As mentioned already, Mīmāṃsakas (at least Kumārila and Somśvara) consider cognition as an activity (karman), and so do Buddhists.
Naiyāyikas and Vaiśeṣikas, on the other hand, regard cognition as a quality of the self. Still, cognition is also defined (e.g., by Bhāṭṭavāgīśvara, NTD 76,9-11 on NS III.1.17) as a kriyā ("action") and it is said to need an instrument, a subject and an object, just like common activities. How can it be? Surely, it helps to remember that cognition (jñāna) is instantaneous (Potter translates it as "judgement") and that qualities in Nyāya-Vaiśeṣika are a heterogeneous list, sharing as only similarities the fact that they inhere in a substance and that they are instantaneous. But kriyā is also often used as a synonym of karman in Nyāya-Vaiśeṣika (see Potter's Encyclopedia, which lists them together). And how can one understand the relation between the cognizing subject (jñātṛ) and his/her judgement as that between a substance and its quality (guṇin/guṇa)?