[HN Gopher] Principal Component Analysis Explained Visually ___________________________________________________________________ Principal Component Analysis Explained Visually Author : spking Score : 93 points Date : 2022-10-29 18:02 UTC (4 hours ago) (HTM) web link (setosa.io) (TXT) w3m dump (setosa.io) | aquafox wrote: | Here is a much better explanation of PCA: | https://stats.stackexchange.com/questions/2691/making-sense-... | | The key insight that many are missing is that PCA solves a series | of optimization problems, namely that reconstructing the data | from the first k PCs gives the best k-dimensional approximation | in terms of the squared error. Even more, this is equivalent to | assuming that the data lives in a k-dimensional subspace and | becomes truly high-dimensional because of normally distributed | noise that spills into every direction (dimension). | larrydag wrote: | I really like the way Harrell uses PCA to build regression | analysis in Regression Modeling Strategies | | https://link.springer.com/book/10.1007/978-3-319-19425-7 | swyx wrote: | Principal Components is a wonderful concept, together with | sister concepts eigenvalues/vectors, and orthogonality. i wish | i could force everyone i talk to to internalize these ideas so | that I could have more useful discussions with them. | | that said, yeah not everything is linearly separable | blt wrote: | In the UK eating example, it would be better to examine the | feature-space singular vector associated with the first singular | value instead of instructing the reader to "go back and look at | the data in the table". PCA has already done that work, no | additional (error-prone, subjective) interpretation needed. | lxe wrote: | Also see | | - Markov Chains (https://setosa.io/ev/markov-chains/) | | - Image Kernels (https://setosa.io/ev/image-kernels/) | | - Bus Bunching (https://setosa.io/bus/) | | Wish these guys kept producing more visualizations! | wjnc wrote: | Best thing I've ever read on PCA is Madeleine Udell's PhD-thesis | [1]. It extends PCA in many directions and shows that well-known | techniques fit into the developed framework. (Was also impressed | with a 138 page thesis in math that is readable as well. Quite | the achievement.) | | [1] https://people.orie.cornell.edu/mru8/doc/udell15_thesis.pdf | Bukhmanizer wrote: | It's kind of crazy that so many people have read this thesis, | but it's really good. I came across it independently a few | years ago when I was trying to understand some stuff, but ended | up saving it as a reference because I liked it so much. | isoprophlex wrote: | This is some hot stuff! Thanks for sharing. Very lucid writing, | clearly she has some deep understanding of the subject matter | to be able to write that down so eloquently | flashfaffe2 wrote: | Indeed, this seems worth a deep read as this especially address | main PCA shortcomings ( heterogeneous data, non numerical | data,.etc...). Thanks mate I've definitely find a way to keep | myself busy this weekend. | nerdponx wrote: | I'm not sure this is an explanation as much as an introductory | demo. Nice visualizations though. ___________________________________________________________________ (page generated 2022-10-29 23:00 UTC)