Why we take Eigenvectors of the Similarity Matrix

A video breaking down the intuition behind a large family of "spectral" dimensionality reduction algorithms e.g. KPCA, LLE, Laplacian eigenmaps and many others

By Michael Lin

Music: "F*ck That''
-Death Grips

[nielszondervan]

Love the intro, sounds like the Akira soundtrack. Nice how you explain the math with a focus on understanding the 'intuition' behind dimensionality reduction opposed to focussing on the formula's. I wished more people would approach it like you do, math would appeal to many more people.

[nataliiadeshko]

thanks, very clear and at the same time laconic explanation!

[nickelandcopper]

Thank you for the videos. How does one assign value / colors of the plots at the end? The plots of the eigenvectors of the kernel? I often see various different units assigned to them, and I wonder if you can please comment on general strategies for assign such colors? Ex) what do the red specks mean over the blue ones here? Sometimes I see a clear rainbow pattern across the plots. Other times I see a more scattered case like you have

[torrecuso]

Could you please explain why doesnt PCA use eigendecomposition?
So far I always understood that PCA is completely based on eigenvectors and values.
Maybe I didnt understand what is the "decomposition" part.

[christophgonzalez]

A PCA can be conducted via eigendecomposition of either a gram, covariance, or correlation matrix fyi.

[nielszondervan]

Just wondering which packages you use for visualization, R ggplot?

[mickolesmana]

i just want to build CFD and somehow stuck in this rabit hole

[fazlfazl]

t-SNE does not involve taking the eigen vectors???? Or does it. Now you have confused me.... I dont think it does!!!

[bhupensinha]

Video is meant for people who hv PhD in dimensionality reduction

[ankur]

A layman would find it impossible to understanding anything from your explanation.