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<h1>Source code for pyFTS.partitioners.FCM</h1><div class="highlight"><pre>
<span></span><span class="sd">"""</span>
<span class="sd">S. T. Li, Y. C. Cheng, and S. Y. Lin, “A FCM-based deterministic forecasting model for fuzzy time series,”</span>
<span class="sd">Comput. Math. Appl., vol. 56, no. 12, pp. 3052–3063, Dec. 2008. DOI: 10.1016/j.camwa.2008.07.033.</span>
<span class="sd">"""</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="kn">import</span> <span class="nn">math</span>
<span class="kn">import</span> <span class="nn">random</span> <span class="k">as</span> <span class="nn">rnd</span>
<span class="kn">import</span> <span class="nn">functools</span><span class="o">,</span> <span class="nn">operator</span>
<span class="kn">from</span> <span class="nn">pyFTS.common</span> <span class="k">import</span> <span class="n">FuzzySet</span><span class="p">,</span> <span class="n">Membership</span>
<span class="kn">from</span> <span class="nn">pyFTS.partitioners</span> <span class="k">import</span> <span class="n">partitioner</span>
<div class="viewcode-block" id="fuzzy_distance"><a class="viewcode-back" href="../../../pyFTS.partitioners.html#pyFTS.partitioners.FCM.fuzzy_distance">[docs]</a><span class="k">def</span> <span class="nf">fuzzy_distance</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="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="p">(</span><span class="nb">list</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)):</span>
<span class="n">tmp</span> <span class="o">=</span> <span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">operator</span><span class="o">.</span><span class="n">add</span><span class="p">,</span> <span class="p">[(</span><span class="n">x</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">-</span> <span class="n">y</span><span class="p">[</span><span class="n">k</span><span class="p">])</span> <span class="o">**</span> <span class="mi">2</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">))])</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">tmp</span> <span class="o">=</span> <span class="p">(</span><span class="n">x</span> <span class="o">-</span> <span class="n">y</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span>
<span class="k">return</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">tmp</span><span class="p">)</span></div>
<div class="viewcode-block" id="membership"><a class="viewcode-back" href="../../../pyFTS.partitioners.html#pyFTS.partitioners.FCM.membership">[docs]</a><span class="k">def</span> <span class="nf">membership</span><span class="p">(</span><span class="n">val</span><span class="p">,</span> <span class="n">vals</span><span class="p">):</span>
<span class="n">soma</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">vals</span><span class="p">:</span>
<span class="k">if</span> <span class="n">k</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">k</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">soma</span> <span class="o">=</span> <span class="n">soma</span> <span class="o">+</span> <span class="p">(</span><span class="n">val</span> <span class="o">/</span> <span class="n">k</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span>
<span class="k">return</span> <span class="n">soma</span></div>
<div class="viewcode-block" id="fuzzy_cmeans"><a class="viewcode-back" href="../../../pyFTS.partitioners.html#pyFTS.partitioners.FCM.fuzzy_cmeans">[docs]</a><span class="k">def</span> <span class="nf">fuzzy_cmeans</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="n">size</span><span class="p">,</span> <span class="n">m</span><span class="p">,</span> <span class="n">deltadist</span><span class="o">=</span><span class="mf">0.001</span><span class="p">):</span>
<span class="n">data_length</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="c1"># Centroid initialization</span>
<span class="n">centroids</span> <span class="o">=</span> <span class="p">[</span><span class="n">data</span><span class="p">[</span><span class="n">rnd</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">data_length</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)]</span> <span class="k">for</span> <span class="n">kk</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">k</span><span class="p">)]</span>
<span class="c1"># Membership table</span>
<span class="n">membership_table</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">k</span><span class="p">,</span> <span class="n">data_length</span><span class="p">))</span> <span class="c1">#[[0 for kk in range(0, k)] for xx in range(0, data_length)]</span>
<span class="n">mean_change</span> <span class="o">=</span> <span class="mi">1000</span>
<span class="n">m_exp</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="n">m</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">iterations</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">while</span> <span class="n">iterations</span> <span class="o"><</span> <span class="mi">1000</span> <span class="ow">and</span> <span class="n">mean_change</span> <span class="o">></span> <span class="n">deltadist</span><span class="p">:</span>
<span class="n">mean_change</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">inst_count</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">instance</span> <span class="ow">in</span> <span class="n">data</span><span class="p">:</span>
<span class="n">dist_groups</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">k</span><span class="p">)</span> <span class="c1">#[0 for xx in range(0, k)]</span>
<span class="k">for</span> <span class="n">group_count</span><span class="p">,</span> <span class="n">group</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">centroids</span><span class="p">):</span>
<span class="n">dist_groups</span><span class="p">[</span><span class="n">group_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">fuzzy_distance</span><span class="p">(</span><span class="n">group</span><span class="p">,</span> <span class="n">instance</span><span class="p">)</span>
