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<h1>Source code for MRCpy.phi.random_fourier_phi</h1><div class="highlight"><pre>
<span></span><span class="sd">''' Gaussian Kernel approximated using Random Features.'''</span>
<span class="kn">import</span> <span class="nn">statistics</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">sklearn.neighbors</span> <span class="kn">import</span> <span class="n">NearestNeighbors</span>
<span class="kn">from</span> <span class="nn">sklearn.utils</span> <span class="kn">import</span> <span class="n">check_array</span><span class="p">,</span> <span class="n">check_random_state</span>
<span class="kn">from</span> <span class="nn">sklearn.utils.validation</span> <span class="kn">import</span> <span class="n">check_is_fitted</span>
<span class="c1"># Import the feature mapping base class</span>
<span class="kn">from</span> <span class="nn">MRCpy.phi</span> <span class="kn">import</span> <span class="n">BasePhi</span>
<div class="viewcode-block" id="RandomFourierPhi"><a class="viewcode-back" href="../../../generated/MRCpy.phi.RandomFourierPhi.html#MRCpy.phi.RandomFourierPhi">[docs]</a><span class="k">class</span> <span class="nc">RandomFourierPhi</span><span class="p">(</span><span class="n">BasePhi</span><span class="p">):</span>
<span class="sd">'''</span>
<span class="sd"> Fourier features</span>
<span class="sd"> Features obtained by approximating the rbf kernel by</span>
<span class="sd"> Random Fourier Feature map -</span>
<span class="sd"> .. math:: z(x) = \sqrt{(2/D)} *</span>
<span class="sd"> [\cos(w_1^t * x), ..., \cos(w_D^t * x),</span>
<span class="sd"> \sin(w_1^t * x), ..., \sin(w_D^t * x)]</span>
<span class="sd"> where w is a vector(dimension d) of random weights</span>
<span class="sd"> from gaussian distribution with mean 0 and variance</span>
<span class="sd"> :math:`\sqrt(2 * \gamma)` and</span>
<span class="sd"> D is the number of components in the resulting feature map.</span>
<span class="sd"> The parameter :math:`\gamma`</span>
<span class="sd"> in the variance is similar to the scaling parameter</span>
<span class="sd"> of the radial basis function kernel -</span>
<span class="sd"> .. math:: K(x, x\') = \exp(-\gamma * \| x-x\'\|^2)</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> n_classes : int</span>
<span class="sd"> The number of classes in the dataset.</span>
<span class="sd"> fit_intercept : bool, default=True</span>
<span class="sd"> Whether to calculate the intercept.</span>
<span class="sd"> If set to false, no intercept will be used in calculations</span>
<span class="sd"> (i.e. data is expected to be already centered).</span>
<span class="sd"> gamma : str {'scale', 'avg_ann', 'avg_ann_50'} or float,</span>
<span class="sd"> default = 'avg_ann_50'</span>
<span class="sd"> It defines the type of heuristic to be used</span>
<span class="sd"> to calculate the scaling parameter using the data or</span>
<span class="sd"> a float value for the parameter.</span>
<span class="sd"> n_components : int, default=300</span>
<span class="sd"> Number of Monte Carlo samples per original features.</span>
<span class="sd"> Equals the dimensionality of the computed (mapped) feature space.</span>
<span class="sd"> random_state : int, RandomState instance, default=None</span>
<span class="sd"> Used to produce the random weights</span>
<span class="sd"> used for the approximation of the gaussian kernel.</span>
<span class="sd"> Attributes</span>
<span class="sd"> ----------</span>
<span class="sd"> random_weights_ : array-like of shape (n_features, n_components/2)</span>
<span class="sd"> The sampled basis.</span>
<span class="sd"> is_fitted_ : bool</span>
<span class="sd"> True if the feature mappings has learned its hyperparameters (if any)</span>
<span class="sd"> and the length of the feature mapping is set.</span>
<span class="sd"> len_ : int</span>
<span class="sd"> Defines the length of the feature mapping vector.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> [1] Random Features for Large-Scale Kernel Machines.</span>
<span class="sd"> Ali Rahimi and Ben Recht.</span>
<span class="sd"> In NIPS 2007.</span>
<span class="sd"> (https://people.eecs.berkeley.edu/~brecht/papers/07.rah.rec.nips.pdf)</span>
<span class="sd"> '''</span>
<div class="viewcode-block" id="RandomFourierPhi.__init__"><a class="viewcode-back" href="../../../generated/MRCpy.phi.RandomFourierPhi.html#MRCpy.phi.RandomFourierPhi.__init__">[docs]</a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">n_classes</span><span class="p">,</span> <span class="n">fit_intercept</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="s1">'avg_ann_50'</span><span class="p">,</span>
<span class="n">n_components</span><span class="o">=</span><span class="mi">300</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="c1"># Call the base class init function.</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">n_classes</span><span class="o">=</span><span class="n">n_classes</span><span class="p">,</span> <span class="n">fit_intercept</span><span class="o">=</span><span class="n">fit_intercept</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">gamma</span> <span class="o">=</span> <span class="n">gamma</span>
<span class="bp">self</span><span class="o">.</span><span class="n">n_components</span> <span class="o">=</span> <span class="n">n_components</span>
<span class="bp">self</span><span class="o">.</span><span class="n">random_state</span> <span class="o">=</span> <span class="n">random_state</span></div>
<div class="viewcode-block" id="RandomFourierPhi.fit"><a class="viewcode-back" href="../../../generated/MRCpy.phi.RandomFourierPhi.html#MRCpy.phi.RandomFourierPhi.fit">[docs]</a> <span class="k">def</span> <span class="nf">fit</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="sd">'''</span>
<span class="sd"> Learns the set of random weights for computing the features.</span>
