In AnderEhu/sme:
library(SME)
library(knitr)
variance
Variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value:
$\sigma^2 = \sum_{1}^{n} \frac{(x_i - mean(x))^2}{n-1}$
Usage
variance(x, margin = 2L)
Arguments
- x : a numeric vector, matrix, or data.frame.
- margin: In case of matrix or dataframe apply variance by columns margin = 2L or by rows margin = 1L. Default 2.
Value
the sample variance of the input.
Examples
example1 <- data.frame("V1" = rep(1, 100), "V2" = 100:1, "V4" = sample.int(3000,100,replace=FALSE))
example2 <- rep(1, 100)
v <- variance(example1)
kable(v)
v <- variance(example1, margin = 1L)
print(v)
v <- variance(example2)
kable(v)
entropy
Entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes.
$H(X)= -\sum_{1}^{n}P(x_i)log[P(x_i)]$
Usage
entropy(x, margin = 2L)
Arguments
-
x : a numeric vector, matrix, or data.frame.
-
margin: In case of matrix or dataframe apply entropy by columns margin = 2L or by rows margin = 1L. Default 2.
Value
the sample entropy of the input.
Examples
col1 <- c('False', 'False', 'True', 'True', 'True', 'True', 'False', 'True', 'False', 'False')
col2 <- c('True', 'False', 'False', 'False', 'True', 'True', 'False', 'False', 'False', 'False')
col3 <- c('a', 'b', 'c', 'a', 'a', 'a', 'l', 'a', 'l', 'a')
df <- data.frame("V1" = col1, "V2" = col2, "V3" = col3)
e <- entropy(df)
kable(e)
conditional.entropy
Conditional entropy quantifies the amount of information needed to describe the outcome of a random variable Y given that the value of another random variable X is known.
$H(X|Y) = -\sum\sum p(x,y)log[\frac{p(x,y)}{p(x)}]$
Usage
conditional.entropy(x, y = NULL, file = "None")
Arguments
- x: a vector, matrix, or data.frame.
- y: a vector. y must be NULL if x is a matrix or a data.frame
- file: In case of x been a data.frame or matrix, represent the name of output file for saving conditional entropy plot
Value
In case of x been a data.frame or matrix, conditional entropy of all variables/columns in x. Otherwise, conditional entropy of x and y.
Examples
df <- data.frame("V1" = sample.int(2,5,replace=TRUE), "V2" =sample.int(2,5,replace=TRUE) , "V3" = sample.int(2,5,replace=TRUE), "V4" = sample.int(2,5,replace=TRUE), "V5" = sample.int(2,5,replace=TRUE), "V6" = sample.int(2,5,replace=TRUE), "V7" = sample.int(2,5,replace=TRUE), "V8" = sample.int(2,5,replace=TRUE))
x <- sample.int(2, 5,replace=TRUE)
y <- sample.int(2,5,replace=TRUE)
c <- conditional.entropy(df, file ="conditionalEntropy")
kable(c)
c <- conditional.entropy(x = x, y = y)
kable(c)
joint.entropy
Joint entropy is a measure of the uncertainty associated with a set of variables.
$H(X, Y) = - \sum\sum p(x, y)log[p(x,y)]$
Usage
joint.entropy(x, y = NULL, file = "None")
Arguments
- x: a vector, matrix, or data.frame.
- y: a vector. y must be NULL if x is a matrix or a data.frame.
- file: In case of x been a data.frame or matrix, represent the name of output file for saving joint entropy plot.
Value
In case of x been a data.frame or matrix, joint entropy of all variables/columns in x. Otherwise, joint entropy of x and y.
Examples
df <- data.frame("V1" = sample.int(2,5,replace=TRUE), "V2" =sample.int(2,5,replace=TRUE) , "V3" = sample.int(2,5,replace=TRUE), "V4" = sample.int(2,5,replace=TRUE), "V5" = sample.int(2,5,replace=TRUE), "V6" = sample.int(2,5,replace=TRUE), "V7" = sample.int(2,5,replace=TRUE), "V8" = sample.int(2,5,replace=TRUE))
x <- sample.int(2, 5,replace=TRUE)
y <- sample.int(2, 5,replace=TRUE)
j <- joint.entropy(df, file ="jointEntropy")
kable(j)
j <- joint.entropy(x = x, y = y)
kable(j)
mutual.information
Mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons (bits), nats or hartleys) obtained about one random variable by observing the other random variable.
