It's hard to say. Recently there have been more and more issues involving gang related violence within the city. Over the summer there were a few targeted hits which occurred in public places or residential areas, not exactly poor places either. I believe one man was killed in a shoot and run incident outside his nice residential home/mansion. Along with gang violence, there is also the issue of homelessness. Which, relates to drug use, beatings etc.
However, other than that, it's not too violent. It just depends on where you are in the city. The homeless usually reside in the Downtown East Side which is mostly a bubble, away from regular society stores. People generally don't travel down in to that area and don't care much for the homeless. Which, is of course wrong.