So Master Yi is physical DPS carry. That means, you must build him for AD pwnage, or Attack Speed/ Crits, with bunch lifesteal items. Right?

Wrong. You maybe heard about AP Yi. I admit, he is fun. He shines greatly late game, when he can tank basically everything with additional 350 (!) armor/MR and bout 1,5k heal. Still, he is not killing machine, unless enemy team will decide to feed you hard, and then not surrender. But what if we combine these two ways?

17/8/3 in first match and quadra kill. That's what I got.

Pros:
-Almost unable to counter, due to splitting dmg into magic and phys,
-Shines throughout entire game (maybe slightly less later, until you'll get Banshee),
-WAY less item dependant,
-All items build up from cheap components (in opposite to bloody BF Swords),
-Still huge dmg,
-Partially splits dmg to multi targets (Alpha Strike),
-When close to death, can always meditate, which will stop all-but-ultranukes (and kill another 2 targets afterwards),
-All usual Yi pros (immune to slows, instant c/d reset, super-pusher);
Cons:
-Still super vulnerable to CC,
-Need initiation,
-In theory, Rammus with 250 MR and Armor will still be annoyance (Have you seen any tank with that high MR and Armor?);

Good ones:
Cleanse: Removes CC, allowing you to GTFO faster than Fiddle can say "Omgwtf"

Flash: Walls are not a obstacle anymore. Plus you just may wanna position yourself closer to the running enemy sometimes.

Exhaust: Can shut down single target pretty well, and after the changes done to it (dmg reduction instead of blinding), it is useful even on Evelynn, or Ryze.


Considerable:
Teleport: For early game shopping, and late game jumping around the map. Kinda useful.

Ignite: Helps a lot early game, and pisses off tanks late game.

Greater Mark of Desolation: +1.67 armor penetration
Still, most of your dmg will come from autoattacks. And MR will be countered by Archaic Knowledge for tanks (15% magic pen), and Malady for everyone else (decreasing MR per hit, even below 0).
Greater Seal of Clarity: +0.1 mana regen / 5 sec. per level (1.8 at champion level 18)
Yea, you will use abilities way more than in regular build. You need mana regen, and these seals are perfect for that. If you really need that additional hp at the beginning, go ahead. But you will suffer later.
Greater Glyph of Focus: -0.65% cooldowns
Cdr is always welcome. But why flat? Well, the "perlevels" will be better when you hit lvl 14. Yes, they're that time consuming to warm up. Plus, later on you should get enough cdr from Highlander, so you need runes more at the beginning.
Greater Quintessence of Fortitude: +32.4 health
Flat HP's. Will grant you almost 100 more hp at start, witch is always useful, and will fix your early squishiness kinda nice.

You shouldn't take regular 9/0/21, or 21/0/9. Not in this build. I focused on what do I need, instead of going "good ol' way". If you dislike it, experiment on your own. Or take this bloody 9/0/21 if you have to.

Not a lot of innovation here. Wuju Style is still to be mastered first. Alpha Strike should follow as it will be nice nuke later on. Meditate is last, but only because something had to be. But you can experiment with leveling both at once. And no, you MUST take Meditation, you cannot take 2nd Alpha at lvl 4. This will save your ***, that temp defense abilities is not to underestimated.

Now we're making it to the whole point. So take your places and listen (or read to be more precise).

Meki Pendant:
Additional mana regen boost at the beginning. Pretty much self explanatory.

Boots:
Boots will help you getting these early kills, or avoid allowing enemies get them.

Stinger:
Att speed plus cdr for reasonable price and builds up to "big" item. Nothing to discuss IMHO.

Mobility Boots:
My choice, you can take what you want. But in battle you will use Highlander, same for att speed.

Malady
Ap, att speed and decreasing mr on target with each hit. Perfect hybrid item.

Nashor's Tooth:
True hybrid item. Att speed, AP, cdr and mana regen. Great thing to take.

Hextech Revolver and Vampiric Scepter:
You will probably need that lifesteal and spellvamp for staying in fight. And they build to another item.

Guinsoo's Rageblade:
Pretty cool item. You've probably seen it often on Akali, Nid, or Jax, but believe me, it fits perfectly. Nice AD and AP, plus growing effectiveness while in combat. Could it be better?

Hextech Gunblade:
Time to finish it. Spellvamp and lifesteal will give you way more durability. AP and AD will grant you extra dmg. And mean active will piss single target off and immobilize him for around 40 secs in his base.

Wit's End:
After patch, it deals magic dmg per hit no matter what. You may hit Akali and it will trigger. New MR per hit feature just makes this item shines brighter. Yet, I overlooked it for Malady, coz of MR removing feature. So thread this as considerable 6th item.

Grand Finale:
As much as all previous items were a must, here you just can take what you want. Wanna keep that legendary all the time? Take Guardian Angel. Wanna some more health and even more chasing abilities? Take Frozen Mallet. Wanna good all-around item that will make you more durable? Take Banshee's Veil. It's all up to you now.

Gameplay as a hybrid Yi won't differ much from usual one. Enemies are alone? Go gank them with teammates. They're all 5 pushing mid? Hide in side, and let your team lower them to around half of HP, then strike. That's how you get quadra's, you're NOT a Rambo. You can't solo entire team. Most likely.
One important thing to keep in mind - your meditation will be extreme viable escape card late game. 350 armor and MR, plus fast HP restoration? That allows you to do sick comebacks, and pull of kills that were supposed to be out of your range. Use it. Even two, or three times when you'll get cooldowns refresh from Highlander.

Second build I added. After a bit of theorycrafting I realized, that why not? Cloth builds into Mared's, where additional AP after short while will clear creeps in a blink. Not yet tried, but should work fine.

Hope you enjoyed it. I'd strongly recommend trying this build out if you have Yi, it is just fun. :P Please leave constructive feedback, both positive and negative. And keep in mind, this is my first build. So don't be harsh, will ya?

And special thanks to Crazy Smurf for suggestion. Unless it will fail me, but then there is person to blame. :P