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<meta property="og:title" content="separability — separability" />
<meta property="og:description" content="Calculates variety of two-class sample separability metrics
Available statistics:
M-Statistic (Kaufman &amp;amp; Remer 1994) - This is a measure of the difference of the
distributional peaks. A large M-statistic indicates good separation between the
two classes as within-class variance is minimized and between-class variance
maximized (M &amp;lt;1 poor, M &amp;gt;1 good).
Bhattacharyya distance (Bhattacharyya 1943; Harold 2003) - Measures the similarity
of two discrete or continuous probability distributions.
Jeffries-Matusita distance (Bruzzone et al., 2005; Swain et al., 1971) - The J-M
distance is a function of separability that directly relates to the probability of
how good a resultant classification will be. The J-M distance is asymptotic to v2,
where values of v2 suggest complete separability
Divergence and transformed Divergence (Du et al., 2004) - Maximum likelihood approach.
Transformed divergence gives an exponentially decreasing weight to increasing distances
between the classes.

" />




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    <h1>separability</h1>
    <small class="dont-index">Source: <a href='https://github.com/jeffreyevans/spatialEco/blob/master/R/separability.R'><code>R/separability.R</code></a></small>
    <div class="hidden name"><code>separability.Rd</code></div>
    </div>

    <div class="ref-description">
    <p>Calculates variety of two-class sample separability metrics</p>
<p>Available statistics:</p><ul>
<li><p>M-Statistic (Kaufman &amp; Remer 1994) - This is a measure of the difference of the
distributional peaks. A large M-statistic indicates good separation between the
two classes as within-class variance is minimized and between-class variance
maximized (M &lt;1 poor, M &gt;1 good).</p></li>
<li><p>Bhattacharyya distance (Bhattacharyya 1943; Harold 2003) - Measures the similarity
of two discrete or continuous probability distributions.</p></li>
<li><p>Jeffries-Matusita distance (Bruzzone et al., 2005; Swain et al., 1971) - The J-M
distance is a function of separability that directly relates to the probability of
how good a resultant classification will be. The J-M distance is asymptotic to v2,
where values of v2 suggest complete separability</p></li>
<li><p>Divergence and transformed Divergence (Du et al., 2004) - Maximum likelihood approach.
Transformed divergence gives an exponentially decreasing weight to increasing distances
between the classes.</p></li>
</ul>

    </div>

    <pre class="usage"><span class='fu'>separability</span><span class='op'>(</span>
  <span class='va'>x</span>,
  <span class='va'>y</span>,
  plot <span class='op'>=</span> <span class='cn'>FALSE</span>,
  cols <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"red"</span>, <span class='st'>"blue"</span><span class='op'>)</span>,
  clabs <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"Class1"</span>, <span class='st'>"Class2"</span><span class='op'>)</span>,
  <span class='va'>...</span>
<span class='op'>)</span></pre>

    <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
    <table class="ref-arguments">
    <colgroup><col class="name" /><col class="desc" /></colgroup>
    <tr>
      <th>x</th>
      <td><p>X vector</p></td>
    </tr>
    <tr>
      <th>y</th>
      <td><p>Y vector</p></td>
    </tr>
    <tr>
      <th>plot</th>
      <td><p>plot separability (TRUE/FALSE)</p></td>
    </tr>
    <tr>
      <th>cols</th>
      <td><p>colors for plot (must be equal to number of classes)</p></td>
    </tr>
    <tr>
      <th>clabs</th>
      <td><p>labels for two classes</p></td>
    </tr>
    <tr>
      <th>...</th>
      <td><p>additional arguments passes to plot</p></td>
    </tr>
    </table>

    <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>

    <p>A data.frame with the following separability metrics:</p><ul>
<li><p>B - Bhattacharryya distance statistic</p></li>
<li><p>JM - Jeffries-Matusita distance statistic</p></li>
<li><p>M - M-Statistic</p></li>
<li><p>D - Divergence index</p></li>
<li><p>TD - Transformed Divergence index</p></li>
</ul>

