A stranger claims to know me? What to do?

A man walked up to me and pretended to know me. He talked while walking next to me for about a block on Union Square. I can't remember since this was a few months ago but he pretended that we hung out somewhere. When I said "Sorry I don't know you," or something similar to try to leave, I turned the block and walked away. I thought he might just be crazy or that he mistook me for another girl. He then ran up to me and tried to convince me that I knew him. I said nothing this time and just glanced at him. He got angry and aggressive, saying things about how I looked like I wanted to kill him. He had a friend along with him who told him to forget it since the girl didn't remember. I walked away really quickly and looked back to make sure that he didn't continue to follow me. I went into a close by Barnes&Noble to pick up a textbook and saw him again. He didn't see me but I ran out of that bookstore. I didn't want him yelling at me again.

Then a few weeks later he came up to me again and asked if I remembered him. I again stayed silent and just kept walking. This time I called the police. Two officers came but didn't take my statement because I didn't know his name. They told me that if he approached me a third time, take a photo, and they would be able to do something.
And then last week, he came up to me again. I forgot to take his photo because I was too focused on trying to speed walk away from him.
What should I do? I take Tae Kwon Do but I'm not sure if I can fight him.

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