The subject of a °clause is its °S-argument when the clause is °intransitive and its °A-argument when the clause is °transitive.
It has often been said that "subject" is a concept that cannot be applied cross-linguistically because of the diverse coding strategies (e.g. Foley & Van Valin 1977), but if it is defined disjunctively as the S-argument or the A-argument (as in Dixon 1994), it can be applied in a general sense.
"Subject: A grammatical relation which refers to the grouping of the A and S arguments of a verb. In English, subject pronouns have a special case‐marking in the first and third person, i.e. I, we, he/she, they. Cross-linguistically, prototypical subjects are agents, but subjects may bear numerous other semantic roles." (Tallerman 2011: 295)