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Mathematical function characterizing set membership
In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all
Indicator_function
Indicator function of positive numbers
notation: H ( x ) := [ x ≥ 0 ] {\displaystyle H(x):=[x\geq 0]} An indicator function: H ( x ) := 1 x ≥ 0 = 1 R + ( x ) {\displaystyle H(x):=\mathbf {1}
Heaviside_step_function
field of mathematics known as convex analysis, the indicator function of a set is a convex function that indicates the membership (or non-membership) of
Indicator function (convex analysis)
Indicator_function_(convex_analysis)
Indicator function of rational numbers
In mathematics, the Dirichlet function is the indicator function 1 Q {\displaystyle \mathbf {1} _{\mathbb {Q} }} of the set of rational numbers Q {\displaystyle
Dirichlet_function
Linear combination of indicator functions of real intervals
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
Step_function
Method of mathematical integration
measurable function is the difference of two integrals of non-negative measurable functions. To assign a value to the integral of the indicator function 1S of
Lebesgue_integral
Notion from the theory of entire functions
the indicator function of an entire function indicates the rate of growth of the function in different directions. Let us consider an entire function f
Indicator function (complex analysis)
Indicator_function_(complex_analysis)
Inverse trigonometric functions. See also Gudermannian function. Most special functions are transcendental. Indicator function: maps x to either 1 or
List of mathematical functions
List_of_mathematical_functions
Limit of sequence of smooth functions
mathematics), the Laplacian of the indicator is obtained by letting the Laplace operator work on the indicator function of some domain D. It is a generalisation
Laplacian_of_the_indicator
Mathematical function having a characteristic S-shaped curve or sigmoid curve
related to Sigmoid functions. Step function – Linear combination of indicator functions of real intervals Sign function – Function returning minus 1,
Sigmoid_function
Pseudoscientific personality questionnaire
organize the Jungian cognitive functions to make it more accessible.[failed verification] As a psychometric indicator, the test exhibits significant deficiencies
Myers–Briggs_Type_Indicator
Special mathematical function defined as sin(x)/x
lattice) is a function whose Fourier transform is the indicator function of the Brillouin zone of that lattice. For example, the sinc function for the hexagonal
Sinc_function
Function returning one of only two values
Pseudo-Boolean function Boolean-valued function Boolean algebra topics Algebra of sets Decision tree model Indicator function Signed set "Boolean function - Encyclopedia
Boolean_function
Concept in machine learning
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
Loss functions for classification
Loss_functions_for_classification
Generalized function whose value is zero everywhere except at zero
x+\varepsilon ]}} is the indicator function of the interval [ x − ε , x + ε ] . {\displaystyle [x-\varepsilon ,x+\varepsilon ].} The delta function is expedient in
Dirac_delta_function
Function that outputs either true or false
applied disciplines, a Boolean-valued function may also be referred to as a characteristic function, indicator function, predicate, or proposition. In all
Boolean-valued_function
Average value of a random variable
utility function. It is possible to construct an expected value equal to the probability of an event by taking the expectation of an indicator function that
Expected_value
Generalization of the indicator function for classical sets in fuzzy logic
In mathematics, the membership function of a fuzzy set is a generalization of the indicator function for classical sets. In fuzzy logic, it represents
Membership function (mathematics)
Membership_function_(mathematics)
Topics referred to by the same term
characteristic function may refer to: The indicator function of a subset Characteristic function (probability theory) The characteristic function of a cooperative
Characteristic_function
Function that returns its argument unchanged
itself is necessarily the identity map. Identity matrix Inclusion map Indicator function Knapp, Anthony W. (2006). Basic algebra. Springer. ISBN 978-0-8176-3248-9
