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 </pre><pre class="rust"><code><span class="doccomment">//! K-means Classification
 //!
 //! Provides implementation of K-Means classification.
 //!
 //! # Usage
 //!
 //! ```
 //! use rusty_machine::linalg::Matrix;
 //! use rusty_machine::learning::k_means::KMeansClassifier;
 //! use rusty_machine::learning::UnSupModel;
 //!
 //! let inputs = Matrix::new(3, 2, vec![1.0, 2.0, 1.0, 3.0, 1.0, 4.0]);
 //! let test_inputs = Matrix::new(1, 2, vec![1.0, 3.5]);
 //!
 //! // Create model with k(=2) classes.
 //! let mut model = KMeansClassifier::new(2);
 //!
 //! // Where inputs is a Matrix with features in columns.
 //! model.train(&amp;inputs).unwrap();
 //!
 //! // Where test_inputs is a Matrix with features in columns.
 //! let a = model.predict(&amp;test_inputs).unwrap();
 //! ```
 //!
 //! Additionally you can control the initialization
 //! algorithm and max number of iterations.
 //!
 //! # Initializations
 //!
 //! Three initialization algorithms are supported.
 //!
 //! ## Forgy initialization
 //!
 //! Choose initial centroids randomly from the data.
 //!
 //! ## Random Partition initialization
 //!
 //! Randomly assign each data point to one of k clusters.
 //! The initial centroids are the mean of the data in their class.
 //!
 //! ## K-means++ initialization
 //!
 //! The [k-means++](https://en.wikipedia.org/wiki/K-means%2B%2B) scheme.

 </span><span class="kw">use </span>linalg::{Matrix, MatrixSlice, Axes, Vector, BaseMatrix};
 <span class="kw">use </span>learning::{LearningResult, UnSupModel};
 <span class="kw">use </span>learning::error::{Error, ErrorKind};

 <span class="kw">use </span>rand::{Rng, thread_rng};
 <span class="kw">use </span>libnum::abs;

 <span class="kw">use </span>std::fmt::Debug;

 <span class="doccomment">/// K-Means Classification model.
 ///
 /// Contains option for centroids.
 /// Specifies iterations and number of classes.
 ///
 /// # Usage
 ///
 /// This model is used through the `UnSupModel` trait. The model is
 /// trained via the `train` function with a matrix containing rows of
 /// feature vectors.
 ///
 /// The model will not check to ensure the data coming in is all valid.
 /// This responsibility lies with the user (for now).
 </span><span class="attribute">#[derive(Debug)]
 </span><span class="kw">pub struct </span>KMeansClassifier&lt;InitAlg: Initializer&gt; {
     <span class="doccomment">/// Max iterations of algorithm to run.
     </span>iters: usize,
     <span class="doccomment">/// The number of classes.
     </span>k: usize,
     <span class="doccomment">/// The fitted centroids .
     </span>centroids: <span class="prelude-ty">Option</span>&lt;Matrix&lt;f64&gt;&gt;,
     <span class="doccomment">/// The initial algorithm to use.
     </span>init_algorithm: InitAlg,
 }

 <span class="kw">impl</span>&lt;InitAlg: Initializer&gt; UnSupModel&lt;Matrix&lt;f64&gt;, Vector&lt;usize&gt;&gt; <span class="kw">for </span>KMeansClassifier&lt;InitAlg&gt; {
     <span class="doccomment">/// Predict classes from data.
     ///
     /// Model must be trained.
     </span><span class="kw">fn </span>predict(<span class="kw-2">&amp;</span><span class="self">self</span>, inputs: <span class="kw-2">&amp;</span>Matrix&lt;f64&gt;) -&gt; LearningResult&lt;Vector&lt;usize&gt;&gt; {
         <span class="kw">if let </span><span class="prelude-val">Some</span>(<span class="kw-2">ref </span>centroids) = <span class="self">self</span>.centroids {
             <span class="prelude-val">Ok</span>(KMeansClassifier::&lt;InitAlg&gt;::find_closest_centroids(centroids.as_slice(), inputs).<span class="number">0</span>)
         } <span class="kw">else </span>{
             <span class="prelude-val">Err</span>(Error::new_untrained())
         }
     }

