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In machine learning, one-class classification (OCC), also known as unary classification or class-modelling, tries to identify objects of a specific class amongst all objects, by primarily learning from a training set containing only the objects of that class, [1] although there exist variants of one-class classifiers where counter-examples are used to further refine the classification boundary.
An element x of K is an S-unit if the principal fractional ideal (x) is a product of primes in S (to positive or negative powers). For the ring of rational integers Z one may take S to be a finite set of prime numbers and define an S-unit to be a rational number whose numerator and denominator are divisible only by the primes in S.
A high-degree polynomial can be wiggly, so that it can fit a given set of training points well. But one can expect that the classifier will make errors on other points, because it is too wiggly. Such a polynomial has a high capacity. A much simpler alternative is to threshold a linear function.
Today's deep neural networks are based on early work in statistics over 200 years ago. The simplest kind of feedforward neural network (FNN) is a linear network, which consists of a single layer of output nodes with linear activation functions; the inputs are fed directly to the outputs via a series of weights. The sum of the products of the ...
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A simple unit is one which represents a single condition without any qualification. A composite unit is one which is formed by adding a qualification word or phrase to a simple unit. For example, labour-hours and passenger-kilometer. Unit of analysis and interpretation: units in terms of which statistical data are analyzed and interpreted.
The idea of the proof of the class number formula is most easily seen when K = Q(i).In this case, the ring of integers in K is the Gaussian integers.. An elementary manipulation shows that the residue of the Dedekind zeta function at s = 1 is the average of the coefficients of the Dirichlet series representation of the Dedekind zeta function.
Equivalently, for any given class number, there are only finitely many imaginary quadratic number fields with that class number. Also in 1934, Heilbronn and Edward Linfoot showed that there were at most 10 imaginary quadratic number fields with class number 1 (the 9 known ones, and at most one further).