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andrewGhazi committed Oct 9, 2024
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Expand Up @@ -452,7 +452,7 @@ As the name suggests, dimensionality reduction aims to reduce the number of dime

### Principal Component Analysis (PCA)

Principal component analysis (PCA) is a dimensionality reduction technique that provides a parsimonious summarization of the data by replacing the original variables (genes) by fewer linear combinations of these variables, that are orthogonal and have successively maximal variance. Such linear combinations seek to "separate out" the observations (cells), while loosing as little information as possible.
Principal component analysis (PCA) is a dimensionality reduction technique that provides a parsimonious summarization of the data by replacing the original variables (genes) by fewer linear combinations of these variables, that are orthogonal and have successively maximal variance. Such linear combinations seek to "separate out" the observations (cells), while losing as little information as possible.

Without getting into the technical details, one nice feature of PCA is that the principal components (PCs) are ordered by how much variance of the original data they "explain". Furthermore, by focusing on the top $k$ PC we are focusing on the most important directions of variability, which hopefully correspond to biological rather than technical variance. (It is however good practice to check this by e.g. looking at correlation between technical QC metrics and PCs).

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