Does "reinventing the wheel" have negative or positive connotation?

I've always assumed that the expression "reinventing the wheel" meant something negative. For me it means doing something that has already be done without making any improvement.

However, a few times I've seen the expression use in a positive way too. For example, in this article, it's written:

Eminem's progressive rap style has raised the bar for Hip-Hop lyricism across the board. [...] he's continued to reinvent the wheel, putting his life on display, through a bevy of syllable-heavy, metaphor-driven cuts.

So it's clearly meant as a praise. Is this usage correct?

Nice catch.

My first thought was, why not? Reinvention can be a good thing, if you make incremental improvements (in the world of clichés, I believe that's called building a better mousetrap).

I wondered if maybe the idiom could be used positively or negatively, depending on the surrounding words. For example, I'd consider the expression:

Don't reinvent the wheel.

to be negative, as you describe. However, the phrase:

...continues to reinvent the wheel.

might have positive connotations, suggesting perpetual improvements. So, I looked for some examples. I did find this one:

The artist continually reinvents the wheel — constantly striving for a sublime composition of balance, harmony and refinement.

but the vast majority of the findings were indeed negative:

The idea behind design patterns is to not continually reinvent the wheel.

Moreover, lack of interchange with other teams also often leads researchers to continually reinvent the wheel.

Clients don't want to pay for suppliers to continually reinvent the wheel.

The more I thought about it, the more I wondered if the writer didn't mean to say:

Eminem has continued to reinvent himself, putting his life on display, through a bevy of syllable-heavy, metaphor-driven cuts.

Reinvention of the wheel seems to be a bad thing – a waste of time – but reinvention of self seems to be associated with quests to remain relevant, or on top of your game.

I don't know if I'd go so far as to call your cited usage incorrect, but I don't think an editor's call to maybe strive for a more apt metaphor would be out of order.

Negative connotation. Invention is creation of something new. Re-creating something already known is wasteful.

Positive version is "building a better mousetrap." The difference being that you are improving the known item.

In this context, reinventing the wheel implies that he's producing something new every time. Yes, it's still a wheel, but it's fancier or faster or lighter or heavier. It's a new style. Think about how few basic plots there are for stories. There's at least one well-known book that claims there's only 100. That means that every novel, play, movie, and short story that you read is a specific example of one of those 100 wheels. Every one of them reinvents a wheel. Sometimes the reinventions are boring, but sometimes they're interesting. Although most of the time reinventing the wheel means that you're wasting your time doing something that's already been done, sometimes, as in the case of this sentence, it's praise for coming up with a new twist on an old theme.

Personally, I wonder whether the author used the idiom mistakenly or cynically.

Reinventing the wheel is definitely negative, meaning coming up with something long known by everyone, common and standard, and present it as if it was something groundbreaking and new, or putting a lot of work and research into coming up with a well known result.

There's an engineer's proverb/joke concerning this:

A week spent in the laboratory can save you from good two hours of visit to the library.

In this case, considering Eminem is not very groundbreaking but owes his massive popularity to enormous marketing campaigns, each new album is reinventing the wheel: a massive marketing campaign to promote a "yet another of the same" as "the completely new and revolutionary". Whether this was a veiled intent of the author to slip personal opinion through censorship of the editors (who would definitely reject a more critical article - lots and lots of dollars depend on that!) or simply the author appeared clueless about the real meaning of the idiom will probably never be known.