A few attempted invasions does not an empire make, or else we'd be left with precious few historical states that weren't empires.
A bit late, but edited to add: An empire is a polity, be it a city-state (Rome), a nation-state (England), or an ethnicity (China's revolving cast), who are in control of a significant amount of imperial holdings. An imperial holding is a foreign-occupied area where the local people have only weak or non-existent identity ties to the controlling entity - i.e., they don't consider themselves to be "Ottoman" or "Aztec", they consider themselves to be Farsi or Mixtec under foreign rule. Japan is a clear-cut nation-state, of the sort that the ideal of nation-states was based upon when it was first conceived, and a nation-state can not be an empire, only control one. Japan's biggest claim to empirehood at present are Hokkaido and Ryukyu, and Hokkaido at least is too Japanified to be considered a foreign territory. Besides that, even if both of those are non-Japanese areas under Japanese occupation, that's still not a significant amount of imperial holdings.
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