Thanks Nathan for this magnificent video! Our lecture at uni on this topic was confusing, but you illustrated Hausdorff distance so intuitively.😁👍🏼 Proof of the Hausdorff metric properties worked out for me on paper, as well. I rate this piece of art lim(n→∞)(cool)ⁿ.
WOW amazing video!! I loved how easy you made the concept, i would suggest placing the camera lower, beacuse you look shorter than the viewer (looking up) and i think you would like how it turns out :)
Yup, you are right! Thanks for pointing that out.😀 I more so did this to align with the notation of the sources I used which used the 1-Norm in place of the k-Norm (or other norms) to avoid clunky notation.
@@CHALKND Well I only spoke about the return values that the function takes and I'm not sure if restricting the domain helps - but this would also be interesting to study. I'm wondering if if we can quantify how often the return value will be rational (say for rational points as input) and, if rarely, whether there is a way to tune the framework so that we get a nice useful theory out of it in which the return value of the function is always or mostly in the rational.
I'm still in my first year, so research focus is superseded in importance by qualifying exams. However, I am currently helping out with a project in Fractal Geometry.
Hi! One question, is Hausdorff distance trustworthy in high dimensional spaces? As far as I know, it computes the 2-norm and in high-dimensional spaces this metric has not as much sense as in low dimensions, and it shows that all points in a space are at the same distance. Thanks!
You can actually define the Hausdorff distance with respect to any metric. Moreover, if the metrics are equivalent (i.e. induce the same topology) then the associated Hausdorff metrics are equivalent. In particular you can use metrics such as the l^1 metric.
Thanks Nathan for this magnificent video! Our lecture at uni on this topic was confusing, but you illustrated Hausdorff distance so intuitively.😁👍🏼
Proof of the Hausdorff metric properties worked out for me on paper, as well.
I rate this piece of art lim(n→∞)(cool)ⁿ.
Glad you enjoyed it Hans! 😄
The explanation is really cool. Thanks for the lecture.
oh, even if knowing so little about this, I was able to follow you; that's because your explanation is insightful; thanks!
Nailed it. Thanks, man.
Hey! What chalk+chalkboard do you use for your videos? The colors are really good and lines are really smooth, looks great.
Thank you kindly ✍️
What a really nice content has this channel
Excellent video!!! Subscribed!
WOW amazing video!! I loved how easy you made the concept, i would suggest placing the camera lower, beacuse you look shorter than the viewer (looking up) and i think you would like how it turns out :)
Wow! A great and intuitive explanation. Thank you!! Wikipedia's and other "explanations" are too terse and formal and assume a knowledge of topology.
Thanks Baruch! I'm glad you thought so!
Thank you sir
Today is a good day
By the way, I’m feeling the pressure from grad school, so seriously no rush XD
Haha 😂 that is very real! I am feeling the grad school pressure myself.
Hey *Chalk* , @3:47 in the definition of A_delta, you have used the 1-norm instead of the 2-norm over points in RxR.
Yup, you are right! Thanks for pointing that out.😀
I more so did this to align with the notation of the sources I used which used the 1-Norm in place of the k-Norm (or other norms) to avoid clunky notation.
@@CHALKND Well,the Manhattan distance isn't all that bad 🚕 🚕 🚕
Sir, may I Ask
How to determine the hausdorff distance between two set-valued random variables f(w) and g(w)?
can you also derive the formula for Hausdorff distance that's on wikipedia ?? that one doesn't use delta
Awesome
Truely
Could you make a video about Noetherian and Artinian rings?
It's definitely a possibility, however, I am not much of an Algebraist so we will see!
wooo nailed it :D
Will the value of d_H(A, B) typically fail to exist if you require that metric function to take values in the rationals?
I'm not entirely sure I understand the question. Do you mean if we were working in
ℚxℚ or if d_H(A,B) is restricted to ℚ ?
@@CHALKND Well I only spoke about the return values that the function takes and I'm not sure if restricting the domain helps - but this would also be interesting to study. I'm wondering if if we can quantify how often the return value will be rational (say for rational points as input) and, if rarely, whether there is a way to tune the framework so that we get a nice useful theory out of it in which the return value of the function is always or mostly in the rational.
What's your PhD research in?
I'm still in my first year, so research focus is superseded in importance by qualifying exams. However, I am currently helping out with a project in Fractal Geometry.
Hi! One question, is Hausdorff distance trustworthy in high dimensional spaces? As far as I know, it computes the 2-norm and in high-dimensional spaces this metric has not as much sense as in low dimensions, and it shows that all points in a space are at the same distance. Thanks!
You can actually define the Hausdorff distance with respect to any metric. Moreover, if the metrics are equivalent (i.e. induce the same topology) then the associated Hausdorff metrics are equivalent. In particular you can use metrics such as the l^1 metric.
Finally
I know right 😅
Nice
First
😂😁😅
no need to explain d_H(A,B) = 0 A=B ... if a person can't get it, they should change their major... (*jokes*)
Professor continues: "Such a fact is _obvious_ " 😂😂