$I(X, Y) = \sum\sum p(x, y)log[\frac{p(x,y)}{p(x)p(y)}]$
$I(X, Y) = H(X) - H(X|Y)
= H(Y) - H(Y|X) = H(X) + H(Y) - H(X, Y) = H(X, Y) - H(X|Y) - H(Y|X)$
Usage
mutual.information(x, y = NULL, file = "None")
Arguments
- x: a vector, matrix, or data.frame.
- y: a vector. y must be NULL if x is a matrix or a data.frame.
- file: In case of x been a data.frame or matrix, represent the name of output file for saving mutual information plot.
Value
In case of x been a data.frame or matrix, mutual information of all variables/columns in x. Otherwise, mutual information of x and y.
Examples
df <- data.frame("V1" = sample.int(2,5,replace=TRUE), "V2" =sample.int(2,5,replace=TRUE) , "V3" = sample.int(2,5,replace=TRUE), "V4" = sample.int(2,5,replace=TRUE), "V5" = sample.int(2,5,replace=TRUE), "V6" = sample.int(2,5,replace=TRUE), "V7" = sample.int(2,5,replace=TRUE), "V8" = sample.int(2,5,replace=TRUE))
x <- sample.int(2, 5,replace=TRUE)
y <- sample.int(2, 5,replace=TRUE)
m <- mutual.information(df, file ="mutualInformation")
kable(m)
m <- mutual.information(x = x, y = y)
kable(m)
correlation
Correlation is a statistic that measures the degree to which two variables move in relation to each other.
Pearson correlation, $r_{pearson}$ It is the ratio between the covariance of two variables and the product of their standard deviations;
$r_{pearson} = \frac{Cov(x,y)}{\sigma(x)\sigma(y)}$
Spearman correlation, $r_{spearman}$, is a nonparametric measure of rank correlation (statistical dependence between the rankings of two variables)
$r_{spearman} = 1 - \frac{6\sum d_i^2}{n(n^2-1)}$
Usage
correlation(x, y = NULL, method = "Pearson", file = "None")
Arguments
- x a numeric vector, matrix, or data.frame.
- y a numeric vector. y must be NULL if x is a matrix or a data.frame.
- method Pearson or Spearman method for calculate correlation. Default Pearson.
- file In case of x been a data.frame or matrix, represent the name of output file for saving mutual information plot.
Value
In case of x been a data.frame or matrix, correlation of all variables/columns in x. Otherwise, correlation of x and y.
Examples
df <- data.frame("V1" = sample.int(3000,100,replace=FALSE), "V2" =sample.int(3000,100,replace=FALSE) , "V3" = sample.int(3000,100,replace=FALSE), "V4" = sample.int(3000,100,replace=FALSE), "V5" = sample.int(3000,100,replace=FALSE), "V6" = sample.int(3000,100,replace=FALSE), "V7" = sample.int(3000,100,replace=FALSE), "V8" = sample.int(3000,100,replace=FALSE))
x <- c(35,23,47, 17, 10, 43, 9, 6, 28)
y <- c(30, 33, 45, 23, 8, 49, 12, 4, 31)
correlation(x = x, y = y, method = "Pearson")
correlation(x = x, y = y, method = "Spearman")
correlation(x = df, method = "Pearson")
correlation(x = df, method = "Spearman")
correlation(x = df, method = "Pearson", file = "pearsonCor")
correlation(x = df, method = "Spearman", file = "spearmanCor")
roc_curve
The Receiver Operator Characteristic (ROC) curve is an evaluation metric for binary classification problems (can also be applied to a variable). It is a probability curve that plots the TPR against FPR.
The higher the AUC, the better the performance of the variable.
