Gaussian Mixture Models for Clustering

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  • Опубликовано: 29 сен 2024
  • Now that we provided some background on Gaussian distributions, we can turn to a very important special case of a mixture model, and one that we're going to emphasize quite a lot in this course and in the assignment, and that's called a mixture of Gaussians.
    And remember that for any one of our image categories, and for any dimension of our observed vector like the blue intensity in that image, we're going to assume a Gaussian distribution to model that random variable.
    So for example, for forest images, if we just look at the blue intensity, then we might have a Gaussian distribution shown with the green curve here, which is centered about this value 0.42. And I want to mention here that we're actually assuming a Gaussian for the entire three-dimensional vector RGB. And that Gaussian can have correlation structure and it will have correlation structure between these different intensities, because the amount of RGB in an image tends not to be independent, especially within a given image class. But for the sake of illustrations and keeping all the drawings simple, we're just going to look at one dimension like this blue intensity here. But really, in your head, imagine these Gaussians in this higher dimensional space.........

Комментарии • 39

  • @emineguven3565
    @emineguven3565 5 лет назад +19

    Thanks a lot for sharing this. It helps me a lot to understand the concept of mixture models.

  • @TammyKoldaMathsciAI
    @TammyKoldaMathsciAI 4 года назад +1

    Nice, Emily!

  • @ahsin.shabbir
    @ahsin.shabbir 3 года назад +10

    this is a really good explanation. Where are the rest of the videos in the series?

  • @LinaNielsen-n8g
    @LinaNielsen-n8g 8 месяцев назад

    Why are the given weights for the distributions, are not really showcasing the distributions on the graph. I mean i would choose π1 = 45, π2 = 35, π3 = 20

  • @gabrielamartinezl.2944
    @gabrielamartinezl.2944 4 года назад +4

    Excellent video! Any about Bernoulli Mixture Models?

  • @ogonkishi6403
    @ogonkishi6403 4 года назад +4

    Thanks! Helped a lot! Especially the visualisations!

  • @MLDawn
    @MLDawn 3 года назад +1

    you could plot 3D Gaussians, with their contours projected on the RGP plains.

  • @vineethm6930
    @vineethm6930 3 года назад +5

    Very well presented, really got all my concepts clear 💯

  • @tomc3213
    @tomc3213 4 года назад +4

    This is gold, thank you so much

  • @riasataliistiaque5206
    @riasataliistiaque5206 2 года назад

    At around 6:05, the sigma_k values, they're all the same 3x3 covariance matrices right? sigma_1 == sigma_2 == sigma_3?

  • @bwessellangan
    @bwessellangan 2 года назад

    Hey EF - randomly found this - hope all is well! Shout out to MITLL

  • @DrSugarrr
    @DrSugarrr Год назад

    This is a great video, thanks a lot for all the details!
    I was wondering, in conclusion, how would the program decides if it's a sunset, a tree or a cloud picture? I am guessing it would calculate p(xi | zi=k, µk, σk) for k = 1,2,3, weighted by πk, and then pic the category with the highest probability?

  • @nehadureja
    @nehadureja 4 года назад +8

    Great explanation. Thank you for the amazing work :)

  • @MLDawn
    @MLDawn 3 года назад +1

    very nice tutorial. Thanks a lot.

  • @bluebox6307
    @bluebox6307 3 года назад +1

    Very well explained! Thank you very much!!

  • @NeilDeshpande313
    @NeilDeshpande313 3 года назад +1

    Thank you so much for this

  • @stewpatterson1369
    @stewpatterson1369 3 месяца назад

    best video i've seen on this. great visuals & explanation

  • @franklinsv1997
    @franklinsv1997 4 года назад +1

    Great Video!! very clear explanation. Does this have a part two where it is explained how it is applied using EM algorithm?

  • @Noah-zp2fn
    @Noah-zp2fn 3 года назад +1

    thanks a lot! explanation was crystal clear!

  • @rasoulmesghali
    @rasoulmesghali 4 года назад +1

    very well explanation

  • @hoavu382
    @hoavu382 2 года назад

    The video sound is pretty good, beyond my imagination

  • @piyushgupta809
    @piyushgupta809 4 года назад +1

    Great explanation

  • @ZinzinsIA
    @ZinzinsIA Год назад

    Great explanation, thank you very much !

  • @abhinaba__saha
    @abhinaba__saha 4 года назад +1

    Amazing

  • @notarandomdude6094
    @notarandomdude6094 2 года назад

    That's great thanks

  • @Malvici.
    @Malvici. 4 года назад +1

    Great!!!

  • @chris-dx6oh
    @chris-dx6oh Год назад

    Great video

  • @xiujiesong3095
    @xiujiesong3095 2 года назад

    thx! it is very helpful.

  • @SPeeDKiLL45
    @SPeeDKiLL45 2 года назад

    beautiful explanation

  • @avamarie7406
    @avamarie7406 2 года назад

    macam mana nak buat?

  • @PG-iq6zv
    @PG-iq6zv 3 года назад

    great video thx!

  • @thirdanonymousacc
    @thirdanonymousacc 3 года назад

    Thank you!

    • @thirdanonymousacc
      @thirdanonymousacc 3 года назад

      This is just what I needed.
      I'm a student that finds it very difficult to find materials that suit me (balance of intuition/ mathematical detail, pace etc.). But this type of teaching of yours works wonders for me. I will watch anything you're willing to teach :)

  • @shashankkumar7920
    @shashankkumar7920 3 года назад

    Why I m seeing a Gaussian curve shape in her hair😂...btw great video thank you so much

  • @sarthaktiwari1889
    @sarthaktiwari1889 5 лет назад

    Very well explained!

  • @muhammadsarimmehdi
    @muhammadsarimmehdi 4 года назад

    you didn't explain what those histograms are in the beginning? Are they RGB histograms? What you started explaining right after made no sense because you didn't clarify how you got these histograms

    • @MeenaKumari-sl5ez
      @MeenaKumari-sl5ez 3 года назад +1

      She did explain. those histograms are the distributions of the blue channel of the images in the 3 clusters.