If you can make a good case, you could potentially group the short stories by whatever common thread you want, including author. You can also subgroup them. Some examples:
Main point in common: author
Secondary point in common: genre
This is the most common, I feel. The best of Stephen King's short-stories will definitely be all in the same genre. But you could have a mix of genres: I own a collection of short-stories by George R. R. Martin which includes fantasy and sci-fi.
When you have two or more genres within, I think it's a nice approach to divide the book in sections so the readers know what to expect and, if they only want to read one genre, they can easily do so.
Main point in common: genre
This is also very common. In this case, the short-stories could all be by the same author or by different authors. If you have more than one tale by author, though, you may still want to not group them by author: that could lead the reader to focus on known authors and overlook the lesser known, I suppose.
Main point in common: characters
The adventures of Poirot or Miss Marple come to mind. This will typically mean the short-stories are in the same genre, but there could be a few which stray away. Imagine that the Adventures of Miss Marple includes a couple of stories of her past, including a tragic love story (no murder or robbery involved).
Such a collection is also a viable way of writing a sort of biography, showcasing important moments in their life.
Main point in common: theme
This can easily get mixed up with the genre, but I find that truly theme based collections tend to go for literary short-stories.
Main point in common: setting
Short-stories written on a specific time frame or location. James Joyce's Dubliners is a collection of short-stories set in Dublin, but of course their aim is to focus on the character of the people who live there. One could have a collection of short-stories set in the Middle Ages in order to convey what life - in different walks of life - was like at the time.
Main point in common: an object
In this example, you'd have an object and all the stories would be connected to it. Say you want to write about the Book of Kells! You start with the story of its creation, then you show how it was moved from place to place, perhaps a story where people go about their normal lives without even realising what a treasure lies there.
I've never seen one like this, but it could work!
Main point in common: photos or images
I've got a book where a photographer challenged different authors to write short-stories inspired by his photos. You got from mystery, to adventure and even a bit of horror and something bordering on fantasy.
In conclusion, find a common point that makes sense and, if need be, group the stories in sections.