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What's the difference between Locality Preserving Projection (LPP) and Principal Component Analysis (PCA)?

This is our data. It's a 3D plot. Here I use LPP and PCA to reduce the 3D data to 2D data. It gives different results. I know that PCA reduces the dimension on maximum variance, but what about LPP?

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Locality Preserving Projection (LPP)

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Principal Component Analysis (PCA)

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As you note in your question, PCA attempts to reduce dimensionality while maximizing variance accounted for. LPP on the other hand attempts to reduce the number of dimensions while maximizing a sense of nearness to one's neighbors.

I located the following website (https://notebook.community/jakevdp/lpproj/Example) which appears to give a nice explanation with some sample code in Python.

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    $\begingroup$ So LPP and PCA are almost the same, but LPP is slightly better than PCA because LPP remove outlisers? $\endgroup$
    – euraad
    Apr 10, 2023 at 8:01
  • $\begingroup$ They are accomplishing similar goals: dimension reduction. And though I'd rather someone with more expertise with LPP speak to that specifically, I can confirm that PCA can be very strongly influenced by outliers in the data. $\endgroup$
    – Gregg H
    Apr 10, 2023 at 12:27
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    $\begingroup$ My goal is to remove outliers and separate the classes from each other as much as possible. I know there exist LDA. I'm using it, it's very good. But I need something better. $\endgroup$
    – euraad
    Apr 10, 2023 at 12:36
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    $\begingroup$ I want to reduce multidimensions to 2D. And hopefully, the data would be like round little balls on the screen. $\endgroup$
    – euraad
    Apr 10, 2023 at 12:38
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    $\begingroup$ Gregg, I think I found what I'm looking for - Independent Component Analysis. $\endgroup$
    – euraad
    Apr 10, 2023 at 14:39

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