The incident happened on a Lanark-bound service from Glasgow Central on Thursday 9 February at about 19:50.
The man sat next to the 18-year-old woman, spoke to her and touched her inappropriately, before a member of the public intervened.
British Transport Police have appealed for the "good Samaritan" to come forward as a witness.
The attacker is described as being white, about 5ft 10ins tall and of a slim build.
He had short brown hair and  was wearing a dark hooded top and dark jogging bottoms with white stripes.
DC Laura McClelland from BTP said: "Intimidating and inappropriate behaviour such as this will not be tolerated and we are working hard to identify the man responsible.
"This was an unsettling experience for this young woman who felt extremely anxious because of his behaviour.
"I would like to thank the member of the public who came to her assistance, it is reassuring that they were willing to help."
A man touched a woman inappropriately on a train in what police described as "an unsettling experience".