Identity_function
Probability theory and statistics concept
{\displaystyle \operatorname {P} (A\mid {\mathcal {G}})=1_{A}} , the indicator function (defined below). Let X : Ω → E {\displaystyle X:\Omega \to E} be a
Conditional probability distribution
Conditional_probability_distribution
Mathematical function for the probability a given outcome occurs in an experiment
a set of probability zero, where 1 A {\displaystyle 1_{A}} is the indicator function of A {\displaystyle A} . This may serve as an alternative definition
Probability_distribution
Concept in mathematics
{\displaystyle x\in \Omega } , where 1 E {\displaystyle 1_{E}} denotes the indicator function of a subset E ⊆ Ω {\displaystyle E\subseteq \Omega } and L ( f , t
Layer_cake_representation
Mathematical notation
}}\end{cases}}} In other words, the Iverson bracket of a statement is the indicator function of the set of values for which the statement is true. The Iverson
Iverson_bracket
Type of number sequence
then this criterion fails. As a counterexample, take f to be the indicator function of some equidistributed sequence. Then in the criterion, the left
Equidistributed_sequence
Branch of functional analysis
measure on the Borel sets E of R. In the above formula 1E denotes the indicator function of E. These measures νξ are called the spectral measures of T. If
Borel_functional_calculus
Topics referred to by the same term
Look up indicator in Wiktionary, the free dictionary. Indicator may refer to: Environmental indicator of environmental health (pressures, conditions and
Indicator
Set with exactly one element
groups are terminal in that category. Let S be a class defined by an indicator function b : X → { 0 , 1 } . {\displaystyle b:X\to \{0,1\}.} Then S is called
Singleton_(mathematics)
Function with a repeating pattern
ISBN 978-0-486-63317-6. For some functions, like a constant function or the Dirichlet function (the indicator function of the rational numbers), a least
Periodic_function
Function that attains finitely many values
functions. Formally, a simple function is a finite linear combination of indicator functions of measurable sets. More precisely, let (X, Σ) be a measurable space
Simple_function
Probability that random variable X is less than or equal to x
A } {\displaystyle 1_{\{A\}}} denotes the indicator function and the second summand is the survivor function, thus using two scales, one for the upslope
Cumulative distribution function
Cumulative_distribution_function
Every set is smaller than its power set
Each row records the values of the indicator function of the set corresponding to the column. The indicator function of B {\displaystyle B} coincides with
Cantor's_theorem
Counting technique in combinatorics
obtained using indicator functions (also known as characteristic functions). The indicator function of a subset S of a set X is the function 𝟏S:X→{0,1}𝟏S(x)={1x∈S0x∉S
Inclusion–exclusion_principle
Mathematical set of all subsets of a set
equivalent to the indicator function IA, and {0,1}S as the set of all the functions from S to {0, 1} consists of all the indicator functions of all the subsets
Power_set
of S is in T, and zero if it is not. An indicator vector is a special (countable) case of an indicator function. If S is the set of natural numbers N {\displaystyle
Indicator_vector
Indicator in technical analysis
The relative strength index (RSI) is a technical indicator used in the analysis of financial markets. It is intended to chart the current and historical
Relative_strength_index
Basic integral in elementary calculus
the indicator function of the rational numbers in [0, 1]; that is, Iℚ takes the value 1 on rational numbers and 0 on irrational numbers. This function does
Riemann_integral
Function spaces generalizing finite-dimensional p norm spaces
integrable simple function f on S given by f=∑j=1naj𝟏Aj, where aj are scalars, Aj∈Σ has finite measure and 𝟏Aj is the indicator function of the set Aj,
Lp_space
Abstract data type for storing distinct values
type theory, sets are generally identified with their indicator function (characteristic function): accordingly, a set of values of type A may be denoted
Set_(abstract_data_type)
Type of mathematical function
log-concave functions are the 0-1 indicator functions of convex sets (which requires the more flexible definition), and the Gaussian function. Similarly
