Michelle Yi was getting ready to teach a pilates class when she was attacked by a woman who appeared to be homeless

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Survivor: Fiji contestant Michelle Yi was beaten with a metal baton early Thursday morning in Santa Monica, Calif. — and police say that her alleged assailant had attacked two other people before her.

Shortly before 6 a.m. on Thursday, Yi arrived at the pilates studio where she taught classes. As her students began to arrive, Yi noticed a disheveled and agitated woman approaching the open front door.

"She was yelling all sorts of things like, 'You stole my identity' and, 'You're a prostitute,'" Yi, 37, tells PEOPLE. "Santa Monica has a homeless problem, and I've dealt with this type of thing before. So I told her, 'Ma'am, you can't be here. You need to leave.'"

But the woman — identified by police as Alexandria Diaz, 25, of Fresno — did not leave. According to Yi, the woman lunged at her with a sharp weapon in one hand and a metal baton in the other. "She stabbed me in the left bicep," says Yi. "And then she hit me on the right hand with the baton. My Apple Watch shattered."

Though Yi tells PEOPLE that she was stabbed, an update from police on Tuesday says Yi was "poked" by the saw blade that officers found on the ground.

Michelle Yi
Credit: Monty Brinton/CBS Photo Archive via Getty Images

Yi says the woman then hit her on the head with the baton. "My face split open," says Yi. "Blood was everywhere."

As the woman ran off, Yi and one of her students tried to call 911, only to get a message that all operators were "currently busy." Minutes later, they flagged down a police car on the street.

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"When we arrived, the suspect was still on the scene," Lieutenant Rudy Flores, a spokesman for the Santa Monica Police Department, tells PEOPLE. "The officers took her into custody and interviewed the victims and the witnesses."

Jessica deBen, Edgardo Rivera, Erica Durousseau, Kenward "Boo" Bernis, Rita Verreos, James Reid, Andria "Dre" Herd, Liliana Gomez, Gary Stritesky, Mookie Lee, Earl Cole, Alex Angarita, Stacy Kimball, Michelle Yi, Cassandra Franklin, Lisette "Lisi" Linares, Yau-Man Chan, Anthony Robinson and Sylvia Kwan
Michelle Yi (bottom left corner) competed on Survivor in 2006
| Credit: Monty Brinton/CBS Photo Archive via Getty Images

Yi was taken to the hospital, where received an X-ray on her hand. "Fortunately, nothing was fractured," she says. She received several stitches on her face.

"I can't say why she attacked me, of all people," says Yi. "But she was a white lady who attacked three people that morning. Another victim was an elderly Asian man who was walking his dog, and the third was also a person of color. I can't prove whether it was racially motivated or not, but she was screaming all sorts of awful things at me. The facts are what they are."

Police confirm to PEOPLE that the woman had allegedly attacked two other people before Yi. "It appeared that she was mentally unstable and maybe off her medication," says Flores. "That probably caused her to do what she did."

The woman has been charged with three counts of assault with a deadly weapon. She remains in police custody. Police have not charged her with a hate crime.

After the attack, Yi says that she sat in the hospital, unsure what to do next. "My parents are in Taiwan," she says. "My siblings live up in the Bay Area. So it was a really lonely place to be."

Yi's attack, which was first reported by reality TV multimedia journalist Murtz Jaffer, has left her reeling. "It was really awful," she says. "It was dark when this happened. I hope that police will have more protections during the hours that we need them most."

Yi, who competed on Survivor in 2006 and became a fan favorite from her season, says that her injuries should heal quickly. "Physically, I'm on the mend," she says. "Emotionally, it's harder, but I should be ok."