Usage
roc.curve(x, y, file = "None", AUC = FALSE)
Arguments
- x: a numerical vector
- y: represent logical class TRUE/FALSE.
- file: name of output file for saving roc curve plot.
- AUC: return auc value AUC = TRUE
Value
dataframe wih TPR and FPR or AUC value
Examples
random.x <- sample.int(3000,1000,replace=FALSE)
class <- c(rep(TRUE, 500), rep(FALSE, 500))
pos <- sample.int(1000, 1000)
random.y <- class[order(pos)]
perfect.x <- 1:3000
perfect.y <- c(rep(TRUE, 1500), rep(FALSE, 1500))
worst.x <- 1:3000
worst.y <- c(rep(FALSE, 1500), rep(TRUE, 1500))
randomRocCurve <- roc.curve(random.x, random.y, file= "randomRocCurve")
perfectRocCurve <- roc.curve(perfect.x, perfect.y, file= "perfectRocCurve")
worstRocCurve <- roc.curve(worst.x, worst.y, file= "worstRocCurve")
filter
Given a dataframe, a metric, an upper limit and a lower limit return a filtered dataframe with the specified metric that satisfies the upper and lower bounds. For AUC metric it is required to specified class name.
Usage
filter(
df,
class,
by = "AUC",
uplimit = .Machine$integer.max,
lowlimit = -.Machine$integer.max
)
Arguments
- df data.frame. Each colum represent a variable
- class name of the class variable
- by metric to apply the filter. AUC, Variance and Entropy are available.
- uplimit metric uplimit value
- lowlimit metric uplimit value. Default
Value
Filtered data.frame
Examples
class <- c(rep(TRUE, 5), rep(FALSE, 5))
pos <- sample.int(10, 10)
random.y <- class[order(pos)]
df.numeric <- data.frame("V1" = sample.int(3,10,replace=TRUE), "V2" = sample.int(3,10,replace=TRUE), "V3" = sample.int(3,10,replace=TRUE), "Class" = random.y)
df.cat <- data.frame("V1" = as.factor(sample.int(3,10,replace=TRUE)), "V2" = as.factor(sample.int(3,10,replace=TRUE)), "V4" = as.factor(sample.int(3,10,replace=TRUE)), "Class" = random.y)
filter(df.numeric, class = "Class", by = "AUC", uplimit = 1, lowlimit = 0.5)
filter(df.numeric, class = "Class", by = "Variance", uplimit = 100, lowlimit = 0)
filter(df.cat, class = "Class", by = "Entropy", uplimit = 2, lowlimit = 0)
filter(df.cat, class = "Class", by = "Entropy")
visualize.infotheo.matrix
Heatmap plot of theory information metrics
Usage
visualize.infotheo.matrix(
df,
type,
file = "None",
colors = c("#DEB841", "white", "#267278")
)
Arguments
df: Conditional Entropy, Joint Entropy or Mutual Information data.frame or matrix.
type: Type of theory information metric. Character
file: In case you want to save the plot, file represents output file name.
colors: Three colors for the gradient. Default c("#DEB841", "white", "#267278").
Value
Heatmap of given dataframe
Example
df <- data.frame("V1" = sample.int(2,5,replace=TRUE), "V2" =sample.int(2,5,replace=TRUE) , "V3" = sample.int(2,5,replace=TRUE), "V4" = sample.int(2,5,replace=TRUE), "V5" = sample.int(2,5,replace=TRUE), "V6" = sample.int(2,5,replace=TRUE), "V7" = sample.int(2,5,replace=TRUE), "V8" = sample.int(2,5,replace=TRUE))
ce <- conditional.entropy(df)
je <- joint.entropy(df)
mi <- mutual.information(df)
p <- visualize.infotheo.matrix(ce, type = "Conditional Entropy", colors = c("#692be2", "White", "#ddcbff"))
print(p)
p <- visualize.infotheo.matrix(je, type = "Joint Entropy", colors = c("#9999ff", "#6b7db3", "#6bb3b3"))
print(p)
p <- visualize.infotheo.matrix(je, type = "Mutual Information", colors = c("#ffd699", "White", "#b3966b"))
print(p)
AnderEhu/sme documentation built on Jan. 31, 2022, 12:01 a.m.
