No surprise there. In every close fight, each fighter thinks they won.

I had to rewatch the whole fight in 720p, pause and take notes but i managed to break it down like this:

First round: Shogun wins by an extremely small margin, but takes the round as he had 1 takedown and 1 punch directly to the head while Machida had a bodykick and a couple of punches to the chest, and also, Shogun gave him several legkicks that could be called unanswered
There was also a knee from Lyoto in first round that could have made it an even round depending on preferences.

Second round: Shogun wins the round clearly. Machida doesnt do much more then 3-4 kicks, 1 questionable punch that braced, and 2 kees, while Shogun gives at least 7 kicks that hit target and around 10 hard knees. Some of the kicks where really hard bodykicks that made Lyotos side go purple and red.
There was a failed takedown attempt from Shogun that could maybe pull down his overall performance in the round but there was no question about who got most hurt and it was Machida.

Third round: "Slow" aka very technical round. Hard to say who won clearly but its very possible that Machida won the round by brawling off in the end of the round. He hit Shogun with some hard punches, while Shogun only hit him back with one hard right punch in that exchange. The rest of the round was Shoguns with about 8 landed kicks and a knee. Machida also scored both knee, elbow and a few kicks, but none where really devastating except 1 kick that hit the body straight on. Machidas round in my opinion.

Fourth round: Yellow card to both fighters for stalling in my opinion! Very technical standing up round, like they had an invisible spring between them. Noone scores anything special. Lyoto explodes shortly and punches 2-3 times towards Shoguns head but he is covering up pretty well. Lyoto also scores 1 good body kick in the round. Shogun has another failed takedaown attempt after Lyoto slips momentarliy. Shogun scores abut 4-5 kicks, a couple of headpunches, 2 knees and an elbow to the chin of Machida. In my opinion an even round with advantage to Shogun.

Fift round: Shogun win the round clearly. He scored 4-6 punches to machidas head depending on how you count. He hurt Machida, his lip broke and started to bleed. He landed around 6 kicks and one nice elbow and a knee or two of minor importance. He looked confident and pushed the pace and had Machida backing off all the round. Machida scored 2-3 kicks and a couple of punches that where partly blocked. A knee that was pretty hard too but that was about it. No doubt in my mind that was Shoguns round.

You can see where I am leaning I guess...

(Remember this is my personal view and not an attempt to proove something. The judges are the judges...)

Edit:

Funny how both Kenny Florini and Rashad Evans had the exact same opinion as I have here above on the MMA Live show just out! (29 Oct)

Also, here is a snapshot of the judges scores from ufc 104:


Judges score card UFC 104