I am trying to understand how linear discriminant analysis (LDA) is related to principal component analysis (PCA) and k-means clustering method. As an example, here is a comparison between PCA and k-means:

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My question is how LDA is related to PCA and k-means?


I'm by no means an expert in the topic, but it seems that K-means clustering can be viewed as a dimensionality reduction technique, of which LDA and PCA are direct examples. Clustering via K-means seems to uncover the latent structure of data, which essentially results in dimensionality reduction. I'm sure that other people will provide some more advanced answers to this question.

Additionally, I would like to share two references that are relevant to the question/topic and IMHO are rather comprehensive. One reference is a highly-cited research paper by Ding and He (2004) on the relationship between K-means and PCA techniques. Another reference is a research paper by Martinez and Kak (2001), presenting the comparison between PCA and LDA techniques.


Ding, C., & He, X. (2004, July). K-means clustering via principal component analysis. In Proceedings of the twenty-first International Conference on Machine Learning (p. 29). ACM.

Martínez, A. M., & Kak, A. C. (2001). PCA versus LDA. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(2), 228-233.

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    $\begingroup$ See stackoverflow.com/a/29731291/2056067 for an attempt to summarize Ding & He. :-) $\endgroup$ – A. Donda May 30 '15 at 16:25
  • $\begingroup$ @A.Donda: Thank you for the link. :-) Both answers are very nice (+1) and I will re-read them, when I'll have a bit more time. However, I think that particular question belongs to either Cross Validated, or Data Science SE site and, therefore, should be migrated. $\endgroup$ – Aleksandr Blekh May 30 '15 at 18:29
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    $\begingroup$ Maybe so, the line is not very clear for programming-related statistics questions (or vice versa). You can flag the question for moderator attention. DS SE is still in beta though. :) $\endgroup$ – A. Donda May 30 '15 at 23:44

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