Statistics/Data Science: Real world example for a donut destribution? - statistics

I'm looking for different real world examples for donut derivations (in the statistic meaning).
donut derivation plot
For the most other derivations, I found good examples.
But for this the only one is the way to focus a laser beam:
https://www.researchgate.net/figure/Donut-shaped-laser-beam-for-thermocapillary-induced-dewetting-a-Microscopic-pictures_fig2_274400395
But this wouldn´t fit to e.g. a classication problem.
Has anybody a good source oder idea, where donut derivations are existing in real world data?
Thanks a lot!

Related

Correlation and graph layout in widyr and ggraph when tidy text mining

I'm using a tutorial (https://www.tidytextmining.com/nasa.html?q=correlation%20ne#networks-of-keywords) to learn about tidy text mining. I am hoping someone might be able to help with two questions:
in this tutorial, the correlation used to make the graph is 0.15. Is this best practice? I can't find any literature to help choose a cut off.
In the graph attached from the tutorial, how are clusters centrality chosen? Are more important words closer to the centre?
Thanks very much
I am not aware of any literature on a correlation threshold to use for this kind of network analysis; this will (I believe) depend on your particular dataset and how language is used in your context. This is a heuristic decision. Given what a correlation coefficient measures, I would expect 0.15 to be on the low side of what you might use.
The graph is represented visually in a two-dimensional plot via the layout argument of ggraph. You can read more about that here but the very high-level takeaways are that there are a lot of options, they have a big impact on what your graph looks like, and often it's not clear what is the best choice.

Are there existing tools that raytrace triangle meshes?

Disclaimer: I'm not 100% on whether this is a well-formed question, so please feel free to comment and suggest improvements. I'll be actively looking out for ways to improve this question.
I have a triangle mesh, let's say the Stanford Bunny. Now, I want to raycast a ray from a source point in 3D along a 3D direction vector, and identify just the first intersection of that ray with the triangle mesh.
I already have a naive implementation cooked up. However, I'm looking for a more advanced implementation. In particular, I'll be casting many millions of rays in many directions, so I'm looking for a multi-threaded or GPU-accelerated implementation.
I have to believe that there must be some pretty complete projects online, as raycasting triangle meshes is a fundamental part of 3D computer graphics. However, I can't find anything beyond personal projects, which leads me to believe that I am using the wrong search terms, or something pretty simple along those lines.
I am looking for suggestions on existing tools that can raytrace polygonal meshes.
If all you need to do is find the distance to the mesh for millions of rays. Then it might be a good idea to look up CUDA raytracing tutorial online. This will show you how to cast many millions of rays. In most tutorials, raytracing is used to render to the screen with the camera matrix. However, this is not necessary. Simply adjust the rays starting parameters to what you need them to be such as 3D vector and position. Then output the data back to the CPU. Be weary of the bandwidth between the GPU and CPU sending millions of intersection points between the CPU and GPU can make the program run exceptionally slow.

3D visualization - rotating cube

I have many 3D vectors. I want to plot them in a cube so that each dimension is on a particular side of the cube.
Now, I am looking for some visualization/tool or library that lets me rotate this cube in 3D and see the vectors in various different angles.
Thanks
Abhishek S
Try Processing, it is somewhat intended for data visualization and in addition to simple control over 3D drawing, it also has the full power of Java programming language. You can see numerous works, done by other people on OpenProcessing.
However, if you are into anything serious, I would suggest you to use some ohter IDE than the default one. I use Eclipse for that, importing Processing as a library into my project. It requires a tiny boilerplate to work, but then you're happy!

Support Vector Machine Illustration

Does anyone can give an example of a SVM? Especially how to get the w and b from a training set?
I tried to search in the internet but it only gives me a large amount of abstract mathematics.
As I am not good at it, so could anyone give me an illustration of a SVM with an example in very details?
Thank you so much.
This diagram on wikipedia provides a good example of what the goal is, but in truth a support vector machine is a lot of complicated math. You find the values for w and b by optimizing a quadratic programming system, and when hidden behind vector mathematics, it's not entirely clear what's going on unless you're well-tuned to the math.

Improvements to the base R graphics

When I'm generating graphics for publications and talks, I tend to use ggplot2. However, for very large data sets where I want to generate a quick plot or for courses where students don't have a good grounding in R, I use the base graphics.
Are there any nice (simple!) ways of spicing up R graphics? For example, do you use a nice combination of colours and line types. I tend to do something like:
#Functional but not that nice
plot(x1,y1, type="l")
lines(x2, y2, col=2, lty=2)
In particular, I'm thinking about the plot, hist, and density functions, but I suppose this question applies to all base R graphics.
Learn to use par. At the very least, make the y-axis label horizontal with par(las = 1). Manually adjusting margins with the mar and oma settings of par are also useful.
Use hue-chroma-luminance (HCL) colours, via the vcd package, especially for plots involving area (histograms or whatever).
The first half of Paul Murrell's R Graphics gives you advice on customising base graphics. If you want more general advice on drawing good graphs, Stephen Few's Now You See It is my personal favourite, and Edward Tufte's books are all staples.
As an alternative to teaching base graphics, you could use latticist to make lattice easier to learn.
I often skip position 3 in the default palette (green) because it generates dichromat-unfriendly plots. I should probably use palette(palette()[c(1:2,4:8,3)]) to do this automatically, but I tend to just do it by hand. I recommend the RColorBrewer package too.
Andrew Gelman (a pretty well-known statistician at Columbia with a very entertaining blog) would like you to adjust the margin and tick spacing.

Resources