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In many cases, such as order theory, the inverse of the indicator function may be defined. This is commonly called the generalized Möbius function, as a generalization of the inverse of the indicator function in elementary number theory, the Möbius function. (See paragraph below about the use of the inverse in classical recursion theory.)
Such indicators have some special properties. For example, the following statements are all true for an indicator function that is trigonometrically convex at least on an interval (,): [1]: 55–57 [2]: 54–61
Indicator function – Mathematical function characterizing set membership; Linear discriminant function – Method used in statistics, pattern recognition, and other fields; Multicollinearity – Linear dependency situation in a regression model; One-hot – Bit-vector representation where only one bit can be set at a time
CORDIC (coordinate rotation digital computer), Volder's algorithm, Digit-by-digit method, Circular CORDIC (Jack E. Volder), [1] [2] Linear CORDIC, Hyperbolic CORDIC (John Stephen Walther), [3] [4] and Generalized Hyperbolic CORDIC (GH CORDIC) (Yuanyong Luo et al.), [5] [6] is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots ...
If C xy is less than one but greater than zero it is an indication that either: noise is entering the measurements, that the assumed function relating x(t) and y(t) is not linear, or that y(t) is producing output due to input x(t) as well as other inputs. If the coherence is equal to zero, it is an indication that x(t) and y(t) are completely ...
Given the binary nature of classification, a natural selection for a loss function (assuming equal cost for false positives and false negatives) would be the 0-1 loss function (0–1 indicator function), which takes the value of 0 if the predicted classification equals that of the true class or a 1 if the predicted classification does not match ...
In particular see "Chapter 4: Artificial Neural Networks" (in particular pp. 96–97) where Mitchell uses the word "logistic function" and the "sigmoid function" synonymously – this function he also calls the "squashing function" – and the sigmoid (aka logistic) function is used to compress the outputs of the "neurons" in multi-layer neural ...
In mathematics, a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals. Informally speaking, a step function is a piecewise constant function having only finitely many pieces. An example of step functions (the red graph).