     <span class="doccomment">/// Train the classifier using input data.
     </span><span class="kw">fn </span>train(<span class="kw-2">&amp;mut </span><span class="self">self</span>, inputs: <span class="kw-2">&amp;</span>Matrix&lt;f64&gt;) -&gt; LearningResult&lt;()&gt; {
         <span class="self">self</span>.init_centroids(inputs)<span class="question-mark">?</span>;
         <span class="kw">let </span><span class="kw-2">mut </span>cost = <span class="number">0.0</span>;
         <span class="kw">let </span>eps = <span class="number">1e-14</span>;

         <span class="kw">for </span>_i <span class="kw">in </span><span class="number">0</span>..<span class="self">self</span>.iters {
             <span class="kw">let </span>(idx, distances) = <span class="self">self</span>.get_closest_centroids(inputs)<span class="question-mark">?</span>;
             <span class="self">self</span>.update_centroids(inputs, idx);

             <span class="kw">let </span>cost_i = distances.sum();
             <span class="kw">if </span>abs(cost - cost_i) &lt; eps {
                 <span class="kw">break</span>;
             }

             cost = cost_i;
         }

         <span class="prelude-val">Ok</span>(())
     }
 }

 <span class="kw">impl </span>KMeansClassifier&lt;KPlusPlus&gt; {
     <span class="doccomment">/// Constructs untrained k-means classifier model.
     ///
     /// Requires number of classes to be specified.
     /// Defaults to 100 iterations and kmeans++ initialization.
     ///
     /// # Examples
     ///
     /// ```
     /// use rusty_machine::learning::k_means::KMeansClassifier;
     ///
     /// let model = KMeansClassifier::new(5);
     /// ```
     </span><span class="kw">pub fn </span>new(k: usize) -&gt; KMeansClassifier&lt;KPlusPlus&gt; {
         KMeansClassifier {
             iters: <span class="number">100</span>,
             k: k,
             centroids: <span class="prelude-val">None</span>,
             init_algorithm: KPlusPlus,
         }
     }
 }

 <span class="kw">impl</span>&lt;InitAlg: Initializer&gt; KMeansClassifier&lt;InitAlg&gt; {
     <span class="doccomment">/// Constructs untrained k-means classifier model.
     ///
     /// Requires number of classes, number of iterations, and
     /// the initialization algorithm to use.
     ///
     /// # Examples
     ///
     /// ```
     /// use rusty_machine::learning::k_means::{KMeansClassifier, Forgy};
     ///
     /// let model = KMeansClassifier::new_specified(5, 42, Forgy);
     /// ```
     </span><span class="kw">pub fn </span>new_specified(k: usize, iters: usize, algo: InitAlg) -&gt; KMeansClassifier&lt;InitAlg&gt; {
         KMeansClassifier {
             iters: iters,
             k: k,
             centroids: <span class="prelude-val">None</span>,
             init_algorithm: algo,
         }
     }

     <span class="doccomment">/// Get the number of classes.
     </span><span class="kw">pub fn </span>k(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; usize {
         <span class="self">self</span>.k
     }

     <span class="doccomment">/// Get the number of iterations.
     </span><span class="kw">pub fn </span>iters(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; usize {
         <span class="self">self</span>.iters
     }

     <span class="doccomment">/// Get the initialization algorithm.
     </span><span class="kw">pub fn </span>init_algorithm(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; <span class="kw-2">&amp;</span>InitAlg {
         <span class="kw-2">&amp;</span><span class="self">self</span>.init_algorithm
     }

     <span class="doccomment">/// Get the centroids `Option&lt;Matrix&lt;f64&gt;&gt;`.
     </span><span class="kw">pub fn </span>centroids(<span class="kw-2">&amp;</span><span class="self">self</span>) -&gt; <span class="kw-2">&amp;</span><span class="prelude-ty">Option</span>&lt;Matrix&lt;f64&gt;&gt; {
         <span class="kw-2">&amp;</span><span class="self">self</span>.centroids
     }

