AP Yi is viable because he hits like a truck with Alpha Strike. He has great farming and laning phase, as he is something similar to AD Katarina: he's a melee but always attacking from distance.
With little mp5 he never runs out of mana. And health isn't a problem, as you can go back, heal, and come back. Or if the other team has not extreme CC or already wasted it, you can heal yourself there.
AP Yi benefits from low cooldowns. Alpha strike can be used every 6 seconds with 40% cdr, Plus you can use it with a Lich Bane to still add more burst damage.
Just by that, it wouldn't be that much viable. But when Highlander comes into action, he can be a beast. The Beast. Someone initiates and you go behind him. Highlander. Autoattack someone, just to proc lichbane. Autoattack a little more or retreat a bit. Then Alpha Strike on a primary target. Autoattack to proc lichbane again. Keep autoattacking if they don't care about you, activate Wuju Style for another Lichbane proc, if they focus you, check out their CC's and Meditate around there or out of battle accordingly. If Meditate inbattle, remember you have another Lichbane proc. Now the thing is: if someone died, which should have happened (because if not most likely you will lose the TF, and you would have lost it anyways being AD) you'll have ALL YOUR COOLDOWNS REFRESHED. Another massive Alpha strike for 700+ x4 AoE damage, plus more lichbane procs.
really find him very similar to Katarina. She's also a beast if someone dies (althrough she only needs assists, Master Yi assist only reduces CD's by 1/2, what is really powerful anyways, but not that great).
Hope this helps people asking for viability of AP Yi. I've played both of them and in TF i find AP to be more usable. Yes, he looses the trademark backdooring from Yi, but he gains great AoE damage and much more survivality and utility from items.
And, for the topic itself, i would say something like:
1.- Sorcerer shoes.
2.- Mejai if you're having a great early game.
3.- Rylai Scepter.
4.- Zhonya's Ring.
5.- Banshee's veil. (Or Archangel staff if you're not getting too much focused)
6.- Lich Bane.
7.- If you din't pick a Mejai, you can get a Deathfire Grasp.
Let's see why those items are good (build may change in order and items accordingly to each one preferences):
1) Sorcerer Shoes: with that and MP runes, you can drop to 0 MR from most people. That will increase Alpha Strike damage by a lot.
2) Mejai: Well, nothing to clarify. Snowball for when you're facerolling.
3) Rylai Scepter: More damage/healing, more HP and a built-in AoE slow with your Alpha Strike. Your survivality gets incredibly more high with this, as well as your chasing capabilities. If you don't find it a really useful slow, pick Rod of Ages instead.
4) Zhonya's Ring: As long as you jump inside the teamfight sreacming "BANZAAAAAAAAAI" you may take lots of profit from it's active. 2 seconds inmunity. Great, you're now just 2-3-4 seconds from another devastating Alpha Strike. His AP boost is hell itself too.
5) Banshee's Veil: Ok, here is the point. I put it on the build in the same place as Archangel. But Archangel also benefits from him, as it gives a chunk of mana. The magic resist and nullifying the first incoming spell (maybe a CC? ) are just awesome. Also, more hp pool.
6) Archangel staff: There are 3 potential items that can improve your mana pool : Banshee, Lich Bane and Archangel itself (There is also Rod of Ages, which could get on Rylai spot if you don't find it useful). That is a really good boost to AP, and literally UNLIMITED POWEEEEERRRR -sorry, wanted to say unlimited mana, but cannot resist the dark side -.
7) Lich Bane: Boosts Archangel Staff. Gives you a nice boost to magic resist (considering it being an offensive item). 80 AP. And the most important thing: The passive that will make you being using an AP build and still hitting autoattacks above 500 damage, which will also help you against MR stackers, as the lichbane proc does physical damage.
8) Deathfire Grasp: It gives more than enough CDR, boosting you up to past 30% cdr with runes and utility masteries at lvl 18. That can also be achieved by getting the golem buff or with blue elixir. There is the mana regen and the sightly AP boost. And the active... which will make you laugh at those tanks that stack health and don't care about MR.
9) Void Staff: If you need to pick this late game (aka everyone on the other team stacking high MR) you could sell your Sorcerer shoes and buy it. Late game movement speed won't be that necessary, and you still have Highlander which gives you "free boots" for 12 seconds, and most TF don't get much longer than that. But 55% magic resist ignore is always a pain in the ass for MR stackers.
Obviously 9/0/21 masteries. Not negotiable.
For runes, MPen reds, as-you-wish yellows (possibly mana regen, but not necessary if you pick any mana regen item) and CDR-per-lvl blues. I would go for Quintessences of flat Hp.
Disclaimer: Yes, that build is expensive, but Yi can get few kills early game (both as AD or AP) and he's a great farmer, still better with AP (6 minions coming, Alpha first, 4 death, lichbane proc, 5 death, and autoattack down the last one).
Give him a try (and don't call someone noob for asking for it!)
P.S: Althrough is nice that if going AP, telling it to your teammates at champ selection screen