Don't be fooled by the public image of an entertainer. Extroverts are "attentive". Introverts want "attention". Extroverts are focused on the world around them. Introverts are focused on themselves. Extroverts want to make a good impression. Introverts think they really are impressive.
Katy Perry craves attention. INTJ's love being admired because they believe they really are admirable.
This is how it works. Katy's dominant system is her nervous system because she is primarily ectomorphic. The nervous system is interested in maintaining the boundary. The nervous system defines the "self" and is really the ego boundary. Thinking is primarily an introverted activity because it is dealing with information that has already been received from the environment and digested. The sensory system is extroverted because it gathers data "outside (external)" in the environment. Thinking is processing the data that has been stored inside (internal) the brain - it is therefore introverted.
Katy's second function is her orientational system. The orientational system scans the environment looking for "difference". So basically the integrated description of Katy's personality is "searching for identity and status". This makes her hyper sensitive to her position on the hierarchy. She's fearfully looking for anything that would knock her off her pedestal. And she looks for ways to distinguish herself as unique over her competition.
Her lowest functions are a combination of endomorphy (feeling) and mesomorphy (control) She is conflicted in areas of control and attachment. She is very independent and resists control on the one hand but wants independence without struggle.
An extroverts bragging and antics is a little easier to tolerate than the insidious fake smiles, and winks of the introvert in her effort to shore up her image by "acting" sociable.