R Package Documentation
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
library(SME) library(knitr)
variance
Variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value:
$\sigma^2 = \sum_{1}^{n} \frac{(x_i - mean(x))^2}{n-1}$
Usage
variance(x, margin = 2L)
Arguments
- x : a numeric vector, matrix, or data.frame.
- margin: In case of matrix or dataframe apply variance by columns margin = 2L or by rows margin = 1L. Default 2.
Value
the sample variance of the input.
Examples
example1 <- data.frame("V1" = rep(1, 100), "V2" = 100:1, "V4" = sample.int(3000,100,replace=FALSE)) example2 <- rep(1, 100)
v <- variance(example1) kable(v) v <- variance(example1, margin = 1L) print(v) v <- variance(example2) kable(v)
entropy
Entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes.
$H(X)= -\sum_{1}^{n}P(x_i)log[P(x_i)]$
Usage
entropy(x, margin = 2L)
Arguments
-
x : a numeric vector, matrix, or data.frame.
-
margin: In case of matrix or dataframe apply entropy by columns margin = 2L or by rows margin = 1L. Default 2.
Value
the sample entropy of the input.
Examples
col1 <- c('False', 'False', 'True', 'True', 'True', 'True', 'False', 'True', 'False', 'False') col2 <- c('True', 'False', 'False', 'False', 'True', 'True', 'False', 'False', 'False', 'False') col3 <- c('a', 'b', 'c', 'a', 'a', 'a', 'l', 'a', 'l', 'a') df <- data.frame("V1" = col1, "V2" = col2, "V3" = col3)
e <- entropy(df) kable(e)
conditional.entropy
Conditional entropy quantifies the amount of information needed to describe the outcome of a random variable Y given that the value of another random variable X is known.
$H(X|Y) = -\sum\sum p(x,y)log[\frac{p(x,y)}{p(x)}]$
Usage
conditional.entropy(x, y = NULL, file = "None")
Arguments
- x: a vector, matrix, or data.frame.
- y: a vector. y must be NULL if x is a matrix or a data.frame
- file: In case of x been a data.frame or matrix, represent the name of output file for saving conditional entropy plot
Value
In case of x been a data.frame or matrix, conditional entropy of all variables/columns in x. Otherwise, conditional entropy of x and y.
Examples
df <- data.frame("V1" = sample.int(2,5,replace=TRUE), "V2" =sample.int(2,5,replace=TRUE) , "V3" = sample.int(2,5,replace=TRUE), "V4" = sample.int(2,5,replace=TRUE), "V5" = sample.int(2,5,replace=TRUE), "V6" = sample.int(2,5,replace=TRUE), "V7" = sample.int(2,5,replace=TRUE), "V8" = sample.int(2,5,replace=TRUE)) x <- sample.int(2, 5,replace=TRUE) y <- sample.int(2,5,replace=TRUE)
c <- conditional.entropy(df, file ="conditionalEntropy") kable(c)
c <- conditional.entropy(x = x, y = y) kable(c)
joint.entropy
Joint entropy is a measure of the uncertainty associated with a set of variables.
$H(X, Y) = - \sum\sum p(x, y)log[p(x,y)]$
Usage
joint.entropy(x, y = NULL, file = "None")
Arguments
- x: a vector, matrix, or data.frame.
- y: a vector. y must be NULL if x is a matrix or a data.frame.
- file: In case of x been a data.frame or matrix, represent the name of output file for saving joint entropy plot.
Value
In case of x been a data.frame or matrix, joint entropy of all variables/columns in x. Otherwise, joint entropy of x and y.
