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  <div class="section" id="feature-list-analysis">
<h1>Feature List Analysis<a class="headerlink" href="#feature-list-analysis" title="Permalink to this headline"></a></h1>
<div class="section" id="canberra-indicator">
<h2>Canberra Indicator<a class="headerlink" href="#canberra-indicator" title="Permalink to this headline"></a></h2>
<p>Canberra stability indicator on top-k positions <a class="reference internal" href="#jurman08">[Jurman08]</a></p>
<dl class="function">
<dt id="mlpy.canberra">
<tt class="descclassname">mlpy.</tt><tt class="descname">canberra</tt><big>(</big><em>lists</em>, <em>k</em>, <em>dist=False</em>, <em>modules=None</em><big>)</big><a class="headerlink" href="#mlpy.canberra" title="Permalink to this definition"></a></dt>
<dd><p>Compute mean Canberra distance indicator on top-k sublists.</p>
<p>Input</p>
<blockquote>
<div><ul class="simple">
<li><em>lists</em>   - [2D numpy array integer] position lists
Positions must be in [0, #elems-1]</li>
<li><em>k</em>       - [integer] top-k sublists</li>
<li><em>modules</em> - [list] modules (list of group indicies)</li>
<li><em>dist</em>    - [bool] return partial distances (True or False)</li>
</ul>
</div></blockquote>
<p>Output</p>
<blockquote>
<div><ul class="simple">
<li><em>cd</em> - [float] canberra distance</li>
<li><em>i1</em> - [1D numpy array integer] index 1 (if dist == True)</li>
<li><em>i2</em> - [1D numpy array integer] index 2 (if dist == True)</li>
<li><em>pd</em> - [1D numpy array float] partial distances for index1 and index2 (if dist == True)</li>
</ul>
</div></blockquote>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">mlpy</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">lists</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span>  <span class="c"># first positions list</span>
<span class="gp">... </span>               <span class="p">[</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span>  <span class="c"># second positions list</span>
<span class="gp">... </span>               <span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span>  <span class="c"># third positions list</span>
<span class="gp">... </span>               <span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">]])</span> <span class="c"># fourth positions list</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">canberra</span><span class="p">(</span><span class="n">lists</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="go">1.0861983059292479</span>
</pre></div>
</div>
</dd></dl>

<dl class="function">
<dt id="mlpy.canberraq">
<tt class="descclassname">mlpy.</tt><tt class="descname">canberraq</tt><big>(</big><em>lists</em>, <em>complete=True</em>, <em>normalize=False</em>, <em>dist=False</em><big>)</big><a class="headerlink" href="#mlpy.canberraq" title="Permalink to this definition"></a></dt>
<dd><p>Compute mean Canberra distance indicator on generic lists.</p>
<p>Input</p>
<blockquote>
<div><ul class="simple">
<li><em>lists</em> - [2D numpy array integer] position lists
Positions must be in [-1, #elems-1],
where -1 indicates features not present in the list</li>
<li><em>complete</em>  - [bool] complete</li>
<li><em>normalize</em> - [bool] normalize</li>
<li><em>dist</em> - [bool] return partial distances (True or False)</li>
</ul>
</div></blockquote>
<p>Output</p>
<blockquote>
<div><ul class="simple">
<li><em>cd</em> - [float] canberra distance</li>
<li><em>i1</em> - [1D numpy array integer] index 1 (if dist == True)</li>
<li><em>i2</em> - [1D numpy array integer] index 2 (if dist == True)</li>
<li><em>pd</em> - [1D numpy array float] partial distances for index1 and index2 (if dist == True)</li>
</ul>
</div></blockquote>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">mlpy</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">lists</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="mi">2</span><span class="p">,</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span>  <span class="c"># first positions list</span>
<span class="gp">... </span>               <span class="p">[</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span>    <span class="c"># second positions list</span>
<span class="gp">... </span>               <span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span>   <span class="c"># third positions list</span>
<span class="gp">... </span>               <span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">]])</span>   <span class="c"># fourth positions list</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">canberraq</span><span class="p">(</span><span class="n">lists</span><span class="p">)</span>
<span class="go">1.0628570368721744</span>
</pre></div>
</div>
</dd></dl>

<dl class="function">
<dt id="mlpy.normalizer">
<tt class="descclassname">mlpy.</tt><tt class="descname">normalizer</tt><big>(</big><em>lists</em><big>)</big><a class="headerlink" href="#mlpy.normalizer" title="Permalink to this definition"></a></dt>
<dd><p>Compute the average length of the partial lists (nm) and the corresponding
normalizing factor (nf) given by 1 - a / b where a is the exact value computed
on the average length and b is the exact value computed on the whole set of
features.</p>
<p>Inputs</p>
<blockquote>
<div><ul class="simple">
<li><em>lists</em> - [2D numpy array integer] position lists
Positions must be in [-1, #elems-1],
where -1 indicates features not present in the list</li>
</ul>
</div></blockquote>
<p>Output</p>
<blockquote>
<div><ul class="simple">
<li><em>(nm, nf)</em> - (float, float)</li>
</ul>
</div></blockquote>
</dd></dl>

