I have a problem with a sentence "A list of items grouped by category". There are two possible ways to understand this sentence:
- (A list of items) that is grouped by category
- A list of (items that are grouped by category)
How to write it correctly?
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I don't think "is" in 1 would be a good choice: if you are grouping a whole, you mean you are grouping its parts; and if those parts are explicitly mentioned, it seems odd to stick the grouping to the whole instead of the parts. If you did this, the fact that "that" comes right after "items" and that the two would be a great fit together would make the sentence awkward.
In 2, are you thinking of a list of items that only includes those items that are grouped by category, which thus leaves out those items that are not grouped by category? That is what the brackets and the that-clause seem to indicate. I find it hard to imagine a situation where you would want to say this.
I'd choose 2, but the type of relative clause is odd. Why not add a comma and change "that" to "which"? The relative clause sounds better as a non-defining clause, since the fact that they are categorised does not limit or define the items for me: it is rather extra information. Whether a participle is defining or not cannot be seen if there is no full clause: that is why you could not see it in "a list of items grouped by category". The comma of a non-defining relative clause is not compulsory with a non-defining participle (I think I am right here, right?).
Let's take Vorrtex's second example:
The part of the picture drawn by me was destroyed by the fire.
(I added "was destroyed by the fire" to put it into a real context.) In this case, "drawn" could belong to either "part" or "picture", so the sentence is ambiguous. There is no way to clear this up without changing the sentence so that "drawn" can only point to one noun:
I drew part of this picture, and [my part | the picture] was destroyed by the fire.
In terms of meaning, whether it is the list that is being grouped or the items that are being grouped, the meaning is the same - grouping the objects written on a piece of paper.
In terms of word choice, the second option seems better, as it is more natural to think in terms of grouping the multiple distinct objects and not the list.