Logarithmically concave function
Logarithmically_concave_function
Mathematical term
} . For r ∈ R {\displaystyle r\in \mathbb {R} } , the indicator function on r is the function 1 r : R → { 0 , 1 } {\displaystyle \mathbf {1} _{r}\colon
Index_set
Evolutionary algorithm
← ( 1 − c c ) ⏟ discount factor p c + 1 [ 0 , α n ] ( ‖ p σ ‖ ) ⏟ indicator function 1 − ( 1 − c c ) 2 ⏞ complements for discounted variance μ w m k +
CMA-ES
Integral expressing the amount of overlap of one function as it is shifted over another
(μ∗ν)(A)=∫𝐑d×𝐑d1A(x+y)d(μ×ν)(x,y), where A⊂𝐑d is a measurable set and 1A is the indicator function of A. This agrees with the convolution defined above when μ and ν
Convolution
Numeric stand-ins in regression analysis
descriptions of redirect targets Indicator function – Mathematical function characterizing set membership Linear discriminant function – Method used in statistics
Dummy_variable_(statistics)
Kind of mathematical function
{\displaystyle A\notin \Sigma ,} one can construct a non-measurable indicator function: 1 A : ( X , Σ ) → R , 1 A ( x ) = { 1 if x ∈ A 0 otherwise , {\displaystyle
Measurable_function
this sense, the term predicate has the meaning of a mathematical indicator function. If p1 and p2, are production rules, the language generated by both
Syntactic_predicate
{\displaystyle \chi } is the indicator function. Truncated power functions are refinable. Macaulay brackets Truncated Power Function on MathWorld Massopust
Truncated_power_function
Inputs for which a function's value is non-zero
|f(x)−IC(x)f(x)|<ε for all x∈X, where IC is the indicator function of C. One then can then choose a continuous cutoff function that vanishes outside a small thickening
Support_(mathematics)
Property of graphs that depends only on abstract structure
Equivalently, a graph property may be formalized using the indicator function of the class, a function from graphs to Boolean values that is true for graphs
Graph_property
Mathematical function with no sudden changes
discontinuous at all rational numbers. In a similar vein, Dirichlet's function, the indicator function for the set of rational numbers, D ( x ) = { 0 if x is irrational
Continuous_function
Mathematical object in category theory
{\displaystyle Y\subseteq X} can be equivalently described by its indicator function χ Y : X → { 0 , 1 } x ↦ { 1 if x ∈ Y 0 if x ∉ Y {\displaystyle
Subobject_classifier
Measurement that evaluates the success of an organization
A performance indicator or key performance indicator (KPI) is a type of performance measurement used to evaluate the success of an organization, activity
Performance_indicator
Value approached by a mathematical object
is given by the positive indicator function, f:ℝ→ℝ, defined such that f(x)=0 if x≤0, and f(x)=1 if x>0. At x=0, the function has a "left-handed limit"
Limit_(mathematics)
Typeface style used in mathematics
mid-1960s. Early examples include Robert Gunning and Hugo Rossi's Analytic Functions of Several Complex Variables (1965) and Lynn Loomis and Shlomo Sternberg's
Blackboard_bold
Uniform distribution on an interval
L]}(t),} where 1 1 [ 0 , L ] {\displaystyle 1\!\!1_{[0,L]}} is the indicator function of [ 0 , L ] . {\displaystyle [0,L].} The confidence interval given
Continuous uniform distribution
Continuous_uniform_distribution
Topics referred to by the same term
algorithm, in computational fluid dynamics Simple function, a finite linear combination of indicator functions of measurable sets Simple machine, a mechanical
Simple
Statistical model for a binary dependent variable
yk) is an indicator function which equals 1 if yk = n and zero otherwise. In the case of two explanatory variables, this indicator function was defined
Logistic_regression
Probability distribution
I is the indicator function, Φ is the cumulative distribution function of the standard normal distribution, and sgn is the sign function. ƒ = 1 gives
Box–Cox_distribution
Cognitive heuristic of searching for an acceptable decision
(equivalent) optimization problem using the indicator function of the satisficing requirements as an objective function. More formally, if X denotes the set
Satisficing
Generalization of mass, length, area and volume
