While (1) and(2) can be acquired directly from the corpus, (3) involves optimization, since the matrix (3) is supposed to account for the verb's disambiguating effect on all its subjects.
pLF proposes to learn matrices via regression problems such as the following (Guevara, 2010), where subj(v) comprises the subjects seen with the verb v: the verb's subject matrix is learned as the matrix which, multiplied with a subject noun vector, best predicts the noun-verb phrase vector.