One way we might imagine reducing the dimension of this data is to zero out all but a few of these basis vectors.įor example, if we use only the first eight pixels, we get an eight-dimensional projection of the data, but it is not very reflective of the whole image: we've thrown out nearly 90% of the pixels! That is, to construct the image, we multiply each element of the vector by the pixel it describes, and then add the results together to build the image: One way we can think about this is in terms of a pixel basis. This meaning can be understood in terms of combinations of basis vectors.įor example, each image in the training set is defined by a collection of 64 pixel values, which we will call the vector $x$: We can go a bit further here, and begin to ask what the reduced dimensions mean.
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