The Dirac measure δa (cf. Dirac delta function) is given by δa(S) = χS(a), where χS is the indicator function of S . {\displaystyle S.} The measure of
Measure_(mathematics)
Type of heuristic technique
|{\mathcal {D}})d\theta ,} where I {\displaystyle \mathbb {I} } is the indicator function. In practice, the rule is implemented by sampling. In each round,
Thompson_sampling
Topics referred to by the same term
(logarithm), integer part of a common logarithm Characteristic function, usually the indicator function of a subset, though the term has other meanings in specific
Characteristic
Metric to evaluate a forecasting method
The function sgn ( ⋅ ) {\displaystyle \operatorname {sgn}(\cdot )} is sign function and 1 {\displaystyle \mathbf {1} } is the indicator function. In
Mean_directional_accuracy
Theorem on genetic algorithms
shown to be a special case of the Price equation with the schema indicator function as the macroscopic measurement. A schema is a template that identifies
Holland's_schema_theorem
Lemma in measure theory
d\mu .} 2. Let 1 X 1 {\displaystyle {\mathbf {1} }_{X_{1}}} be the indicator function of the set X 1 . {\displaystyle X_{1}.} It can be deduced from the
Fatou's_lemma
Elements in exactly one of two sets
the indicator function (denoted here by χ {\displaystyle \chi } ) of the symmetric difference, being the XOR (or addition mod 2) of the indicator functions
Symmetric_difference
Distance from origin of tangent hyperplanes
convex, real valued function is the (convex) indicator function of a compact convex set. Many authors restrict the support function to the Euclidean unit
Support_function
Concept in probability theory
for all B ∈ B {\displaystyle B\in {\mathcal {B}}} . Note that the indicator function 1 f − 1 ( B ) {\displaystyle \mathbf {1} _{f^{-1}(B)}} is A {\displaystyle
Markov_kernel
Concept in statistics
the indicator functions. In cases where the Cesàro limit does not exist this function can actually be defined as the Banach limit of the indicator functions
Exchangeable_random_variables
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
Dirac measure Heaviside step function Indicator function Levi-Civita symbol Minkowski metric 't Hooft symbol Unit function XNOR gate Nakahara, Mikio (2003)
Kronecker_delta
Theory of probability
1\leq i\leq n\right\}\right|,} where I C {\displaystyle I_{C}} is the indicator function of the set C . {\displaystyle C.} For every (fixed) x , {\displaystyle
Glivenko–Cantelli_theorem
Method of determining when the economy has entered a recession
In macroeconomics, the Sahm rule, or Sahm rule recession indicator, is a heuristic measure by the United States' Federal Reserve for determining when
Sahm_rule
Real number whose nth binary digit is 1 if n is prime and 0 if n is composite or 1
{\displaystyle \rho } is the number whose binary expansion corresponds to the indicator function of the set of prime numbers. That is, ρ = ∑ p 1 2 p = ∑ n = 1 ∞ χ
Prime_constant
Random measure in probability theory
of A is simply the empirical mean of the indicator function, Pn(A) = Pn IA. For a fixed measurable function f {\displaystyle f} , P n f {\displaystyle
Empirical_measure
Theorem from probability theory
for all ε > 0 {\displaystyle \varepsilon >0} , where 1{…} is the indicator function, then the central limit theorem holds, i.e. the random variables Z
Lindeberg's_condition
Mathematical set with repetitions allowed
the elements has been fixed. This multiplicity function is a generalization of the indicator function of a subset, and shares some properties with it
Multiset
Generalized alphabetical order
set of countably infinite binary sequences (by definition, the set of functions from natural numbers to { 0 , 1 } , {\displaystyle \{0,1\},} also known
Lexicographic_order
function f {\displaystyle f} by letting f = f + I constraints {\displaystyle f=f+I_{\text{constraints}}} where I {\displaystyle I} is the indicator function
Duality_gap
Variety of proofs provided for the different types of convergence of random variables
\right)\end{aligned}}} (here 1{...} denotes the indicator function; the expectation of the indicator function is equal to the probability of corresponding
Proofs of convergence of random variables
Proofs_of_convergence_of_random_variables
Rogantin had created an indicator function for two-level fractional factorial designs, and in 2003 Ye expanded the indicator function for regular and nonregular
