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Arriving at the most meaningful words eliminating the noise is the hardest when you try to get these working for some real world scenarios.
Also separating documents about unix text processing tools from those about cats, or those about breeds of cats from those about the middle east. Word sense disambiguation.
What would be some real world scenarios? It's unfortunate the author chose a play example in kitty/cat.
One might even look at this matrix and realize that the word “kitty” is pretty closely related to “cat.”

It's not clear to me, how this can be referred from the matrix. Here are the two rows

cat 0 1 0 2 kitty 0 2 0 0

The main thing is that they have a document in common, while neither of them share any docs with "dog" or "pooch". And while "the" also appears in those docs, it seems to be common to every document, so it isn't very informative.