Examples
df <- data.frame("V1" = sample.int(2,5,replace=TRUE), "V2" =sample.int(2,5,replace=TRUE) , "V3" = sample.int(2,5,replace=TRUE), "V4" = sample.int(2,5,replace=TRUE), "V5" = sample.int(2,5,replace=TRUE), "V6" = sample.int(2,5,replace=TRUE), "V7" = sample.int(2,5,replace=TRUE), "V8" = sample.int(2,5,replace=TRUE)) x <- sample.int(2, 5,replace=TRUE) y <- sample.int(2, 5,replace=TRUE)
j <- joint.entropy(df, file ="jointEntropy") kable(j)
j <- joint.entropy(x = x, y = y) kable(j)
mutual.information
Mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons (bits), nats or hartleys) obtained about one random variable by observing the other random variable.
$I(X, Y) = \sum\sum p(x, y)log[\frac{p(x,y)}{p(x)p(y)}]$
$I(X, Y) = H(X) - H(X|Y) = H(Y) - H(Y|X) = H(X) + H(Y) - H(X, Y) = H(X, Y) - H(X|Y) - H(Y|X)$
Usage
mutual.information(x, y = NULL, file = "None")
Arguments
- x: a vector, matrix, or data.frame.
- y: a vector. y must be NULL if x is a matrix or a data.frame.
- file: In case of x been a data.frame or matrix, represent the name of output file for saving mutual information plot.
Value
In case of x been a data.frame or matrix, mutual information of all variables/columns in x. Otherwise, mutual information of x and y.
Examples
df <- data.frame("V1" = sample.int(2,5,replace=TRUE), "V2" =sample.int(2,5,replace=TRUE) , "V3" = sample.int(2,5,replace=TRUE), "V4" = sample.int(2,5,replace=TRUE), "V5" = sample.int(2,5,replace=TRUE), "V6" = sample.int(2,5,replace=TRUE), "V7" = sample.int(2,5,replace=TRUE), "V8" = sample.int(2,5,replace=TRUE)) x <- sample.int(2, 5,replace=TRUE) y <- sample.int(2, 5,replace=TRUE)
m <- mutual.information(df, file ="mutualInformation") kable(m)
m <- mutual.information(x = x, y = y) kable(m)
correlation
Correlation is a statistic that measures the degree to which two variables move in relation to each other.
Pearson correlation, $r_{pearson}$ It is the ratio between the covariance of two variables and the product of their standard deviations;
$r_{pearson} = \frac{Cov(x,y)}{\sigma(x)\sigma(y)}$
Spearman correlation, $r_{spearman}$, is a nonparametric measure of rank correlation (statistical dependence between the rankings of two variables)
$r_{spearman} = 1 - \frac{6\sum d_i^2}{n(n^2-1)}$
Usage
correlation(x, y = NULL, method = "Pearson", file = "None")
Arguments
- x a numeric vector, matrix, or data.frame.
- y a numeric vector. y must be NULL if x is a matrix or a data.frame.
- method Pearson or Spearman method for calculate correlation. Default Pearson.
- file In case of x been a data.frame or matrix, represent the name of output file for saving mutual information plot.
Value
In case of x been a data.frame or matrix, correlation of all variables/columns in x. Otherwise, correlation of x and y.
Examples
df <- data.frame("V1" = sample.int(3000,100,replace=FALSE), "V2" =sample.int(3000,100,replace=FALSE) , "V3" = sample.int(3000,100,replace=FALSE), "V4" = sample.int(3000,100,replace=FALSE), "V5" = sample.int(3000,100,replace=FALSE), "V6" = sample.int(3000,100,replace=FALSE), "V7" = sample.int(3000,100,replace=FALSE), "V8" = sample.int(3000,100,replace=FALSE)) x <- c(35,23,47, 17, 10, 43, 9, 6, 28) y <- c(30, 33, 45, 23, 8, 49, 12, 4, 31)
correlation(x = x, y = y, method = "Pearson") correlation(x = x, y = y, method = "Spearman") correlation(x = df, method = "Pearson") correlation(x = df, method = "Spearman")
correlation(x = df, method = "Pearson", file = "pearsonCor")
correlation(x = df, method = "Spearman", file = "spearmanCor")
roc_curve
The Receiver Operator Characteristic (ROC) curve is an evaluation metric for binary classification problems (can also be applied to a variable). It is a probability curve that plots the TPR against FPR.
The higher the AUC, the better the performance of the variable.
