The incident occurred around 10 p.m.in the No. 12 auto of the 16-car bullet train as it was traveling between Shin-Yokohama and Odawara stations on the Tokaido Shinkansen Line.
The 22-year-old assailant, named by authorities as Ichiro Kojima, was arrested late Saturday after police stormed the train when it made a stop at Odawara station west of Tokyo.
The 22-year-old suspect told investigators that he was irritated and picked the targets at random.
News reports said two women who appeared to be in their 20s were wounded but their injuries were not life-threatening. At some point, Kojima then overpowered and stabbed Umeda, who tried to stop him.
Under questioning, Kojima admitted to the allegations, saying he attacked the people because he was feeling frustrated and that the victims were chosen at random, according to the Kanagawa police. Some were holding removed seats, apparently to protect themselves.
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A female passenger told NHK: "Everyone fled and fell like one domino falling after another".
According to the Kanagawa prefectural police and other sources, three passengers on the train were attacked.
"I have been always anxious about him", his grandmother said in a telephone interview early Sunday.
The stabbings had occurred in the 12th carriage of the 16-car train service Nozomi 265, which runs between Tokyo and Shin-Osaka stations - considered to be one of the world's busiest train routes. She had been calling his mobile phone recently but could not reach him.
The train was carrying about 880 passengers when the attack took place.
The fire, which also occurred on the Tokaido Shinkansen Line, prompted operators to increase station patrols and install security cameras on trains, though checking baggage has been viewed as impractical due to the huge numbers of passengers.