</div>
<div class="section" id="borda-count-extraction-indicator-mean-position-indicator">
<h2>Borda Count, Extraction Indicator, Mean Position Indicator<a class="headerlink" href="#borda-count-extraction-indicator-mean-position-indicator" title="Permalink to this headline"></a></h2>
<p>Borda Count <a class="reference internal" href="#borda1781">[Borda1781]</a></p>
<dl class="function">
<dt id="mlpy.borda">
<tt class="descclassname">mlpy.</tt><tt class="descname">borda</tt><big>(</big><em>lists</em>, <em>k</em>, <em>modules=None</em><big>)</big><a class="headerlink" href="#mlpy.borda" title="Permalink to this definition"></a></dt>
<dd><p>Compute the number of extractions on top-k sublists and
the mean position on lists for each element.
Sort the element ids with decreasing number of extractions,
AND element ids with equal number of extractions should be
sorted with increasing mean positions.</p>
<p>Input</p>
<blockquote>
<div><ul class="simple">
<li><em>lists</em> - [2D numpy array integer] ranked feature-id lists.
Feature-id must be in [0, #elems-1].</li>
<li><em>k</em>     - [integer] on top-k sublists</li>
<li><em>modules</em> - [list] modules (list of group indicies)</li>
</ul>
</div></blockquote>
<p>Output</p>
<blockquote>
<div><ul class="simple">
<li><em>borda</em> - (feature-id, number of extractions,  mean positions)</li>
</ul>
</div></blockquote>
<p>Example:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">mlpy</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">lists</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span>  <span class="c"># first ranked feature-id list</span>
<span class="gp">... </span>               <span class="p">[</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span>  <span class="c"># second ranked feature-id list</span>
<span class="gp">... </span>               <span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span>  <span class="c"># third ranked feature-id list</span>
<span class="gp">... </span>               <span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">]])</span> <span class="c"># fourth ranked feature-id list</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">borda</span><span class="p">(</span><span class="n">lists</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="go">(array([4, 1, 2, 3, 0]), array([4, 3, 2, 2, 1]), array([ 1.25      ,  1.66666667,  0.        ,  1.        ,  0.        ]))</span>
</pre></div>
</div>
<blockquote>
<div><ul class="simple">
<li>Element 4 is in the first position with 4 extractions and mean position 1.25.</li>
<li>Element 1 is in the first position with 3 extractions and mean position 1.67.</li>
<li>Element 2 is in the first position with 2 extractions and mean position 0.00.</li>
<li>Element 3 is in the first position with 2 extractions and mean position 1.00.</li>
<li>Element 0 is in the first position with 1 extractions and mean position 0.00.</li>
</ul>
</div></blockquote>
</dd></dl>

<dl class="function">
<dt id="mlpy.borda_weighted">
<tt class="descclassname">mlpy.</tt><tt class="descname">borda_weighted</tt><big>(</big><em>lists</em>, <em>w</em>, <em>decimals=2</em><big>)</big><a class="headerlink" href="#mlpy.borda_weighted" title="Permalink to this definition"></a></dt>
<dd><p>Compute the mean position on lists for each element.
Sort the element ids with increasing mean weighted positions.</p>
<p>Input</p>
<blockquote>
<div><ul class="simple">
<li><em>lists</em> - [2D numpy array integer] ranked feature-id lists.
Feature-id must be in [0, #elems-1].</li>
<li><em>w</em>  - [1D numpy array float] weights</li>
<li><em>decimals</em> - [integer &gt;=0] decimals</li>
</ul>
</div></blockquote>
<p>Output</p>
<blockquote>
<div><ul class="simple">
<li><em>borda</em> - (feature-id, mean positions)</li>
</ul>
</div></blockquote>
</dd></dl>

<table class="docutils citation" frame="void" id="jurman08" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id1">[Jurman08]</a></td><td>G Jurman, S Merler, A Barla, S Paoli, A Galea, and C Furlanello. Algebraic stability indicators for ranked lists in molecular profiling. Bioinformatics, 24(2):258-264, 2008.</td></tr>
</tbody>
</table>
<table class="docutils citation" frame="void" id="borda1781" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id2">[Borda1781]</a></td><td>J C Borda. Mémoire sur les élections au scrutin. Histoire de l&#8217;Académie Royale des Sciences, 1781.</td></tr>
</tbody>
</table>
</div>
</div>


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  <h3><a href="index.html">Table Of Contents</a></h3>
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<li><a class="reference internal" href="#">Feature List Analysis</a><ul>
<li><a class="reference internal" href="#canberra-indicator">Canberra Indicator</a></li>
<li><a class="reference internal" href="#borda-count-extraction-indicator-mean-position-indicator">Borda Count, Extraction Indicator, Mean Position Indicator</a></li>
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