OpenI
/
graphkit-learn



<!DOCTYPE html>
<!--[if IE 8]><html class="no-js lt-ie9" lang="en" > <![endif]-->
<!--[if gt IE 8]><!--> <html class="no-js" lang="en" > <!--<![endif]-->
<head>
  <meta charset="utf-8">
  
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  
  <title>pygraph.utils.kernels &mdash; py-graph  documentation</title>
  

  <script type="text/javascript" src="../../../_static/js/modernizr.min.js"></script>
  
    
      <script type="text/javascript" id="documentation_options" data-url_root="../../../" src="../../../_static/documentation_options.js"></script>
        <script type="text/javascript" src="../../../_static/jquery.js"></script>
        <script type="text/javascript" src="../../../_static/underscore.js"></script>
        <script type="text/javascript" src="../../../_static/doctools.js"></script>
        <script async="async" type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
    
    <script type="text/javascript" src="../../../_static/js/theme.js"></script>

    
  <link rel="stylesheet" href="../../../_static/css/theme.css" type="text/css" />
  <link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
    <link rel="index" title="Index" href="../../../genindex.html" />
    <link rel="search" title="Search" href="../../../search.html" /> 
</head>

<body class="wy-body-for-nav">

   
  <div class="wy-grid-for-nav">
    
    <nav data-toggle="wy-nav-shift" class="wy-nav-side">
      <div class="wy-side-scroll">
        <div class="wy-side-nav-search" >
          

            <a href="../../../index.html" class="icon icon-home"> py-graph
          

          </a>

          
              <div class="version">
                1.0
              </div>
            
          
<div role="search">
  <form id="rtd-search-form" class="wy-form" action="../../../search.html" method="get">
    <input type="text" name="q" placeholder="Search docs" />
    <input type="hidden" name="check_keywords" value="yes" />
    <input type="hidden" name="area" value="default" />
  </form>
</div>

          
        </div>

        <div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="main navigation">
          
            
              <!-- Local TOC -->
              <div class="local-toc"></div>
            
          
        </div>
      </div>
    </nav>

    <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap">

      
      <nav class="wy-nav-top" aria-label="top navigation">
        
          <i data-toggle="wy-nav-top" class="fa fa-bars"></i>
          <a href="../../../index.html">py-graph</a>
        
      </nav>


      <div class="wy-nav-content">
        
        <div class="rst-content">
        
          
<div role="navigation" aria-label="breadcrumbs navigation">

  <ul class="wy-breadcrumbs">
    
      <li><a href="../../../index.html">Docs</a> &raquo;</li>
        
          <li><a href="../../index.html">Module code</a> &raquo;</li>
        
      <li>pygraph.utils.kernels</li>
    
    
      <li class="wy-breadcrumbs-aside">
        
      </li>
    
  </ul>

  
  <hr/>
</div>
          <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
           <div itemprop="articleBody">
            
  <h1>Source code for pygraph.utils.kernels</h1><div class="highlight"><pre>
<span></span><span class="sd">&quot;&quot;&quot;Those who are not graph kernels. We can be kernels for nodes or edges!</span>
<span class="sd">These kernels are defined between pairs of vectors.</span>
<span class="sd">&quot;&quot;&quot;</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>

<div class="viewcode-block" id="deltakernel"><a class="viewcode-back" href="../../../pygraph.utils.html#pygraph.utils.kernels.deltakernel">[docs]</a><span class="k">def</span> <span class="nf">deltakernel</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;Delta kernel. Return 1 if x == y, 0 otherwise.</span>

<span class="sd">    Parameters</span>
<span class="sd">    ----------</span>
<span class="sd">    x, y : any</span>
<span class="sd">        Two parts to compare.</span>

<span class="sd">    Return</span>
<span class="sd">    ------</span>
<span class="sd">    kernel : integer</span>
<span class="sd">        Delta kernel.</span>

<span class="sd">    References</span>
<span class="sd">    ----------</span>
<span class="sd">    [1] H. Kashima, K. Tsuda, and A. Inokuchi. Marginalized kernels between </span>
<span class="sd">    labeled graphs. In Proceedings of the 20th International Conference on </span>
<span class="sd">    Machine Learning, Washington, DC, United States, 2003.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">return</span> <span class="n">x</span> <span class="o">==</span> <span class="n">y</span>  <span class="c1">#(1 if condition else 0)</span></div>


<div class="viewcode-block" id="gaussiankernel"><a class="viewcode-back" href="../../../pygraph.utils.html#pygraph.utils.kernels.gaussiankernel">[docs]</a><span class="k">def</span> <span class="nf">gaussiankernel</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;Gaussian kernel.</span>
<span class="sd">    Compute the rbf (gaussian) kernel between x and y:</span>

