Why is Master Yi labelled as an assassin?

Correct me if I'm wrong, but aren't assassins supposed to have burst? Yi doesn't really have this. I think a more appropriate term is hyper-scaling dps champ who also gets cooldowns reduced on kills/assists. He's essentially the AD version of Katarina (minus the burst). Having said this, Master Yi is in kind of a weird spot right now. He's played as an assassin, but due to his lack of burst, his early game is extremely weak. Since Master Yi is also kind of a bruiser (let's face it, he is usually your front line), I think we should give him more bruiser stats (increase his base HP and defenses, and/or HP and def per level). In exchange for this, we make his early game a little bit weaker, but he will still be just as strong late game. TLDR, turn Master Yi into a bruiser that scales into late game. Assassin Yi is too weak to carry, but late game bruiser Yi is an absolute monster (kind of like Jax). We should improve bruiser Yi to make him more viable.