How does Tom Cruises relationship with Taka change during the movie?

Algren falls in love with Katsumoto's sister, Taka. Eventually, Algren joins the Samurai's cause in full and helps them battle against the Japanese army forces led by both Omura and Algren's old nemesis Colonel Bagley.The ending reveals that Algren returned to the village to live with Taka, possibly they became a couple.