<span class="sd">        K(x, y) = exp(-gamma ||x-y||^2).</span>

<span class="sd">    Read more in the :ref:`User Guide &lt;rbf_kernel&gt;`.</span>

<span class="sd">    Parameters</span>
<span class="sd">    ----------</span>
<span class="sd">    x, y : array</span>

<span class="sd">    gamma : float, default None</span>
<span class="sd">        If None, defaults to 1.0 / n_features</span>

<span class="sd">    Returns</span>
<span class="sd">    -------</span>
<span class="sd">    kernel : float</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">if</span> <span class="n">gamma</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
        <span class="n">gamma</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>

    <span class="n">xt</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="nb">float</span><span class="p">(</span><span class="n">itm</span><span class="p">)</span> <span class="k">for</span> <span class="n">itm</span> <span class="ow">in</span> <span class="n">x</span><span class="p">])</span>
    <span class="n">yt</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="nb">float</span><span class="p">(</span><span class="n">itm</span><span class="p">)</span> <span class="k">for</span> <span class="n">itm</span> <span class="ow">in</span> <span class="n">y</span><span class="p">])</span>
    <span class="n">kernel</span> <span class="o">=</span> <span class="n">xt</span> <span class="o">-</span> <span class="n">yt</span>
    <span class="n">kernel</span> <span class="o">=</span> <span class="n">kernel</span> <span class="o">**</span> <span class="mi">2</span>
    <span class="n">kernel</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">kernel</span><span class="p">)</span>
    <span class="n">kernel</span> <span class="o">*=</span> <span class="o">-</span><span class="n">gamma</span>
    <span class="n">kernel</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">kernel</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">kernel</span></div>


<div class="viewcode-block" id="polynomialkernel"><a class="viewcode-back" href="../../../pygraph.utils.html#pygraph.utils.kernels.polynomialkernel">[docs]</a><span class="k">def</span> <span class="nf">polynomialkernel</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">d</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;Polynomial kernel.</span>
<span class="sd">    Compute the polynomial kernel between x and y:</span>

<span class="sd">        K(x, y) = &lt;x, y&gt; ^d + c.</span>

<span class="sd">    Parameters</span>
<span class="sd">    ----------</span>
<span class="sd">    x, y : array</span>

<span class="sd">    d : integer, default 1</span>
<span class="sd">    </span>
<span class="sd">    c : float, default 0</span>

<span class="sd">    Returns</span>
<span class="sd">    -------</span>
<span class="sd">    kernel : float</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span> <span class="o">**</span> <span class="n">d</span> <span class="o">+</span> <span class="n">c</span></div>


<div class="viewcode-block" id="linearkernel"><a class="viewcode-back" href="../../../pygraph.utils.html#pygraph.utils.kernels.linearkernel">[docs]</a><span class="k">def</span> <span class="nf">linearkernel</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;Polynomial kernel.</span>
<span class="sd">    Compute the polynomial kernel between x and y:</span>

<span class="sd">        K(x, y) = &lt;x, y&gt;.</span>

<span class="sd">    Parameters</span>
<span class="sd">    ----------</span>
<span class="sd">    x, y : array</span>

<span class="sd">    d : integer, default 1</span>
<span class="sd">    </span>
<span class="sd">    c : float, default 0</span>

<span class="sd">    Returns</span>
<span class="sd">    -------</span>
<span class="sd">    kernel : float</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span></div>


<div class="viewcode-block" id="kernelsum"><a class="viewcode-back" href="../../../pygraph.utils.html#pygraph.utils.kernels.kernelsum">[docs]</a><span class="k">def</span> <span class="nf">kernelsum</span><span class="p">(</span><span class="n">k1</span><span class="p">,</span> <span class="n">k2</span><span class="p">,</span> <span class="n">d11</span><span class="p">,</span> <span class="n">d12</span><span class="p">,</span> <span class="n">d21</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">d22</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">lamda1</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">lamda2</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;Sum of a pair of kernels.</span>

<span class="sd">    k = lamda1 * k1(d11, d12) + lamda2 * k2(d21, d22)</span>

<span class="sd">    Parameters</span>
<span class="sd">    ----------</span>
<span class="sd">    k1, k2 : function</span>
<span class="sd">        A pair of kernel functions.</span>
<span class="sd">    d11, d12:</span>
<span class="sd">        Inputs of k1. If d21 or d22 is None, apply d11, d12 to both k1 and k2.</span>
<span class="sd">    d21, d22:</span>
<span class="sd">        Inputs of k2.</span>
<span class="sd">    lamda1, lamda2: float</span>
<span class="sd">        Coefficients of the product.</span>

