LDA, PCA and k-means: how are they related? 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:

My question is how LDA is related to PCA and k-means? 
 A: 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.
References
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.
A: LDA & PCA are used just in different circumstances.
Clustering & PCA are unsupervised. LDA is supervised. - here is good explanation of differencies b/w unsupervised & supervised methods.
The main aim of Clustering, as part of EDA, is grouping... or even if outliers are forming Gaussian mixture => Novelty appearance in ds (e.g. compared with another ds). Then you can calc. responces to these generalized groups. But either such grouping will lead to dimensionality reduction or not depends on data themselves. But whether such grouping will lead to dim_reduction or not - depends on case/chance (on data).
PCA (also part of EDA) really aims for dimensionality reduction if you have tooo great quantity of features, extracting Principal Components that input into variety in ds. Also used for outliers removal in pre-modelling stage (as is before modelling dependencies). N.B. Non-Gaussian distributed data causes PCA to fail.
