Hi @jbed,
I have sent an email to you, as my colleague and I are in the space of assisting people to progress through the interview process.
Cheers, Martin
Hi,
I'm happy to chat with your brother, to help him work out what are some good questions to ask, when looking for the best kind of service provider / consultant is best for him. I might then either be able to help him myself, or I recommend someone from my network, or send a wider call on my linkedin profile for someone to help him.
This new coefficient of correlation is really really awesome, and this visualization shows its value in such a beautifully simple presentation.
It would be great if someone who has Wikipedia edit privileges, can edit the Wikipedia article at [1] to describe/link how the Chatarjee's correlation coefficient solves many of the known limitation of Pearson's correlation coefficient.
;)
Easy there. New correlation coefficients get proposed all the time (eg. the introduction of the linked paper lists ~10-20 alone!). It's not a good idea to add every newly proposed coefficient to established wiki pages, just because they trend on social media. Yes, the paper looks nice, but if you read any new paper proposing a new measure, they all do! They're meant to be written that way. Let the community decide and test and discuss, and if in 10 years this new coefficient is well accepted and has proven itself, we can think about your proposed edit. Doing it before is putting the cart before the horse, and is a recipe for astroturfing.
But the part that one would add would not necessarily be the definition of the coefficient ξn, but rather the interesting discussion at the beginning about what makes for a good correlation coefficient.
This is an order-based algorithm, so it is more related to the median than the mean.
Another very useful consequence of being order-based, is that this new coefficient is much more robust to noise/outliers than the canonical correlation coefficient.
One reason/situation where the Fibonacci method is preferred is because it is a direct construction method, which can be coded in a few lines, rather than an indirect iterative method.
The second is that because an energy minmization method is minimizing the sum of forces, it more closely minimizes average distance between points, rather than absolute minimum distance which is what packing distance focuses on.
As I describe in the article, different methods produce similar but slightly different solutions. An optimal solution for one objective function, may not be the optimal for a different objective function. I then give details about how the solution that optimizes volume of the convex hull is different to the solution that optimizes for packing distance, etc.
If you just want N in a certain range, we can use the triangle-based polyhedron and successively quadruple or triple the number of faces. Then use the face normals as points. This gives visually appealing distributions without any real oddities.
For purposes of nearest neighbors this seems like an incredibly interesting shape to inscribe into:
The sphere, despite having spherical properties also maintains linear properties due to the corrugation. To me that means we can try to inscribe orthogonal properties into both of the spaces.
My understanding of these geometries isn't complex enough to make the connections, so my question is this:
Do you think its feasible to use shapes with this 'corrugated' property to make better nearest neighbor compression?
My intuition tells me that you can use the shape's linear nature to push apart independent components and inscribe the rest of the details into the spherical components. Or perhaps the opposite way.
I don't have any intelligent comments on your question, but I wanted to say that I am a fan of Quanta magazine, but somehow had missed this really cool article. So thanks for pointing me to this fascinating field. ;)
Good article, but it'll take some time to understand it. %1 is interesting, I used to use {..} for taking fractional part, %1 is intuitively easy, though not looking particularly good...
yeah. I think his website is extremely old and hasn’t been updated in the last decade or so. Despite this I linked to it because he is a legend in this field and so i think this is still the definitive reference.
As far as i understand, part of the story as to why dodecahedron and the cube fall short is due their non-triangular faces.
Did the article switch the dodecahedron and icosahedron? It specified that the icosahedron is optimal for 12 points and the dodecahedron for 20 which seems backwards to me.
Can you explain the notation [0,1)^2 unit square, does the 2 represent the spatial dimensionality? So,[0,1)^3 is the unit cube? Why is 0 inclusive, but the 1 is exclusive?
"The first is that this mapping is area-preserving, not distance-preserving." Which area is being preserved?
Is there a volume preserving choice function?
What are points t0 and t3, are those the location of the singularity points? What is the definition of those "singularity points"? Is it that seeming void in the center of the fibonacci spiral? And that void doesn't exist within the unit square case?
So[0,1)^1 is a line interval, [0,1)^2 is a unit square and [0,1)^3 is the unit cube, and [0,1]^d is a d-dimensional cube.
2.Only one boundary can be included
It includes 0 but not 1 because it can only the context is usually that practitioners want a region where one edge will wrap to the opposite edge.
Thus they treat [0,1)^2 as if it is actually a 2-dimensional torus.
thus the the 2 boundaries acutally map to the same point, so you can only include one of them.
In our case as we are using x %1 = fractional part of x, the fractional part could be 0, if x=3.0, but it could never be exactly 1.
I was given the book "The 85 ways to Tie a Tie" as a gift many years ago. It is a wonderful read for nerds.
"Two physicists prove that there are not just four ways to tie a tie, but a further eighty-one. ‘The 85 Ways to Tie a Tie’ unravels the history of ties, the story of the discovery of the new knots and some very elegant mathematics in action."