Robust_parameter_design
Flight instrument which displays the aircraft's orientation relative to Earth's horizon
The attitude indicator (AI), also known as the gyro horizon or artificial horizon, is a flight instrument that informs the pilot of the aircraft orientation
Attitude_indicator
Function in number theory
called the unit function because it is the identity element for Dirichlet convolution. It may be described as the "indicator function of 1" within the
Unit_function
Framework for machine learning
used: V(f(𝐱),y)=|y−f(𝐱)| In some sense the 0-1 indicator function is the most natural loss function for classification. It takes the value 0 if the predicted
Statistical_learning_theory
Mathematical function
In some sense, the Mittag-Leffler function is the simplest entire function of its order. The indicator function of E α ( z ) {\displaystyle E_{\alpha
Mittag-Leffler_function
Measure of similarity and diversity between sets
vectors, where a set corresponds to a binary vector given by the indicator function, i.e. x i ∈ { 0 , 1 } {\displaystyle x_{i}\in \{0,1\}} . However,
Jaccard_index
Metric in computer science
where 1 ( a i ≠ b j ) {\displaystyle 1_{(a_{i}\neq b_{j})}} is the indicator function equal to 0 when a i = b j {\displaystyle a_{i}=b_{j}} and equal to
Damerau–Levenshtein_distance
Algorithm in mathematics
bi∗(vk)=∑t=1T1yt=vkγi(t)∑t=1Tγi(t), where 1yt=vk={1if yt=vk,0otherwise is an indicator function, and bi∗(vk) is the expected number of times the output observations
Baum–Welch_algorithm
Theorem in measure theory
as can be demonstrated by example. Consider Dirichlet function, that is the indicator function 1 Q : [ 0 , 1 ] → { 0 , 1 } {\displaystyle 1_{\mathbb {Q}
Lusin's_theorem
Option's fixed price to exercise it on the expiration date
{\displaystyle 1_{S\geq K}} , where 1 { } {\displaystyle 1_{\{\}}} is the indicator function: 1 S ≥ K = { 1 if S ≥ K , 0 otherwise. {\displaystyle 1_{S\geq
Strike_price
Chemical detector for metal ions in complexometric titrations
influenced by the removal of the metal ions, a redox indicator can function as a complexometric indicator. Flaschka, H.; Schwarzenbach, G.; Schwarzenbach,
Complexometric_indicator
Chemical added to show pH of a solution
A pH indicator is a halochromic chemical compound added in small amounts to a solution so the pH (acidity or basicity) of the solution can be determined
PH_indicator
Whose values lie in an infinite-dimensional vector space
} {\displaystyle \mathbb {1} _{[0,\,t]}:(0,1)\to \{0,1\}} is the indicator function defined by x ↦ { 1 if x ∈ [ 0 , t ] 0 otherwise {\displaystyle
Infinite-dimensional vector function
Infinite-dimensional_vector_function
Integral transform in mathematics
Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional) space of lines in
Radon_transform
Avionics instrument
A course deviation indicator (CDI) is an avionics instrument used in aircraft navigation to determine an aircraft's lateral position in relation to a
Course_deviation_indicator
Algebraic manipulation of "true" and "false"
totality of subsets of a set E: to a subset F of E, one can define the indicator function that takes the value 1 on F, and 0 outside F. The most general example
Boolean_algebra
Fundamental theorem in probability theory and statistics
limn→∞1sn2∑i=1nE[(Xi−μi)2⋅𝟏{|Xi−μi|>εsn}]=0 where 𝟏{…} is the indicator function. Then the distribution of the standardized sums 1sn∑i=1n(Xi−μi) converges
Central_limit_theorem
Complexity class consisting of all recursive languages
computable functions in the sense that: a decision problem is in R if and only if its indicator function is computable, a total function is computable
R_(complexity)
Method of interpolation
x} . Indicator kriging uses indicator functions instead of the process itself, in order to estimate transition probabilities. Multiple-indicator kriging
Kriging
Result in geometry
Let E be some measurable subset of ℝd and let fj=𝟏πj(E) be the indicator function of the projection of E onto the jth coordinate hyperplane. It follows
Loomis–Whitney_inequality
Inequality between integrals in Lp spaces
} with μ ( S ) = ∞ . {\displaystyle \mu (S)=\infty .} ) Then the indicator function 1 A {\displaystyle 1_{A}} satisfies ‖ 1 A ‖ ∞ = 1 , {\displaystyle
Hölder's_inequality
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