    <h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2>

    <p>Anderson, M. J., &amp; Clements, A. (2000) Resolving environmental disputes: a
statistical method for choosing among competing cluster models. Ecological
Applications 10(5):1341-1355</p>
<p>Bhattacharyya, A. (1943) On a measure of divergence between two statistical
populations defined by their probability distributions'. Bulletin of the
Calcutta Mathematical Society 35:99-109</p>
<p>Bruzzone, L., F. Roli, S.B. Serpico (1995) An extension to multiclass cases of
the Jefferys-Matusita distance. IEEE Transactions on Pattern Analysis and
Machine Intelligence 33:1318-1321</p>
<p>Du, H., C.I. Chang, H. Ren, F.M. D'Amico, J. O. Jensen, J., (2004) New
Hyperspectral Discrimination Measure for Spectral Characterization. Optical
Engineering 43(8):1777-1786.</p>
<p>Kailath, T., (1967) The Divergence and Bhattacharyya measures in signal
selection. IEEE Transactions on Communication Theory 15:52-60</p>
<p>Kaufman Y., and L. Remer (1994) Detection of forests using mid-IR reflectance:
An application for aerosol studies. IEEE T. Geosci.Remote. 32(3):672-683.</p>
    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>

    <p>Jeffrey S. Evans  <a href='mailto:jeffrey_evans@tnc.org'>jeffrey_evans@tnc.org</a></p>

    <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
    <pre class="examples"><div class='input'>   <span class='va'>norm1</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/Normal.html'>dnorm</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span><span class='op'>(</span><span class='op'>-</span><span class='fl'>20</span>,<span class='fl'>20</span>,length<span class='op'>=</span><span class='fl'>5000</span><span class='op'>)</span>,mean<span class='op'>=</span><span class='fl'>0</span>,sd<span class='op'>=</span><span class='fl'>1</span><span class='op'>)</span> 
   <span class='va'>norm2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/Normal.html'>dnorm</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span><span class='op'>(</span><span class='op'>-</span><span class='fl'>20</span>,<span class='fl'>20</span>,length<span class='op'>=</span><span class='fl'>5000</span><span class='op'>)</span>,mean<span class='op'>=</span><span class='fl'>0.2</span>,sd<span class='op'>=</span><span class='fl'>2</span><span class='op'>)</span>                          
     <span class='fu'>separability</span><span class='op'>(</span><span class='va'>norm1</span>, <span class='va'>norm2</span><span class='op'>)</span> 
</div><div class='output co'>#&gt;            B         JM M mdif         D         TD
#&gt; 1 0.03854306 0.07561946 0    0 0.3333837 0.08163315</div><div class='input'>           
   <span class='va'>s1</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>1362</span>,<span class='fl'>1411</span>,<span class='fl'>1457</span>,<span class='fl'>1735</span>,<span class='fl'>1621</span>,<span class='fl'>1621</span>,<span class='fl'>1791</span>,<span class='fl'>1863</span>,<span class='fl'>1863</span>,<span class='fl'>1838</span><span class='op'>)</span>
   <span class='va'>s2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>1362</span>,<span class='fl'>1411</span>,<span class='fl'>1457</span>,<span class='fl'>10030</span>,<span class='fl'>1621</span>,<span class='fl'>1621</span>,<span class='fl'>1791</span>,<span class='fl'>1863</span>,<span class='fl'>1863</span>,<span class='fl'>1838</span><span class='op'>)</span>
     <span class='fu'>separability</span><span class='op'>(</span><span class='va'>s1</span>, <span class='va'>s2</span>, plot<span class='op'>=</span><span class='cn'>TRUE</span><span class='op'>)</span> 
</div><div class='img'><img src='separability-1.png' alt='' width='700' height='433' /></div><div class='output co'>#&gt;           B       JM         M  mdif        D       TD
#&gt; 1 0.9940818 1.259874 0.2910931 829.5 104.1721 1.999996</div><div class='input'>      
</div></pre>
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