     <span class="doccomment">/// Set the number of iterations.
     </span><span class="kw">pub fn </span>set_iters(<span class="kw-2">&amp;mut </span><span class="self">self</span>, iters: usize) {
         <span class="self">self</span>.iters = iters;
     }

     <span class="doccomment">/// Initialize the centroids.
     ///
     /// Used internally within model.
     </span><span class="kw">fn </span>init_centroids(<span class="kw-2">&amp;mut </span><span class="self">self</span>, inputs: <span class="kw-2">&amp;</span>Matrix&lt;f64&gt;) -&gt; LearningResult&lt;()&gt; {
         <span class="kw">if </span><span class="self">self</span>.k &gt; inputs.rows() {
             <span class="prelude-val">Err</span>(Error::new(ErrorKind::InvalidData,
                            <span class="macro">format!</span>(<span class="string">&quot;Number of clusters ({0}) exceeds number of data points \
                                     ({1}).&quot;</span>,
                                    <span class="self">self</span>.k,
                                    inputs.rows())))
         } <span class="kw">else </span>{
             <span class="kw">let </span>centroids = <span class="self">self</span>.init_algorithm.init_centroids(<span class="self">self</span>.k, inputs)<span class="question-mark">?</span>;

             <span class="kw">if </span>centroids.rows() != <span class="self">self</span>.k {
                 <span class="prelude-val">Err</span>(Error::new(ErrorKind::InvalidState,
                                     <span class="string">&quot;Initial centroids must have exactly k rows.&quot;</span>))
             } <span class="kw">else if </span>centroids.cols() != inputs.cols() {
                 <span class="prelude-val">Err</span>(Error::new(ErrorKind::InvalidState,
                                     <span class="string">&quot;Initial centroids must have the same column count as inputs.&quot;</span>))
             } <span class="kw">else </span>{
                 <span class="self">self</span>.centroids = <span class="prelude-val">Some</span>(centroids);
                 <span class="prelude-val">Ok</span>(())
             }
         }

     }

     <span class="doccomment">/// Updated the centroids by computing means of assigned classes.
     ///
     /// Used internally within model.
     </span><span class="kw">fn </span>update_centroids(<span class="kw-2">&amp;mut </span><span class="self">self</span>, inputs: <span class="kw-2">&amp;</span>Matrix&lt;f64&gt;, classes: Vector&lt;usize&gt;) {
         <span class="kw">let </span><span class="kw-2">mut </span>new_centroids = Vec::with_capacity(<span class="self">self</span>.k * inputs.cols());

         <span class="kw">let </span><span class="kw-2">mut </span>row_indexes = <span class="macro">vec!</span>[Vec::new(); <span class="self">self</span>.k];
         <span class="kw">for </span>(i, c) <span class="kw">in </span>classes.into_vec().into_iter().enumerate() {
             row_indexes.get_mut(c <span class="kw">as </span>usize).map(|v| v.push(i));
         }

         <span class="kw">for </span>vec_i <span class="kw">in </span>row_indexes {
             <span class="kw">let </span>mat_i = inputs.select_rows(<span class="kw-2">&amp;</span>vec_i);
             new_centroids.extend(mat_i.mean(Axes::Row).into_vec());
         }

         <span class="self">self</span>.centroids = <span class="prelude-val">Some</span>(Matrix::new(<span class="self">self</span>.k, inputs.cols(), new_centroids));
     }

     <span class="kw">fn </span>get_closest_centroids(<span class="kw-2">&amp;</span><span class="self">self</span>,
                              inputs: <span class="kw-2">&amp;</span>Matrix&lt;f64&gt;)
                              -&gt; LearningResult&lt;(Vector&lt;usize&gt;, Vector&lt;f64&gt;)&gt; {
         <span class="kw">if let </span><span class="prelude-val">Some</span>(<span class="kw-2">ref </span>c) = <span class="self">self</span>.centroids {
             <span class="prelude-val">Ok</span>(KMeansClassifier::&lt;InitAlg&gt;::find_closest_centroids(c.as_slice(), inputs))
         } <span class="kw">else </span>{
             <span class="prelude-val">Err</span>(Error::new(ErrorKind::InvalidState,
                            <span class="string">&quot;Centroids not correctly initialized.&quot;</span>))
         }
     }

