed: Why do buses bunch?: http://setosa.io/bus/

I think this simulation[1] explains why even a small change in traffic patterns can have huge consequences to the stop-and-go behavior. (experiment holding one of the buses for just a couple of seconds...) [1] http://setosa.io/bus/

I had problems with Principal Component Analysis; nice to see he's got one on that as well! http://setosa.io/ev/principal-component-analysis/ (edit: ugh, contains an ad for MacKeeper)

Principal Component Analysis Explained Visually: http://setosa.io/ev/principal-component-analysis/

Woah, spent way too much time making this: http://setosa.io/markov/index.html#%7B%22tm%22%3A%5B%5B0%2C0.9%2C0%2C0…