Package 'msu'

Estimate the sample size for a variable in function of its categories.

Description

Estimate the sample size for a variable in function of its categories.

Usage

categorical_sample_size(categories, increment = 10)

Arguments

categories	A vector containing the number of categories of each variable.
increment	A number as a constant to which the sample size is incremented as a product.

Value

The sample size for a categorical variable based on a ordered permutation heuristic approximation of its categories.

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Estimating information gain between two categorical variables.

Description

Information gain (also called mutual information) is a measure of the mutual dependence between two variables (see https://en.wikipedia.org/wiki/Mutual_information).

Usage

information_gain(x, y)

IG(x, y)

Arguments

x	A factor representing a categorical variable.
y	A factor representing a categorical variable.

Value

Information gain estimation based on Sannon entropy for variables x and y.

Examples

information_gain(factor(c(0,1)), factor(c(1,0)))
information_gain(factor(c(0,0,1,1)), factor(c(0,1,1,1)))
information_gain(factor(c(0,0,1,1)), factor(c(0,1,0,1)))
## Not run: 
information_gain(c(0,1), c(1,0))

## End(Not run)

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Estimation of the Joint Shannon entropy for two categorical variables.

Description

The joint Shannon entropy provides an estimation of the measure of uncertainty between two random variables (see https://en.wikipedia.org/wiki/Joint_entropy).

Usage

joint_shannon_entropy(x, y)

joint_H(x, y)

Arguments

x	A factor as the represented categorical variable.
y	A factor as the represented categorical variable.

Value

Joint Shannon entropy estimation for variables x and y.

See Also

shannon_entropy for the entropy for a single variable and multivar_joint_shannon_entropy for the entropy associated with more than two random variables.

Examples

joint_shannon_entropy(factor(c(0,0,1,1)), factor(c(0,1,0,1)))
joint_shannon_entropy(factor(c('a','b','c')), factor(c('c','b','a')))
## Not run: 
joint_shannon_entropy(1)
joint_shannon_entropy(c('a','b'), c('d','e'))

## End(Not run)

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Estimating Multivariate Symmetrical Uncertainty.

Description

MSU is a generalization of symmetrical uncertainty (SU) where it is considered the interaction between two or more variables, whereas SU can only consider the interaction between two variables. For instance, consider a table with two variables X1 and X2 and a third variable, Y (the class of the case), that results from the logical XOR operator applied to X1 and X2

X1	X2	Y
0	0	0
0	1	1
1	0	1
1	1	0

For this case

$MSU(X1, X2, Y) = 0.5.$

This, in contrast to the measurements obtained by SU of the variables X1 and X2 against Y,

$SU(X1, Y) = 0$

and

$SU(X2, Y) = 0.$

Usage

msu(table_variables, table_class)

Arguments

table_variables	A list of factors as categorical variables.
table_class	A factor representing the class of the case.

Value

Multivariate symmetrical uncertainty estimation for the variable set {table_variables, table_class}. The result is rounded to 7 decimal places.

See Also

symmetrical_uncertainty

Examples

# completely predictable
msu(list(factor(c(0,0,1,1))), factor(c(0,0,1,1)))
# XOR
msu(list(factor(c(0,0,1,1)), factor(c(0,1,0,1))), factor(c(0,1,1,0)))
## Not run: 
msu(c(factor(c(0,0,1,1)), factor(c(0,1,0,1))), factor(c(0,1,1,0)))
msu(list(factor(c(0,0,1,1)), factor(c(0,1,0,1))), c(0,1,1,0))

## End(Not run)

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Estimation of joint Shannon entropy for a set of categorical variables.

Description

The multivariate joint Shannon entropy provides an estimation of the measure of the uncertainty associated with a set of variables (see https://en.wikipedia.org/wiki/Joint_entropy).

Usage

multivar_joint_shannon_entropy(table_variables, table_class)

multivar_joint_H(table_variables, table_class)

Arguments

table_variables	A list of factors as categorical variables.
table_class	A factor representing the class of the case.

Value

Joint Shannon entropy estimation for the variable set table.variables, table.class.

See Also

shannon_entropy for the entropy for a single variable and joint_shannon_entropy for the entropy associated with two random variables.

Examples

multivar_joint_shannon_entropy(list(factor(c(0,1)), factor(c(1,0))),
    factor(c(1,1)))

---

Create an informative uniform categorical random variable.

Description

The sampling for the items of the created variable is done with replacement.

Usage

new_informative_variable(variable_labels, variable_class,
  information_level = 1)

Arguments

variable_labels	A factor as the labels for the new informative variable.
variable_class	A factor as the class of the variable.
information_level	A integer as the information level of the new variable.