<span class="sd"> Also, compute the scaling parameter if the value is not given.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> X : array-like of shape (n_samples, n_dimensions)</span>
<span class="sd"> Unlabeled training instances</span>
<span class="sd"> used to learn the feature configurations.</span>
<span class="sd"> Y : array-like of shape (n_samples,), default=None</span>
<span class="sd"> This argument will never be used in this case.</span>
<span class="sd"> It is present in the signature for consistency</span>
<span class="sd"> in the signature of the function among different feature mappings.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> self :</span>
<span class="sd"> Fitted estimator</span>
<span class="sd"> '''</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">check_array</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">accept_sparse</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">d</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="c1"># Evaluate the gamma according to the gamma type given in self.gamma</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span> <span class="o">==</span> <span class="s1">'scale'</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">gamma_val</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="n">d</span> <span class="o">*</span> <span class="n">X</span><span class="o">.</span><span class="n">var</span><span class="p">())</span>
<span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span> <span class="o">==</span> <span class="s1">'avg_ann_50'</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">gamma_val</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">rff_gamma</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="k">elif</span> <span class="nb">type</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">gamma</span><span class="p">)</span> <span class="o">!=</span> <span class="nb">str</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">gamma_val</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">'Unexpected value for gamma ...'</span><span class="p">)</span>
<span class="c1"># Obtain the random weight from a normal distribution.</span>
<span class="bp">self</span><span class="o">.</span><span class="n">random_state</span> <span class="o">=</span> <span class="n">check_random_state</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">random_state</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">random_weights_</span> <span class="o">=</span> \
<span class="bp">self</span><span class="o">.</span><span class="n">random_state</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">gamma_val</span><span class="p">),</span>
<span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="nb">int</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_components</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)))</span>
<span class="c1"># Sets the length of the feature mapping</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">fit</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">return</span> <span class="bp">self</span></div>
<div class="viewcode-block" id="RandomFourierPhi.transform"><a class="viewcode-back" href="../../../generated/MRCpy.phi.RandomFourierPhi.html#MRCpy.phi.RandomFourierPhi.transform">[docs]</a> <span class="k">def</span> <span class="nf">transform</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">X</span><span class="p">):</span>
<span class="sd">'''</span>
<span class="sd"> Compute the random Fourier features ((:math:`z(x)`)).</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> X : array-like of shape (n_samples, n_dimensions)</span>
<span class="sd"> Unlabeled training instances.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> X_feat : array-like of shape (n_samples, n_features)</span>
<span class="sd"> Transformed features from the given instances.</span>
<span class="sd"> '''</span>
<span class="n">check_is_fitted</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="p">[</span><span class="s2">"random_weights_"</span><span class="p">,</span> <span class="s2">"is_fitted_"</span><span class="p">])</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">check_array</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">accept_sparse</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">X_trans</span> <span class="o">=</span> <span class="n">X</span> <span class="o">@</span> <span class="bp">self</span><span class="o">.</span><span class="n">random_weights_</span>
<span class="n">X_feat</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_components</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)))</span> <span class="o">*</span> \
<span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">X_trans</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">X_trans</span><span class="p">)))</span>
<span class="k">return</span> <span class="n">X_feat</span></div>
<div class="viewcode-block" id="RandomFourierPhi.heuristic_gamma"><a class="viewcode-back" href="../../../generated/MRCpy.phi.RandomFourierPhi.html#MRCpy.phi.RandomFourierPhi.heuristic_gamma">[docs]</a> <span class="k">def</span> <span class="nf">heuristic_gamma</span><span class="p">(</span><span class="bp">self</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">'''</span>
<span class="sd"> Computes the scaling parameter for relu features</span>
<span class="sd"> using the heuristic -</span>
<span class="sd"> .. math:: \sigma = median(\min(\| x_i-x_j \|^2, y_j = +1), y_i = -1)</span>
<span class="sd"> .. math:: \gamma = 1 / (2 * \sigma^2)</span>
<span class="sd"> for two classes {+1, -1}. For multi-class, we use the same strategy</span>
<span class="sd"> by finding median of minimum distances between the points of</span>
<span class="sd"> each class against all other classes</span>
<span class="sd"> and then taking the average value of the medians of all the classes.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> X : array-like of shape (n_samples, n_dimensions)</span>
<span class="sd"> Unlabeled instances.</span>
<span class="sd"> Y : array-like of shape (n_samples,)</span>
