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Why did Columbes think he had arrived near Japan?

This question came to our mind as a long discussion in chat between some users over ELU including me and we thought to post the question here. Wikipedia states he thought he had arrived Japan.

In his first journey, Columbus visited San Salvador in The Bahamas (which he was convinced was Japan), Cuba (which he thought was China) and Hispaniola (where he found gold).

That made us think, what made him think so? In the mean time, Cerberus came up with a helpful map of his journey, but we could not conclude anything from here. So does anybody have any information on this? We would really like to know.

The Map is uploaded separately for the users convenience.

Columebes Journey overview