Support Vector Machines Part 3: The Radial (RBF) Kernel (Part 3 of 3)

Support Vector Machines use kernel functions to do all the hard work and this StatQuest dives deep into one of the most popular: The Radial (RBF) Kernel. We talk about the parameter values, how they calculate high-dimensional coordinates and then we'll figure out, step-by-step, how the Radial Kernel works in infinite dimensions.
NOTE: This StatQuest assumes you already know about...
Support Vector Machines: • Support Vector Machine...
Cross Validation: • Machine Learning Funda...
The Polynomial Kernel: • Support Vector Machine...
ALSO NOTE: This StatQuest is based on...
1) The description of Kernel Functions, and associated concepts on pages 352 to 353 of the Introduction to Statistical Learning in R: faculty.marshall.usc.edu/garet...
2) The derivation of the of the infinite dot product is based on Matthew Bernstein's notes: pages.cs.wisc.edu/~matthewb/pa...
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Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/

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@@statquest Hey Josh, what would be an intuitive way to understand how SVM uses the high dimensional relationship between each pair of points to make the actual classification

[@statquest]

@@arunavsaikia2678 This is a good question. The dot product between two points, which we use to create the "high-dimensional relationships," can be interpreted in a geometric way that includes the cosine of the angle between the two points multiplied by their magnitudes (the distances from the origin). With that in mind, check out slide 18 in this PDF: web.mit.edu/6.034/wwwbob/svm.pdf

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the mathematical reasoning behind the radial kernel has been plaguing me for so long, finally after many tries now it starts to click and my mind can visualize better what is happening and why. Thank you so much :)

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What an interesting application of the Taylor Series. Such a beautiful explanation, thank you!

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This is actually the 3rd place I've seen the Taylor Series in Machine Learning - so it's a super useful trick.

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Glad it was helpful!

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nobody explains the concepts better than you do. I have to study ML for a project and I haven't found a channel better than yours. That is why I have a request: please make a video on Support Vector Regression.

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I have gone through 85% of the full list and found this series extremely useful. The instructions are simple to understand and give the sufficient overview into Machine learning. Highly recommend for starters like me. Looking forward to the advanced parts, e.g. Deep learning. Many thanks!

[@statquest]

SVM and the Radial is actually pretty advanced, so you've made huge progress. The current series, on XGBoost, is also very advanced. After this, I'll do deep learning and neural networks.

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Glad you like it. I try to teach the way I want to be taught myself. I'm not super good at this stuff, so I try to keep it simple.

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Bam! I'm glad you enjoy the videos. :)

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Thanks! :)

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[@statquest]

UMAP is on the to-do list.

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[@statquest]

Thank you!

[@amishgoel2377]

Awesome Video and clear explanations! I had one doubt. In the end when forming dot product of RBF kernel, you have used s to multiply the two dot products. But s is a function of both a and b. In the dot product of a pair of observations in high dimension, each term in the product should be a function of one observation since it corresponds to high dimensional feature of an observation. I think one should multiply e^(-0.5a^2) to the first term and e^(-0.5b^2) to the second term of the dot product.

[@statquest]

All 's' is doing is scaling the dot-product by a constant value. For more details, see: pages.cs.wisc.edu/~matthewb/pages/notes/pdf/svms/RBFKernel.pdf

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Glad you enjoyed it!

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I benefit so much from your video. From a Chinese Ph.D.

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Beautiful video! Thank you so much! I have a question. May you explain why we can use Taylor series assuming a=0? Why can we do this assumption?

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I learned RBF from the Gaussian process, and seems the idea of "kernal" has numerous applications!

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[@statquest]

Unfortunately, my next series of videos will be on XGBoost. If there if there is a demand, I'll return to SVMs as soon as I can.

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[@statquest]

XGBoost videos should start coming out in the next few weeks. The first step is to learn how regression trees are traditionally pruned. XGBoost uses a different method and we need to learn the traditional way to appreciate how XGBoost does it.

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better late than never! :)