Similar to M.I.A.

The music of Sri Lankan and English creator M.I.A. is a revelation when you hear her best pieces for the first time [like the well known 'Bad Girls']. After you hear it though, it's difficult to find anything similar, [other than the older work of 'Sleigh Bells', ie 'Crown on the ground']. While no artist is exactly the same, here are some ideas:

More ambient:
--English creator Forest Swords' album 'Engravings' [2013] is beautiful
--American Laurel Halo's work ['Logic Hour'] [2011] is very interesting
--3 hours of Nordic Ambient Music [ie. artists: Ulf Söderberg, Sephiroth, Empyrium, Tenhi]
--Music of Bali esp. at minute mark 29 and onwards [ie. song "Lüytheon" by László Hortobágyi - Gáyan Uttejak Orchestra, from album Gabevaildenor] is very unique and atmospheric

More indie [Pitchfork-ish, or Joanna Newsom-ish, for lack of a better descriptor]
--The obvious one to mention is perhaps Azealia Banks 'Broke with expensive taste'
--múm's 'Finally we are no one' album, from the experimental Icelandic group Múm
--Minimalist Balmhorea's 'Stranger' album [very instrumental and soothing]

More ancient but very rhythmic:
--Andes native music and the instrumental 'Music from the Andes Vol. 3' [Musica Andina, 2005]
--Persian folk music [ie. "Sarmast" by Shahram Nazeri & Dastan Ensemble, etc]
--Turkish Sufi music [ie Yemen Ellerinde Veysel Karani (Poem of Yunus Emre, a minstrel Sufi wandering, etc...]
--Tibetan folk music [ie. "Harvest Song" by Jhalakman etc]