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  <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>

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