A linear perfume is one that is like a lady dressed in a fur coat wearing nothing underneath who flashes it open revealing everything and strikes the same pose overtime, unafraid to catch cold.
This type of perfume is generally opposed to the kind that offers a pyramidal construction, developing academically in 3 stages........
A fragrance constructed around an olfactory pyramid is like a woman wearing not only a fur coat but a fur hat with more clothing underneath and who starts stripteasing in front of you, starting from the top and slowly working towards the bottom until she reaches those base animalic notes. Some people think that this type of perfume is unpredictable, but it is not. It always ends in the same spot.
Alternative whimsical definitions of the same terms were elaborated earlier on by myself and Sali Oguri from Pink Manhattan in an exchange on MUA in July of 2007,
Sali: You don't always need a choir [3 stages]. Just make them sing louder! :-)[linear]
Marie-Hélène: and hold the same notes longer.
Sali: But now they can sustain notes forever through digital sampling!"[synthetic ingredients]
From The Whimsical Unofficial Dictionary of Perfume Terms by Mimi Froufrou