"The former selects the most unique and important elements from a set of data, while the latter attempts, in the case of lossy compression, to find a smaller ap

"The former selects the most unique and important elements from a set of data, while the latter attempts, in the case of lossy compression, to find a smaller approximation of the original data set." The compressor finds a smaller approximation of the data by finding the most redundant data, and as a byproduct it also finds the most unique. At least from the description you gave there is no difference between the two. "For example imagine a data set of paintings. Feature extraction might simply identify what color paints were used in each painting. That alone might allow classification of paintings with respect to the painter, style or period. But this would not be an approximation of the original picture, unless you consider resizing a Jackson Pollock into an 8x1 pixel image to be compression." You can and we do use compressors to do exactly that. Take a painting (or a set) as reference and use it to compress other paintings and the greater the compression the more similar the styles are. For an example see: https://www.sciencedirect.com/science/article/abs/pii/S0031320321000510 https://www.sciencedirect.com/science/article/abs/pii/S00313... EDIT: In fact one step in a compressor is feature extraction (usually called modelling) and the other is coding.