Usage
roc.curve(x, y, file = "None", AUC = FALSE)
Arguments
- x: a numerical vector
- y: represent logical class TRUE/FALSE.
- file: name of output file for saving roc curve plot.
- AUC: return auc value AUC = TRUE
Value
dataframe wih TPR and FPR or AUC value
Examples
random.x <- sample.int(3000,1000,replace=FALSE) class <- c(rep(TRUE, 500), rep(FALSE, 500)) pos <- sample.int(1000, 1000) random.y <- class[order(pos)] perfect.x <- 1:3000 perfect.y <- c(rep(TRUE, 1500), rep(FALSE, 1500)) worst.x <- 1:3000 worst.y <- c(rep(FALSE, 1500), rep(TRUE, 1500))
randomRocCurve <- roc.curve(random.x, random.y, file= "randomRocCurve")
perfectRocCurve <- roc.curve(perfect.x, perfect.y, file= "perfectRocCurve")
worstRocCurve <- roc.curve(worst.x, worst.y, file= "worstRocCurve")
filter
Given a dataframe, a metric, an upper limit and a lower limit return a filtered dataframe with the specified metric that satisfies the upper and lower bounds. For AUC metric it is required to specified class name.
Usage
filter( df, class, by = "AUC", uplimit = .Machine$integer.max, lowlimit = -.Machine$integer.max )
Arguments
- df data.frame. Each colum represent a variable
- class name of the class variable
- by metric to apply the filter. AUC, Variance and Entropy are available.
- uplimit metric uplimit value
- lowlimit metric uplimit value. Default
Value
Filtered data.frame
Examples
class <- c(rep(TRUE, 5), rep(FALSE, 5)) pos <- sample.int(10, 10) random.y <- class[order(pos)] df.numeric <- data.frame("V1" = sample.int(3,10,replace=TRUE), "V2" = sample.int(3,10,replace=TRUE), "V3" = sample.int(3,10,replace=TRUE), "Class" = random.y) df.cat <- data.frame("V1" = as.factor(sample.int(3,10,replace=TRUE)), "V2" = as.factor(sample.int(3,10,replace=TRUE)), "V4" = as.factor(sample.int(3,10,replace=TRUE)), "Class" = random.y)
filter(df.numeric, class = "Class", by = "AUC", uplimit = 1, lowlimit = 0.5) filter(df.numeric, class = "Class", by = "Variance", uplimit = 100, lowlimit = 0) filter(df.cat, class = "Class", by = "Entropy", uplimit = 2, lowlimit = 0) filter(df.cat, class = "Class", by = "Entropy")
visualize.infotheo.matrix
Heatmap plot of theory information metrics
Usage
visualize.infotheo.matrix( df, type, file = "None", colors = c("#DEB841", "white", "#267278") )
Arguments
df: Conditional Entropy, Joint Entropy or Mutual Information data.frame or matrix.
type: Type of theory information metric. Character
file: In case you want to save the plot, file represents output file name.
colors: Three colors for the gradient. Default c("#DEB841", "white", "#267278").
Value
Heatmap of given dataframe
Example
df <- data.frame("V1" = sample.int(2,5,replace=TRUE), "V2" =sample.int(2,5,replace=TRUE) , "V3" = sample.int(2,5,replace=TRUE), "V4" = sample.int(2,5,replace=TRUE), "V5" = sample.int(2,5,replace=TRUE), "V6" = sample.int(2,5,replace=TRUE), "V7" = sample.int(2,5,replace=TRUE), "V8" = sample.int(2,5,replace=TRUE)) ce <- conditional.entropy(df) je <- joint.entropy(df) mi <- mutual.information(df)
p <- visualize.infotheo.matrix(ce, type = "Conditional Entropy", colors = c("#692be2", "White", "#ddcbff")) print(p) p <- visualize.infotheo.matrix(je, type = "Joint Entropy", colors = c("#9999ff", "#6b7db3", "#6bb3b3")) print(p) p <- visualize.infotheo.matrix(je, type = "Mutual Information", colors = c("#ffd699", "White", "#b3966b")) print(p)
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