<span class="n">dist_groups_total</span> <span class="o">=</span> <span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">operator</span><span class="o">.</span><span class="n">add</span><span class="p">,</span> <span class="p">[</span><span class="n">xk</span> <span class="k">for</span> <span class="n">xk</span> <span class="ow">in</span> <span class="n">dist_groups</span><span class="p">])</span>
<span class="k">for</span> <span class="n">grp</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">k</span><span class="p">):</span>
<span class="k">if</span> <span class="n">dist_groups</span><span class="p">[</span><span class="n">grp</span><span class="p">]</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">membership_table</span><span class="p">[</span><span class="n">inst_count</span><span class="p">][</span><span class="n">grp</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">membership_table</span><span class="p">[</span><span class="n">inst_count</span><span class="p">][</span><span class="n">grp</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">membership</span><span class="p">(</span><span class="n">dist_groups</span><span class="p">[</span><span class="n">grp</span><span class="p">],</span> <span class="n">dist_groups</span><span class="p">)</span>
<span class="c1"># membership_table[inst_count][grp] = 1/(dist_groups[grp] / dist_grupos_total)</span>
<span class="c1"># membership_table[inst_count][grp] = (1/(dist_groups[grp]**2))**m_exp / (1/(dist_grupos_total**2))**m_exp</span>
<span class="n">inst_count</span> <span class="o">=</span> <span class="n">inst_count</span> <span class="o">+</span> <span class="mi">1</span>
<span class="k">for</span> <span class="n">group_count</span><span class="p">,</span> <span class="n">group</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">centroids</span><span class="p">):</span>
<span class="k">if</span> <span class="n">size</span> <span class="o">></span> <span class="mi">1</span><span class="p">:</span>
<span class="n">oldgrp</span> <span class="o">=</span> <span class="p">[</span><span class="n">xx</span> <span class="k">for</span> <span class="n">xx</span> <span class="ow">in</span> <span class="n">group</span><span class="p">]</span>
<span class="k">for</span> <span class="n">atr</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">size</span><span class="p">):</span>
<span class="n">soma</span> <span class="o">=</span> <span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">operator</span><span class="o">.</span><span class="n">add</span><span class="p">,</span>
<span class="p">[</span><span class="n">membership_table</span><span class="p">[</span><span class="n">xk</span><span class="p">][</span><span class="n">group_count</span><span class="p">]</span> <span class="o">*</span> <span class="n">data</span><span class="p">[</span><span class="n">xk</span><span class="p">][</span><span class="n">atr</span><span class="p">]</span> <span class="k">for</span> <span class="n">xk</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">data_length</span><span class="p">)])</span>
<span class="n">norm</span> <span class="o">=</span> <span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">operator</span><span class="o">.</span><span class="n">add</span><span class="p">,</span> <span class="p">[</span><span class="n">membership_table</span><span class="p">[</span><span class="n">xk</span><span class="p">][</span><span class="n">group_count</span><span class="p">]</span> <span class="k">for</span> <span class="n">xk</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">data_length</span><span class="p">)])</span>
<span class="n">centroids</span><span class="p">[</span><span class="n">group_count</span><span class="p">][</span><span class="n">atr</span><span class="p">]</span> <span class="o">=</span> <span class="n">soma</span> <span class="o">/</span> <span class="n">norm</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">oldgrp</span> <span class="o">=</span> <span class="n">group</span>
<span class="n">soma</span> <span class="o">=</span> <span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">operator</span><span class="o">.</span><span class="n">add</span><span class="p">,</span>
<span class="p">[</span><span class="n">membership_table</span><span class="p">[</span><span class="n">xk</span><span class="p">][</span><span class="n">group_count</span><span class="p">]</span> <span class="o">*</span> <span class="n">data</span><span class="p">[</span><span class="n">xk</span><span class="p">]</span> <span class="k">for</span> <span class="n">xk</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">data_length</span><span class="p">)])</span>
<span class="n">norm</span> <span class="o">=</span> <span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">operator</span><span class="o">.</span><span class="n">add</span><span class="p">,</span> <span class="p">[</span><span class="n">membership_table</span><span class="p">[</span><span class="n">xk</span><span class="p">][</span><span class="n">group_count</span><span class="p">]</span> <span class="k">for</span> <span class="n">xk</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">data_length</span><span class="p">)])</span>
<span class="n">centroids</span><span class="p">[</span><span class="n">group_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">soma</span> <span class="o">/</span> <span class="n">norm</span>
<span class="n">mean_change</span> <span class="o">=</span> <span class="n">mean_change</span> <span class="o">+</span> <span class="n">fuzzy_distance</span><span class="p">(</span><span class="n">oldgrp</span><span class="p">,</span> <span class="n">group</span><span class="p">)</span>
<span class="n">mean_change</span> <span class="o">=</span> <span class="n">mean_change</span> <span class="o">/</span> <span class="n">k</span>
<span class="n">iterations</span> <span class="o">=</span> <span class="n">iterations</span> <span class="o">+</span> <span class="mi">1</span>
<span class="k">return</span> <span class="n">centroids</span></div>