<span class="sd"> Labels corresponding to the instances.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> gamma : float value</span>
<span class="sd"> Scaling parameter computed using the heuristic.</span>
<span class="sd"> '''</span>
<span class="c1"># List to store the median of min norm value for each class</span>
<span class="n">dist_x_i</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="n">n_classes</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">Y</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_classes</span><span class="p">):</span>
<span class="n">x_i</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">Y</span> <span class="o">==</span> <span class="n">i</span><span class="p">,</span> <span class="p">:]</span>
<span class="n">x_not_i</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">Y</span> <span class="o">!=</span> <span class="n">i</span><span class="p">,</span> <span class="p">:]</span>
<span class="c1"># Find the distance of each point of this class</span>
<span class="c1"># with every other point of other class</span>
<span class="n">norm_vec</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">tile</span><span class="p">(</span><span class="n">x_not_i</span><span class="p">,</span> <span class="p">(</span><span class="n">x_i</span><span class="o">.</span><span class="n">shape</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="o">-</span>
<span class="n">np</span><span class="o">.</span><span class="n">repeat</span><span class="p">(</span><span class="n">x_i</span><span class="p">,</span> <span class="n">x_not_i</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span>
<span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">dist_mat</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">norm_vec</span><span class="p">,</span> <span class="p">(</span><span class="n">x_not_i</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">x_i</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]))</span>
<span class="c1"># Find the min distance for each point and take the median distance</span>
<span class="n">minDist_x_i</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">dist_mat</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">dist_x_i</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">statistics</span><span class="o">.</span><span class="n">median</span><span class="p">(</span><span class="n">minDist_x_i</span><span class="p">))</span>
<span class="n">sigma</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">average</span><span class="p">(</span><span class="n">dist_x_i</span><span class="p">)</span>
<span class="c1"># Evaluate gamma</span>
<span class="n">gamma</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">sigma</span> <span class="o">*</span> <span class="n">sigma</span><span class="p">)</span>
<span class="k">return</span> <span class="n">gamma</span></div>
<div class="viewcode-block" id="RandomFourierPhi.rff_gamma"><a class="viewcode-back" href="../../../generated/MRCpy.phi.RandomFourierPhi.html#MRCpy.phi.RandomFourierPhi.rff_gamma">[docs]</a> <span class="k">def</span> <span class="nf">rff_gamma</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">X</span><span class="p">):</span>
<span class="sd">'''</span>
<span class="sd"> Computes the scaling parameter for the fourier features</span>
<span class="sd"> using the heuristic given in the paper -</span>
<span class="sd"> "Compact Nonlinear Maps and Circulant Extensions"</span>
<span class="sd"> The heuristic states that the scaling parameter is obtained as</span>
<span class="sd"> the average distance to the 50th nearest neighbour estimated</span>
<span class="sd"> from 1000 samples of the dataset.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> X : array-like of shape (n_samples, n_dimensions)</span>
<span class="sd"> Unlabeled instances.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> gamma : float value</span>
<span class="sd"> Scaling parameter computed using the heuristic.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> [1] Compact Nonlinear Maps and Circulant Extensions</span>
<span class="sd"> Felix X. Yu, Sanjiv Kumar, Henry Rowley and Shih-Fu Chang</span>
<span class="sd"> (https://arxiv.org/pdf/1503.03893.pdf)</span>
<span class="sd"> '''</span>
<span class="k">if</span> <span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o"><</span> <span class="mi">50</span><span class="p">:</span>
<span class="n">neighbour_ind</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="mi">2</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">neighbour_ind</span> <span class="o">=</span> <span class="mi">50</span>
<span class="c1"># Find the nearest neighbors</span>
<span class="n">nbrs</span> <span class="o">=</span> <span class="n">NearestNeighbors</span><span class="p">(</span><span class="n">n_neighbors</span><span class="o">=</span><span class="p">(</span><span class="n">neighbour_ind</span> <span class="o">+</span> <span class="mi">1</span><span class="p">),</span>
<span class="n">algorithm</span><span class="o">=</span><span class="s1">'ball_tree'</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">distances</span><span class="p">,</span> <span class="n">indices</span> <span class="o">=</span> <span class="n">nbrs</span><span class="o">.</span><span class="n">kneighbors</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="c1"># Compute the average distance to the 50th nearest neighbour</span>
<span class="n">sigma</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">average</span><span class="p">(</span><span class="n">distances</span><span class="p">[:,</span> <span class="n">neighbour_ind</span><span class="p">])</span>
<span class="n">gamma</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">sigma</span> <span class="o">*</span> <span class="n">sigma</span><span class="p">)</span>
<span class="k">return</span> <span class="n">gamma</span></div></div>
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