<span class="sd">    Return</span>
<span class="sd">    ------</span>
<span class="sd">    kernel : integer</span>

<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">if</span> <span class="n">d21</span> <span class="o">==</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">d22</span> <span class="o">==</span> <span class="kc">None</span><span class="p">:</span>
        <span class="n">kernel</span> <span class="o">=</span> <span class="n">lamda1</span> <span class="o">*</span> <span class="n">k1</span><span class="p">(</span><span class="n">d11</span><span class="p">,</span> <span class="n">d12</span><span class="p">)</span> <span class="o">+</span> <span class="n">lamda2</span> <span class="o">*</span> <span class="n">k2</span><span class="p">(</span><span class="n">d11</span><span class="p">,</span> <span class="n">d12</span><span class="p">)</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="n">kernel</span> <span class="o">=</span> <span class="n">lamda1</span> <span class="o">*</span> <span class="n">k1</span><span class="p">(</span><span class="n">d11</span><span class="p">,</span> <span class="n">d12</span><span class="p">)</span> <span class="o">+</span> <span class="n">lamda2</span> <span class="o">*</span> <span class="n">k2</span><span class="p">(</span><span class="n">d21</span><span class="p">,</span> <span class="n">d22</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">kernel</span></div>


<div class="viewcode-block" id="kernelproduct"><a class="viewcode-back" href="../../../pygraph.utils.html#pygraph.utils.kernels.kernelproduct">[docs]</a><span class="k">def</span> <span class="nf">kernelproduct</span><span class="p">(</span><span class="n">k1</span><span class="p">,</span> <span class="n">k2</span><span class="p">,</span> <span class="n">d11</span><span class="p">,</span> <span class="n">d12</span><span class="p">,</span> <span class="n">d21</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">d22</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">lamda</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;Product of a pair of kernels.</span>

<span class="sd">    k = lamda * k1(d11, d12) * k2(d21, d22)</span>

<span class="sd">    Parameters</span>
<span class="sd">    ----------</span>
<span class="sd">    k1, k2 : function</span>
<span class="sd">        A pair of kernel functions.</span>
<span class="sd">    d11, d12:</span>
<span class="sd">        Inputs of k1. If d21 or d22 is None, apply d11, d12 to both k1 and k2.</span>
<span class="sd">    d21, d22:</span>
<span class="sd">        Inputs of k2.</span>
<span class="sd">    lamda: float</span>
<span class="sd">        Coefficient of the product.</span>

<span class="sd">    Return</span>
<span class="sd">    ------</span>
<span class="sd">    kernel : integer</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">if</span> <span class="n">d21</span> <span class="o">==</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">d22</span> <span class="o">==</span> <span class="kc">None</span><span class="p">:</span>
        <span class="n">kernel</span> <span class="o">=</span> <span class="n">lamda</span> <span class="o">*</span> <span class="n">k1</span><span class="p">(</span><span class="n">d11</span><span class="p">,</span> <span class="n">d12</span><span class="p">)</span> <span class="o">*</span> <span class="n">k2</span><span class="p">(</span><span class="n">d11</span><span class="p">,</span> <span class="n">d12</span><span class="p">)</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="n">kernel</span> <span class="o">=</span> <span class="n">lamda</span> <span class="o">*</span> <span class="n">k1</span><span class="p">(</span><span class="n">d11</span><span class="p">,</span> <span class="n">d12</span><span class="p">)</span> <span class="o">*</span> <span class="n">k2</span><span class="p">(</span><span class="n">d21</span><span class="p">,</span> <span class="n">d22</span><span class="p">)</span>
    <span class="k">return</span> <span class="n">kernel</span></div>


<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">&#39;__main__&#39;</span><span class="p">:</span>
    <span class="n">o</span> <span class="o">=</span> <span class="n">polynomialkernel</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="p">[</span><span class="mi">3</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>
</pre></div>

           </div>
           
          </div>
          <footer>
  

  <hr/>

  <div role="contentinfo">
    <p>
        &copy; Copyright 2020, Linlin Jia

    </p>
  </div>
  Built with <a href="http://sphinx-doc.org/">Sphinx</a> using a <a href="https://github.com/rtfd/sphinx_rtd_theme">theme</a> provided by <a href="https://readthedocs.org">Read the Docs</a>. 

</footer>

        </div>
      </div>

    </section>

  </div>
  

  <script type="text/javascript">
      jQuery(function () {
          SphinxRtdTheme.Navigation.enable(true);
      });
  </script>

  
</body>
</html>