let' come back to the specific case of pcathough we introduced the pca transformation as rotating the data and then dropping the components with low variance another useful interpretation is to try to find some numbers (the new feature values after the pca rotationso that we can express the test points as weighted sum of the principal components (see figure - figure - schematic view of pca as decomposing an image into weighted sum of components herex and so on are the coefficients of the principal components for this data pointin other wordsthey are the representation of the image in the rotated space dimensionality reductionfeature extractionand manifold learning