Eigenvectors and Eigenvalues (2015)
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Eigenvectors and Eigenvalues (2015)
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Re: Eigenvectors and Eigenvalues (2015)
#2I highly recommend 1Blue1Brown's Essence of Linear Algebra series[0] to highly grasp and comprehend linear algebra.
[0] https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...
Re: Eigenvectors and Eigenvalues (2015)
#3Whenever this kind of stuff comes up I feel like a bit of a fraud...
I’ve written a bunch of scientific data analysis code. I have a science PhD. Written large image analysis pipelines that worked as well as the state of the art... been published etc.
For the most part I’ve found basic math and heuristics to be good enough. Every so often I go relearn calculus. But honestly, none of this stuff ever seems to come in handy. Maybe it’s because most of what I encounter is novel datasets where there’s no established method?
I reasonably regularly pick up new discrete methods, but the numerical stuff never seems super useful...
I don’t know, just a confession I guess... it never comes up on interviews either for what it’s worth.
Re: Eigenvectors and Eigenvalues (2015)
#4Whenever this kind of stuff comes up I feel like a bit of a fraud... I’ve written a bunch of scientific data analysis code. I have a science PhD. Written large image analysis pipelines that worked as well as the state of the art... been published etc. For the most part I’ve found basic math and heuristics to be good enough. Every so often I go relearn calculus. But honestly, none of this stuff ever seems to come in h…
Just my anecdotal experience, I've seen it come up in interviews for an algorithms group at a medium sized biomed company.
Re: Eigenvectors and Eigenvalues (2015)
#53Blue1Brown has a good series on YouTube for building intuition in linear algebra:
https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...
In one of the last videos in the (relatively short) series, he discusses eigen-*:
~'eigen-stuffs are straight-forward but only make sense if you have a solid visual understanding of the pre-requisites (linear transformations, determinants, linear systems of equations, change of basis, etc.). Confusion about eigen-stuffs usually has more to do with a shaky foundation than the eigen-things themselves'
All of the videos in the series, including this later one on eigen-things, focus on animations to show what the number crunching is doing to the coordinate system.
Re: Eigenvectors and Eigenvalues (2015)
#6Whenever this kind of stuff comes up I feel like a bit of a fraud... I’ve written a bunch of scientific data analysis code. I have a science PhD. Written large image analysis pipelines that worked as well as the state of the art... been published etc. For the most part I’ve found basic math and heuristics to be good enough. Every so often I go relearn calculus. But honestly, none of this stuff ever seems to come in h…
What kind of novel dataset are we talking about?
Just from the top of my head, you could have encountered eigenvectors/eigenvalues:
- if you ever used spectral graph algorithms
- if you ever done dimensionality reduction via principal component analysis
- if you ever calculated the steady state distribution of a Markov chain
Re: Eigenvectors and Eigenvalues (2015)
#7Whenever this kind of stuff comes up I feel like a bit of a fraud... I’ve written a bunch of scientific data analysis code. I have a science PhD. Written large image analysis pipelines that worked as well as the state of the art... been published etc. For the most part I’ve found basic math and heuristics to be good enough. Every so often I go relearn calculus. But honestly, none of this stuff ever seems to come in h…
Eigenvectors and Eigenvalues show up everywhere, although sometimes it's in the form of an iterative estimate (PageRank is basically the power method estimation of the first eigenvector of a connected graph of web pages).
They're in the same class as logarithms and Fourier transforms IMHO. You won't need to calculate them by hand, but you should know what they do and why they're important.
Re: Eigenvectors and Eigenvalues (2015)
#8Whenever this kind of stuff comes up I feel like a bit of a fraud... I’ve written a bunch of scientific data analysis code. I have a science PhD. Written large image analysis pipelines that worked as well as the state of the art... been published etc. For the most part I’ve found basic math and heuristics to be good enough. Every so often I go relearn calculus. But honestly, none of this stuff ever seems to come in h…
What kind of novel dataset are we talking about? Just from the top of my head, you could have encountered eigenvectors/eigenvalues: - if you ever used spectral graph algorithms - if you ever done dimensionality reduction via principal component analysis - if you ever calculated the steady state distribution of a Markov chain
Image analysis and signal corrections on time series data. Extracting features from microscope images for example, correcting for signal convolutions.
Re: Eigenvectors and Eigenvalues (2015)
#9Whenever this kind of stuff comes up I feel like a bit of a fraud... I’ve written a bunch of scientific data analysis code. I have a science PhD. Written large image analysis pipelines that worked as well as the state of the art... been published etc. For the most part I’ve found basic math and heuristics to be good enough. Every so often I go relearn calculus. But honestly, none of this stuff ever seems to come in h…
It comes up all the time when trying to build second order optimization methods. With the eigensystem of your objective in hand you have a complete understanding of the (non-) convexity of your energy landscape, which is useful to ensure you always have good search directions, etc.
Re: Eigenvectors and Eigenvalues (2015)
#10Whenever this kind of stuff comes up I feel like a bit of a fraud... I’ve written a bunch of scientific data analysis code. I have a science PhD. Written large image analysis pipelines that worked as well as the state of the art... been published etc. For the most part I’ve found basic math and heuristics to be good enough. Every so often I go relearn calculus. But honestly, none of this stuff ever seems to come in h…
Eigenvectors and Eigenvalues show up everywhere, although sometimes it's in the form of an iterative estimate (PageRank is basically the power method estimation of the first eigenvector of a connected graph of web pages). They're in the same class as logarithms and Fourier transforms IMHO. You won't need to calculate them by hand, but you should know what they do and why they're important.
Interesting, perhaps that’s it... I’ve used FFTs a few times, but even FFTs have never been make or break in terms of getting a pipeline or analysis working well.