"each corresponding to" is correct and usable in written English.
You can use it to refer to two or more things that have a relationship to each other. For example: "The school library has four separate sections, each corresponding to a different subject".
"We've broken the space into four quadrants, each corresponding to one camera," she said.
He had to play his scenes in a blue bodysuit peppered with dots, each corresponding to a different joint.
Customers choose one of four design palettes -- Classic, Minimal, Nature and Culture -- each corresponding to a lexicon of portentous and expensive attributes.
Actions in the minigames, each corresponding to a domestic or international policy topic, affect the ease of playing in the other minigames.
The gadget listens to a crying baby, considers and calculates for 20 seconds or so, then illuminates one of five icons, each corresponding to a distinct physiological or emotional state: "hungry," "sleepy," "uncomfortable," "stressed" or simply "bored".
It offers what resembles an altered map of the London Underground with a cluster of overlapping dots, each corresponding to a form of legal status (for example, "British citizen") or social status ("poor").
A total of 475 samples, each corresponding to one hour of effective fieldwork, were taken.
We model the problem using a sequence of periods, each corresponding to a season.
Are there really that many different names, each corresponding to an different description?
With only four face buttons, each corresponding to a separate phone number, it simplifies the arduous task of remembering, well, four different phone numbers.
Line spectra (peaks) are obtained, each corresponding to a particular element.
