one of the best explanation of PCA online! thanks.
@tahirkmr
2 жыл бұрын
Nicely explained sir
@artemfediai7206
2 жыл бұрын
The first 2d example is actually the case where pca does not work. The first PC is actually useless to separate the groups. If you ‘understood’ how pca works from this video, you actually don’t, cause you have not noticed the case where it fails
@RasmusBroJ
2 жыл бұрын
Hi Artem. I would politely disagree with you. The aim of PCA is not to find directions that distinguish so it is not a failure that it doesn't. PCA aims to find directions that explain the most variance and does so very nicely. No failures here.
@artemfediai7206
2 жыл бұрын
@@RasmusBroJ I am open for discussion;) > PCA aims to find directions that explain the most variance. This is not the aim of the PCA (not the reason why it is used in practice), this is a somewhat loose definition of it. PCA is used to reduce the dimensionality by rotating the coordinate system in a way that the first axes (PC) points in the direction of the largest variance, second axes is orthogonal to the first PC and again points in the direction of the most vaiance (under the orthogonality contrain) and so on. This is how PCA problem is formulated by words. How is it most often used in practice? For the dimistionality reduction and possibly for the vizualization. The dimensionality reduction is achieved by selecting several PCs starting from the first one. In this case, this is the direction along the axes, which is approx. 45 degree wrt x-axis. And now if you drop the axis which is minus 45 degree (2-nd PC), and project the data onto 1-st PC, the data is not separated. It is not clear that monkeys and humans are different. This is what I mean when I say that PCA fails and the LDA (for instance) has to be used instead. Here, the video that explains what I mean: kzitem.info/news/bejne/l36qk6J_n5F_fpg Please, correct me if I am not right.
@RasmusBroJ
2 жыл бұрын
@@artemfediai7206 I agree 100% that if you want to separate, then LDA is appropriate. There is no way that PCA can separate. There is no classification step in PCA. PCA compresses your data and if you want to separate groups you will have use a classification method. PCA does not fail in any sense of the word I can think of since it doesn't aim to separate. It aims to describe the variation and succeeds in that
@redherring0077
2 жыл бұрын
@@RasmusBroJ this seems true. Pca could separate in some sense as in after components are derived and plotted on a loading plot , you can in certain cases look for clusters and aim to separate. Thought not the objective of pca it has been done in remote sensing research for quite long time.
@soliarv
6 жыл бұрын
Great video. Thank you for sharing it!
@ryanondocin3731
3 жыл бұрын
I believe since you centered the data that your loading vectors are actually capturing the covariance coefficients between the variables and the vectors. Correct me if I'm wrong? I thought when you standardize the data (different units perhaps to obtain z-scores) that we are capturing correlations and when we center the data, covariance is captured
@QualityAndTechnology
3 жыл бұрын
Centering makes the model focus on covariance (with no scaling) or correlation (with scaling to unit standard deviation / standardize). So centering is needed to use PCA as a covariance- or correlation explorer, while to-scale or not-to-scale switch between a correlation or covariance monocle.
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