If possible don't carry a purse to prevent attracting purse snatchers. Do not put it on the floor or under a seat. Keep it in your lap where you have control of it. Take a serious look at what you carry in your purse and decide what is necessary for your day to day existence. Carry only what you can afford to lose.
Smaller purses are better.
Large purses are easier to spot and grab. Don't fight for your purse or with a purse snatcher. There is nothing in the purse that would be worth the injuries you could sustain. If your purse is grabbed, let it go. Holler and shout to call attention to the purse snatcher, but do no fight with him.