     <span class="doccomment">/// Find the centroid closest to each data point.
     ///
     /// Used internally within model.
     /// Returns the index of the closest centroid and the distance to it.
     </span><span class="kw">fn </span>find_closest_centroids(centroids: MatrixSlice&lt;f64&gt;,
                               inputs: <span class="kw-2">&amp;</span>Matrix&lt;f64&gt;)
                               -&gt; (Vector&lt;usize&gt;, Vector&lt;f64&gt;) {
         <span class="kw">let </span><span class="kw-2">mut </span>idx = Vec::with_capacity(inputs.rows());
         <span class="kw">let </span><span class="kw-2">mut </span>distances = Vec::with_capacity(inputs.rows());

         <span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..inputs.rows() {
             <span class="comment">// This works like repmat pulling out row i repeatedly.
             </span><span class="kw">let </span>centroid_diff = centroids - inputs.select_rows(<span class="kw-2">&amp;</span><span class="macro">vec!</span>[i; centroids.rows()]);
             <span class="kw">let </span>dist = <span class="kw-2">&amp;</span>centroid_diff.elemul(<span class="kw-2">&amp;</span>centroid_diff).sum_cols();

             <span class="comment">// Now take argmin and this is the centroid.
             </span><span class="kw">let </span>(min_idx, min_dist) = dist.argmin();
             idx.push(min_idx);
             distances.push(min_dist);
         }

         (Vector::new(idx), Vector::new(distances))
     }
 }

 <span class="doccomment">/// Trait for algorithms initializing the K-means centroids.
 </span><span class="kw">pub trait </span>Initializer: Debug {
     <span class="doccomment">/// Initialize the centroids for the initial state of the K-Means model.
     ///
     /// The `Matrix` returned must have `k` rows and the same column count as `inputs`.
     </span><span class="kw">fn </span>init_centroids(<span class="kw-2">&amp;</span><span class="self">self</span>, k: usize, inputs: <span class="kw-2">&amp;</span>Matrix&lt;f64&gt;) -&gt; LearningResult&lt;Matrix&lt;f64&gt;&gt;;
 }

 <span class="doccomment">/// The Forgy initialization scheme.
 </span><span class="attribute">#[derive(Debug)]
 </span><span class="kw">pub struct </span>Forgy;

 <span class="kw">impl </span>Initializer <span class="kw">for </span>Forgy {
     <span class="kw">fn </span>init_centroids(<span class="kw-2">&amp;</span><span class="self">self</span>, k: usize, inputs: <span class="kw-2">&amp;</span>Matrix&lt;f64&gt;) -&gt; LearningResult&lt;Matrix&lt;f64&gt;&gt; {
         <span class="kw">let </span><span class="kw-2">mut </span>random_choices = Vec::with_capacity(k);
         <span class="kw">let </span><span class="kw-2">mut </span>rng = thread_rng();
         <span class="kw">while </span>random_choices.len() &lt; k {
             <span class="kw">let </span>r = rng.gen_range(<span class="number">0</span>..inputs.rows());

             <span class="kw">if </span>!random_choices.contains(<span class="kw-2">&amp;</span>r) {
                 random_choices.push(r);
             }
         }

         <span class="prelude-val">Ok</span>(inputs.select_rows(<span class="kw-2">&amp;</span>random_choices))
     }
 }

 <span class="doccomment">/// The Random Partition initialization scheme.
 </span><span class="attribute">#[derive(Debug)]
 </span><span class="kw">pub struct </span>RandomPartition;

 <span class="kw">impl </span>Initializer <span class="kw">for </span>RandomPartition {
     <span class="kw">fn </span>init_centroids(<span class="kw-2">&amp;</span><span class="self">self</span>, k: usize, inputs: <span class="kw-2">&amp;</span>Matrix&lt;f64&gt;) -&gt; LearningResult&lt;Matrix&lt;f64&gt;&gt; {

