you can see that in the first componentall features have the same sign (it' negativebut as we mentioned earlierit doesn' matter which direction the arrow points inthat means that there is general correlation between all features as one measurement is highthe others are likely to be high as well the second component has mixed signsand both of the components involve all of the features this mixing of all features is what makes explaining the axes in figure - so tricky eigenfaces for feature extraction another application of pca that we mentioned earlier is feature extraction the idea behind feature extraction is that it is possible to find representation of your data that is better suited to analysis than the raw representation you were given great example of an application where feature extraction is helpful is with images images are made up of pixelsusually stored as redgreenand blue (rgbintensities objects in images are usually made up of thousands of pixelsand only together are they meaningful we will give very simple application of feature extraction on images using pcaby working with face images from the labeled faces in the wild dataset this dataset contains face images of celebrities downloaded from the internetand it includes faces of politicianssingersactorsand athletes from the early we use grayscale versions of these imagesand scale them down for faster processing you can see some of the images in figure - in[ ]from sklearn datasets import fetch_lfw_people people fetch_lfw_people(min_faces_per_person= resize= image_shape people images[ shape fixaxes plt subplots( figsize=( )subplot_kw={'xticks'()'yticks'()}for targetimageax in zip(people targetpeople imagesaxes ravel())ax imshow(imageax set_title(people target_names[target]dimensionality reductionfeature extractionand manifold learning