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Lior Pachter

Whereas @jameszou.bsky.social's approach to contrastive PCA has a parameter alpha (that can be difficult / impossible to choose), maximizing the RQ (we call this ρPCA) is straightforward, and produced much better results. We show this with many examples. 4/

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Lior Pachter

ρPCA is super useful in anytime one wants to examine differences in variance (rather than just the mean), while performing dim. reduction. Our preprint gives an example using single-cell RNA-seq: we find differentially variable genes (rather than differentially expressed). 5/

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1 прямых ответов · 10 сообщений

Lior Pachter

The fundamental flaw with @jameszou.bsky.social's heuristic contrastive PCA is a subtraction of covariance matrices (which many not be +ve semidefinite!). Even worse is differential robust PCA (drPCA) by Eric Xing which subtracts data matrices 😱. Unfortunately Var(X-Y) = Var(X+Y)... 6/

Ответ для Lior Pachter
Lior Pachter

We found the field as a whole (contrastive PCA) to consist of heuristics layered on heuristics, and in this case it turns out doing the math right really matters. There are of course non-linear contrastive methods but ρPCA is interpretable which can matter a lot 7/

Ответ для Lior Pachter
Lior Pachter

The ρPCA method is implemented in an easy to use Python package github.com/pachterlab/r... Quick to install. Fast. We now use it routinely whenever engaging in exploratory data analysis. 8/

GitHub - pachterlab/rhopcaContribute to pachterlab/rhopca development by creating an account on GitHub.github.com
Ответ для Lior Pachter
Lior Pachter

In Part II, we develop ρPCA in two ways: adding kernel weighting (from spatial PCA), and also operating in the space of basis coefficients (from functional PCA). The former is great for spatial analysis, the latter for time series. 9/

Ответ для Lior Pachter
Ответ для Lior Pachter
Lior Pachter

The contrastive spatial analysis is incredibly powerful. Examining a colorectal spatial single-cell RNA-seq sample (Visium HD) as target with a matched normal (non-spatial) as background, we are able to delineate tumor cells, and find interesting and relevant gene programs. 11/

Ответ для Lior Pachter
Lior Pachter

Particularly powerful here is the approach to "integrate" spatial data with non-spatial controls. Moreover, since k-ρPCA (the k is for kernel) is a variant of ρPCA it is efficient, which is non-trivial. We are able to process very large datasets easily (e.g. Visium HD). 12/

Ответ для Lior Pachter
Lior Pachter

Functional PCA has a long history dating back to the 1990s. I think the contrastive version we introduce via the Rayleigh quotient is going to be very useful. We showcase the power on a bulk RNA-seq time series, finding relevant and interesting differentially variable genes. 13/

Ответ для Lior Pachter
Lior Pachter

Thus, ρPCA, k-ρPCA, f-ρPCA are immediately useful across a wide variety of applications. Moreover, they can be combined (e.g. kernel weighted PCA on basis coefficients). The interpretability is especially useful in biology, but we expect also in other scientific domains. 14/