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Dj Joofa
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When Joofa speaks, I STFU. :innocent:
Oh no Fredrik, please no.
Let me give a little more detail. There are two major parts to compression:
(1) Change of basis (axes)
(2) Quantization
When we say that one used say, DCT, then no compression has occurred at that stage as it is just the change of basis (typically matrix multiplication for image data). I.e., we have just changed axes in the multi-dimensional space. Think of it like in 3-D you rotate the co-ordinate axes. We do that so that we align the data along those axes which will help us in:
(1) We either throw away some of those axes that have little data content. Therefore it is very important to de-correlate the axes data, which DCT type transforms do.
Or.,
(2) Even for those axes we keep, we quantize them so that we coarsely define the axis co-ordinates.
Therefore, compression is actually happening in this second stage where we decide to throw away some axes and coarsely quantize some axes.
Hence, it is important to choose those axes which will help us keep a lot of image while throwing away some axes and its data, and for that it is not easy to beat PCA.