With security you have to think of animal behaviour too.
The last thing you want is to deactivate the alarm because the cat is a traitor and follows the burglar around lol.
You can combine things, this is very time consuming, but more effective, with pets its always more difficult because you cant predict what they will do, and they can knock things over giving false noise and shock readings.
A heat sensor however is FAR more accurate, and ideal for a pi, pets are completely diff temp to humans, instead of PIR get in FLIR with vector tracing, now even a traitor pet wont give a false negative. The unintentional added bonus is immediate early fire alarm warning. (they are not cheap tho

something like $200 for a dev kit) And the sun shining on a wall can give a false positive too, and last thing u want is to be told your house is on fire, just because the sun is streaming through the windows onto a work surface etc. but you can have bits masked and ignored.
Your alarm range is then a signature of 36.5-37.2'C
Cats are 37.7 - 39.1'C
Dogs are 38.39.2'C
So your device would tell the difference from human and pets, and when its outside those ranges it would take pics and upload them to FTP for you, and send a "unsure" via app to your mobile.
There are other ways, but thats one way i know that can difference between cat / dog / human. But as said be careful of traitor pet, scan the entire image, if it hits a large area of 36-37 u got a burglar.