The incident happened between 9.50pm and 10.05pm on a service from Glasgow Central Station on Saturday February 9.
A man on the train reportedly used his phone to take pictures of the woman in the aisle.
She was alerted to the incident by a female passenger and challenged the suspect who left the train at Clarkston station.
British Transport Police (BTP) believe he originally intended to travel to East Kilbride.
Officers are now appealing for information from anyone who witnessed the incident, including the passenger who spoke to the woman.
The man is described as white, aged between 40 and 50, of average build and wearing a light coloured baseball cap, a khaki green jacket, a green scarf and blue jeans.
BTP can be contacted by text on 61016 or calling 0800 40 50 40, quoting reference number 727 of 09/02/2019.