Value

A factor that represents an informative uniform categorical random variable created using the Kononenko method.

---

Create a uniform categorical random variable.

Description

The sampling for the items of the created variable is done with replacement.

Usage

new_variable(elements, n)

Arguments

elements	A vector with the elements from which to choose to create the variable.
n	An integer indicating the number of items to be contained in the variable.

Value

A factor that represents a uniform categorical variable.

Examples

new_variable(c(0,1), 4)
new_variable(c('a','b','c'), 10)

---

Create a set of categorical variables using the logical XOR operator.

Description

Create a set of categorical variables using the logical XOR operator.

Usage

new_xor_variables(n_variables = 2, n_instances = 1000, noise = 0)

Arguments

n_variables	An integer as the number of variables to be created. It is the number of column variables of the table, an additional column is added as a result of the XOR operator over the instances.
n_instances	An integer as the number of instances to be created. It is the number of rows of the table.
noise	A float number as the noise level for the variables.

Value

A set of random variables constructed using the logical XOR operator.

Examples

new_xor_variables(2, 4, 0)
new_xor_variables(5, 10, 0.5)

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Relative frequency of values of a categorical variable.

Description

Relative frequency of values of a categorical variable.

Usage

rel_freq(variable)

Arguments

variable

A factor as a categorical variable

Value

Relative frecuency distribution table for the values in variable.

Examples

rel_freq(factor(c(0,1)))
rel_freq(factor(c('a','a','b')))
## Not run: 
rel_freq(c(0,1))

## End(Not run)

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Estimate the sample size for a categorical variable.

Description

Estimate the sample size for a categorical variable.

Usage

sample_size(max, min = 1, z = 1.96, error = 0.05)

Arguments

max	A number as the maximum value of the possible categories.
min	A number as the minimum value of the possible categories.
z	A number as the confidence coefficient.
error	Admissible sampling error.

Value

The sample size for a categorical variable based on a variance heuristic approximation.

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Estimation of Shannon entropy for a categorical variable.

Description

The Shannon entropy estimates the average minimum number of bits needed to encode a string of symbols, based on the frequency of the symbols (see http://www.bearcave.com/misl/misl_tech/wavelets/compression/shannon.html).

Usage

shannon_entropy(x)

H(x)

Arguments

x	A factor as the represented categorical variable.

Value

Shannon entropy estimation of the categorical variable.

Examples

shannon_entropy(factor(c(1,0)))
shannon_entropy(factor(c('a','b','c')))
## Not run: 
shannon_entropy(1)
shannon_entropy(c('a','b','c'))

## End(Not run)

---

Estimating Symmetrical Uncertainty of two categorical variables.

Description

Symmetrical uncertainty (SU) is the product of a normalization of the information gain (IG) with respect to entropy. SU(X,Y) is a value in the range [0,1], where $SU(X,Y) = 0$ if X and Y are totally independent and $SU(X,Y) = 1$ if X and Y are totally dependent.

Usage

symmetrical_uncertainty(x, y)

SU(x, y)

Arguments

x	A factor as the represented categorical variable.
y	A factor as the represented categorical variable.

Value

Symmetrical uncertainty estimation based on Sannon entropy. The result is rounded to 7 decimal places.

See Also

msu

Examples

# completely predictable
symmetrical_uncertainty(factor(c(0,1,0,1)), factor(c(0,1,0,1)))
# XOR factor variables
symmetrical_uncertainty(factor(c(0,0,1,1)), factor(c(0,1,1,0)))
symmetrical_uncertainty(factor(c(0,1,0,1)), factor(c(0,1,1,0)))
## Not run: 
symmetrical_uncertainty(c(0,1,0,1), c(0,1,1,0))

## End(Not run)

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Estimation of total correlation for a set of categorical random variables.

Description

Total Correlation is a generalization of information gain (IG) to measure the dependency of a set of categorical random variables (see https://en.wikipedia.org/wiki/Total_correlation).

Usage

total_correlation(table_variables, table_class)

C(table_variables, table_class)

Arguments

table_variables	A list of factors as categorical variables.
table_class	A factor representing the class of the case.

Value

Total correlation estimation for the variable set table.variables, table.class.

Examples

total_correlation(list(factor(c(0,1)), factor(c(1,0))), factor(c(0,0)))
total_correlation(list(factor(c('a','b')), factor(c('a','b'))),
    factor(c('a','b')))
## Not run: 
total_correlation(list(factor(c(0,1)), factor(c(1,0))), c(0,0))
total_correlation(c(factor(c(0,1)), factor(c(1,0))), c(0,0))

## End(Not run)

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