<div class="viewcode-block" id="FCMPartitioner"><a class="viewcode-back" href="../../../pyFTS.partitioners.html#pyFTS.partitioners.FCM.FCMPartitioner">[docs]</a><span class="k">class</span> <span class="nc">FCMPartitioner</span><span class="p">(</span><span class="n">partitioner</span><span class="o">.</span><span class="n">Partitioner</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> </span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="nb">super</span><span class="p">(</span><span class="n">FCMPartitioner</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">name</span><span class="o">=</span><span class="s2">"FCM"</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<div class="viewcode-block" id="FCMPartitioner.build"><a class="viewcode-back" href="../../../pyFTS.partitioners.html#pyFTS.partitioners.FCM.FCMPartitioner.build">[docs]</a> <span class="k">def</span> <span class="nf">build</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">data</span><span class="p">):</span>
<span class="n">sets</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">kwargs</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'type'</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">type</span><span class="p">,</span> <span class="s1">'variable'</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">variable</span><span class="p">}</span>
<span class="n">centroids</span> <span class="o">=</span> <span class="n">fuzzy_cmeans</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">partitions</span><span class="p">,</span> <span class="n">data</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="n">centroids</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">max</span><span class="p">)</span>
<span class="n">centroids</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">min</span><span class="p">)</span>
<span class="n">centroids</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">centroids</span><span class="p">))</span>
<span class="n">centroids</span><span class="o">.</span><span class="n">sort</span><span class="p">()</span>
<span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">centroids</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="n">_name</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_name</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">membership_function</span> <span class="o">==</span> <span class="n">Membership</span><span class="o">.</span><span class="n">trimf</span><span class="p">:</span>
<span class="n">sets</span><span class="p">[</span><span class="n">_name</span><span class="p">]</span> <span class="o">=</span> <span class="n">FuzzySet</span><span class="o">.</span><span class="n">FuzzySet</span><span class="p">(</span><span class="n">_name</span><span class="p">,</span> <span class="n">Membership</span><span class="o">.</span><span class="n">trimf</span><span class="p">,</span>
<span class="p">[</span><span class="nb">round</span><span class="p">(</span><span class="n">centroids</span><span class="p">[</span><span class="n">c</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="nb">round</span><span class="p">(</span><span class="n">centroids</span><span class="p">[</span><span class="n">c</span><span class="p">],</span> <span class="mi">3</span><span class="p">),</span>
<span class="nb">round</span><span class="p">(</span><span class="n">centroids</span><span class="p">[</span><span class="n">c</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="nb">round</span><span class="p">(</span><span class="n">centroids</span><span class="p">[</span><span class="n">c</span><span class="p">],</span> <span class="mi">3</span><span class="p">),</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">membership_function</span> <span class="o">==</span> <span class="n">Membership</span><span class="o">.</span><span class="n">trapmf</span><span class="p">:</span>
<span class="n">q1</span> <span class="o">=</span> <span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">centroids</span><span class="p">[</span><span class="n">c</span><span class="p">],</span> <span class="mi">3</span><span class="p">)</span> <span class="o">-</span> <span class="nb">round</span><span class="p">(</span><span class="n">centroids</span><span class="p">[</span><span class="n">c</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="o">/</span> <span class="mi">2</span>
<span class="n">q2</span> <span class="o">=</span> <span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">centroids</span><span class="p">[</span><span class="n">c</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="o">-</span> <span class="nb">round</span><span class="p">(</span><span class="n">centroids</span><span class="p">[</span><span class="n">c</span><span class="p">],</span> <span class="mi">3</span><span class="p">))</span> <span class="o">/</span> <span class="mi">2</span>
<span class="n">sets</span><span class="p">[</span><span class="n">_name</span><span class="p">]</span> <span class="o">=</span> <span class="n">FuzzySet</span><span class="o">.</span><span class="n">FuzzySet</span><span class="p">(</span><span class="n">_name</span><span class="p">,</span> <span class="n">Membership</span><span class="o">.</span><span class="n">trimf</span><span class="p">,</span>
<span class="p">[</span><span class="nb">round</span><span class="p">(</span><span class="n">centroids</span><span class="p">[</span><span class="n">c</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="nb">round</span><span class="p">(</span><span class="n">centroids</span><span class="p">[</span><span class="n">c</span><span class="p">],</span> <span class="mi">3</span><span class="p">)</span> <span class="o">-</span> <span class="n">q1</span><span class="p">,</span>
<span class="nb">round</span><span class="p">(</span><span class="n">centroids</span><span class="p">[</span><span class="n">c</span><span class="p">],</span> <span class="mi">3</span><span class="p">)</span> <span class="o">+</span> <span class="n">q2</span><span class="p">,</span> <span class="nb">round</span><span class="p">(</span><span class="n">centroids</span><span class="p">[</span><span class="n">c</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="nb">round</span><span class="p">(</span><span class="n">centroids</span><span class="p">[</span><span class="n">c</span><span class="p">],</span> <span class="mi">3</span><span class="p">),</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="k">return</span> <span class="n">sets</span></div></div>
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