auc.xy

The <code>auc.xy()</code>-function calculates the area under the curve.

Performance evaluation metrics for supervised and unsupervised machine learning, statistical learning and artificial intelligence applications. Core computations are implemented in 'C++' for scalability and efficiency.

Serkan Korkmaz

SLmetrics

Machine Learning Performance Evaluation on Steroids

auc.xy function

<dl><dt>...</dt>
<dd>Arguments passed on to <code>auc.xy.numeric</code><dl>
 <dt><code>y,x</code></dt>
<dd>A pair of &lt;<a href="/link/double?package=SLmetrics&version=0.3-4" data-mini-rdoc="SLmetrics::double">double</a>&gt; vectors of <a href="/link/length?package=SLmetrics&version=0.3-4" data-mini-rdoc="SLmetrics::length">length</a> $n$.</dd></dl></dd> <dt><code>method</code></dt>
<dd>A &lt;<a href="/link/integer?package=SLmetrics&version=0.3-4" data-mini-rdoc="SLmetrics::integer">integer</a>&gt; value (default: $0$). Defines the underlying method of calculating the area under the curve. If $0$ it is calculated using the <code>trapezoid</code>-method, if $1$ it is calculated using the <code>step</code>-method.</dd> <dt><code>presorted</code></dt>
<dd>A &lt;<a href="/link/logical?package=SLmetrics&version=0.3-4" data-mini-rdoc="SLmetrics::logical">logical</a>&gt;-value <a href="/link/length?package=SLmetrics&version=0.3-4" data-mini-rdoc="SLmetrics::length">length</a> 1 (default: <a href="/link/FALSE?package=SLmetrics&version=0.3-4" data-mini-rdoc="SLmetrics::FALSE">FALSE</a>). If <a href="/link/TRUE?package=SLmetrics&version=0.3-4" data-mini-rdoc="SLmetrics::TRUE">TRUE</a> the input will not be sorted by threshold.</dd> 
</dl>

Arguments

Trapezoidal rule
The trapezoidal rule approximates the integral of a function $f(x)$ between
$x = a$ and $x = b$ using trapezoids formed between consecutive points. If
we have points $x_0, x_1, \ldots, x_n$ (with $a = x_0 &lt; x_1 &lt; \cdots &lt; x_n = b$)
and corresponding function values $f(x_0), f(x_1), \ldots, f(x_n)$, the area under
the curve $A_T$ is approximated by:
$$
 A_T \approx \sum_{k=1}^{n} \frac{f(x_{k-1}) + f(x_k)}{2} \bigl[x_k - x_{k-1}\bigr].
$$
Step-function method
The step-function (rectangular) method uses the value of the function at one
endpoint of each subinterval to form rectangles. With the same partition
$x_0, x_1, \ldots, x_n$, the rectangular approximation $A_S$ can be written as:
$$
 A_S \approx \sum_{k=1}^{n} f(x_{k-1}) \bigl[x_k - x_{k-1}\bigr].
$$

Definition

Area under the curve — auc.xy

<dl>

<dt>...</dt>
<dd>Arguments passed on to <code>auc.xy.numeric</code><dl>
 <dt><code>y,x</code></dt>
<dd>A pair of &lt;<a href='https://rdrr.io/r/base/double.html'>double</a>&gt; vectors of <a href='https://rdrr.io/r/base/length.html'>length</a> $n$.</dd>

 <dt><code>method</code></dt>
<dd>A &lt;<a href='https://rdrr.io/r/base/integer.html'>integer</a>&gt; value (default: $0$). Defines the underlying method of calculating the area under the curve. If $0$ it is calculated using the <code>trapezoid</code>-method, if $1$ it is calculated using the <code>step</code>-method.</dd>

 <dt><code>presorted</code></dt>
<dd>A &lt;<a href='https://rdrr.io/r/base/logical.html'>logical</a>&gt;-value <a href='https://rdrr.io/r/base/length.html'>length</a> 1 (default: <a href='https://rdrr.io/r/base/logical.html'>FALSE</a>). If <a href='https://rdrr.io/r/base/logical.html'>TRUE</a> the input will not be sorted by threshold.</dd>

 
</dl></dd>

</dl>

Trapezoidal rule
The trapezoidal rule approximates the integral of a function $f(x)$ between
$x = a$ and $x = b$ using trapezoids formed between consecutive points. If
we have points $x_0, x_1, \ldots, x_n$ (with $a = x_0 &lt; x_1 &lt; \cdots &lt; x_n = b$)
and corresponding function values $f(x_0), f(x_1), \ldots, f(x_n)$, the area under
the curve $A_T$ is approximated by:
$$
 A_T \approx \sum_{k=1}^{n} \frac{f(x_{k-1}) + f(x_k)}{2} \bigl[x_k - x_{k-1}\bigr].
$$
Step-function method
The step-function (rectangular) method uses the value of the function at one
endpoint of each subinterval to form rectangles. With the same partition
$x_0, x_1, \ldots, x_n$, the rectangular approximation $A_S$ can be written as:
$$
 A_S \approx \sum_{k=1}^{n} f(x_{k-1}) \bigl[x_k - x_{k-1}\bigr].
$$

auc.xy: Area under the curve

Description

Usage

Value

Arguments

Definition