A hairstyle that consists of the hair at the temples pulled back into a bun, short ponytail, or just a bow at the back of the head, while the rest of the hair remains flowing loosely. The hair being pulled back can also be tied into braids.
On pixiv, the tag (half up) is often used for any variation of a half updo hairstyle. On the other hand, the tag (princess knot) is often used to denote a more specific kind of half updo where the hair at the temples pull back into a hair bow, hair ribbon, a proper knot, or a ponytail at the very center of the back of the head, and this is also typically indicated by the presence of such a bow or ribbon from the front view. Both tags are almost equally popular on pixiv and are used interchangeably.