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Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or events.
In statistics, naive Bayes classifiers are a family of linear "probabilistic classifiers" which assumes that the features are conditionally independent, given the target class. The strength (naivety) of this assumption is what gives the classifier its name. These classifiers are among the simplest Bayesian network models.
where x is the instance, [] the expectation value, C k is a class into which an instance is classified, P(C k |x) is the conditional probability of label k for instance x, and L() is the 0–1 loss function:
In theoretical terms, a classifier is a measurable function , with the interpretation that C classifies the point x to the class C (x). The probability of misclassification, or risk, of a classifier C is defined as. The Bayes classifier is. Bayes argmax K ∣ {\displaystyle C^ {\text {Bayes}} (x)= {\underset {r\in \ {1,2,\dots ,K ...
In k-NN classification, the output is a class membership. An object is classified by a plurality vote of its neighbors, with the object being assigned to the class most common among its k nearest neighbors (k is a positive integer, typically small). If k = 1, then the object is simply assigned to the class of that single nearest neighbor.
A decision boundary is the region of a problem space in which the output label of a classifier is ambiguous. [1] If the decision surface is a hyperplane, then the classification problem is linear, and the classes are linearly separable. Decision boundaries are not always clear cut. That is, the transition from one class in the feature space to ...
A function of class or -function (pronounced C-infinity function) is an infinitely differentiable function, that is, a function that has derivatives of all orders (this implies that all these derivatives are continuous). Generally, the term smooth function refers to a -function. However, it may also mean "sufficiently differentiable" for the ...
Boundary value problems are similar to initial value problems.A boundary value problem has conditions specified at the extremes ("boundaries") of the independent variable in the equation whereas an initial value problem has all of the conditions specified at the same value of the independent variable (and that value is at the lower boundary of the domain, thus the term "initial" value).