Probability-theoretic Definition of Category Utility
The probability-theoretic definition of category utility given in Fisher (1987) and Witten & Frank (2005) is as follows:
where is a size- set of -ary features, and is a set of categories. The term designates the marginal probability that feature takes on value, and the term designates the category-conditional probability that feature takes on value given that the object in question belongs to category .
The motivation and development of this expression for category utility, and the role of the multiplicand as a crude overfitting control, is given in the above sources. Loosely (Fisher 1987), the term is the expected number of attribute values that can be correctly guessed by an observer using a probability-matching strategy together with knowledge of the category labels, while is the expected number of attribute values that can be correctly guessed by an observer the same strategy but without any knowledge of the category labels. Their difference therefore reflects the relative advantage accruing to the observer by having knowledge of the category structure.
Read more about this topic: Category Utility
Famous quotes containing the words definition, category and/or utility:
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)
“Despair is typical of those who do not understand the causes of evil, see no way out, and are incapable of struggle. The modern industrial proletariat does not belong to the category of such classes.”
—Vladimir Ilyich Lenin (1870–1924)
“Moral sensibilities are nowadays at such cross-purposes that to one man a morality is proved by its utility, while to another its utility refutes it.”
—Friedrich Nietzsche (1844–1900)