         <span class="comment">// Populate so we have something in each class.
         </span><span class="kw">let </span><span class="kw-2">mut </span>random_assignments = (<span class="number">0</span>..k).map(|i| <span class="macro">vec!</span>[i]).collect::&lt;Vec&lt;Vec&lt;usize&gt;&gt;&gt;();
         <span class="kw">let </span><span class="kw-2">mut </span>rng = thread_rng();
         <span class="kw">for </span>i <span class="kw">in </span>k..inputs.rows() {
             <span class="kw">let </span>idx = rng.gen_range(<span class="number">0</span>..k);
             <span class="kw">unsafe </span>{
                 random_assignments.get_unchecked_mut(idx).push(i);
             }
         }

         <span class="kw">let </span><span class="kw-2">mut </span>init_centroids = Vec::with_capacity(k * inputs.cols());

         <span class="kw">for </span>vec_i <span class="kw">in </span>random_assignments {
             <span class="kw">let </span>mat_i = inputs.select_rows(<span class="kw-2">&amp;</span>vec_i);
             init_centroids.extend_from_slice(<span class="kw-2">&amp;*</span>mat_i.mean(Axes::Row).into_vec());
         }

         <span class="prelude-val">Ok</span>(Matrix::new(k, inputs.cols(), init_centroids))
     }
 }

 <span class="doccomment">/// The K-means ++ initialization scheme.
 </span><span class="attribute">#[derive(Debug)]
 </span><span class="kw">pub struct </span>KPlusPlus;

 <span class="kw">impl </span>Initializer <span class="kw">for </span>KPlusPlus {
     <span class="kw">fn </span>init_centroids(<span class="kw-2">&amp;</span><span class="self">self</span>, k: usize, inputs: <span class="kw-2">&amp;</span>Matrix&lt;f64&gt;) -&gt; LearningResult&lt;Matrix&lt;f64&gt;&gt; {
         <span class="kw">let </span><span class="kw-2">mut </span>rng = thread_rng();

         <span class="kw">let </span><span class="kw-2">mut </span>init_centroids = Vec::with_capacity(k * inputs.cols());
         <span class="kw">let </span>first_cen = rng.gen_range(<span class="number">0usize</span>..inputs.rows());

         <span class="kw">unsafe </span>{
             init_centroids.extend_from_slice(inputs.row_unchecked(first_cen).raw_slice());
         }

         <span class="kw">for </span>i <span class="kw">in </span><span class="number">1</span>..k {
             <span class="kw">unsafe </span>{
                 <span class="kw">let </span>temp_centroids = MatrixSlice::from_raw_parts(init_centroids.as_ptr(),
                                                                  i,
                                                                  inputs.cols(),
                                                                  inputs.cols());
                 <span class="kw">let </span>(<span class="kw">_</span>, dist) =
                     KMeansClassifier::&lt;KPlusPlus&gt;::find_closest_centroids(temp_centroids, inputs);

                 <span class="comment">// A relatively cheap way to validate our input data
                 </span><span class="kw">if </span>!dist.data().iter().all(|x| x.is_finite()) {
                     <span class="kw">return </span><span class="prelude-val">Err</span>(Error::new(ErrorKind::InvalidData,
                                           <span class="string">&quot;Input data led to invalid centroid distances during \
                                            initialization.&quot;</span>));
                 }

                 <span class="kw">let </span>next_cen = sample_discretely(<span class="kw-2">&amp;</span>dist);
                 init_centroids.extend_from_slice(inputs.row_unchecked(next_cen).raw_slice());
             }
         }

         <span class="prelude-val">Ok</span>(Matrix::new(k, inputs.cols(), init_centroids))
     }
 }

 <span class="doccomment">/// Sample from an unnormalized distribution.
 ///
 /// The input to this function is assumed to have all positive entries.
 </span><span class="kw">fn </span>sample_discretely(unnorm_dist: <span class="kw-2">&amp;</span>Vector&lt;f64&gt;) -&gt; usize {
     <span class="macro">assert!</span>(unnorm_dist.size() &gt; <span class="number">0</span>, <span class="string">&quot;No entries in distribution vector.&quot;</span>);

     <span class="kw">let </span>sum = unnorm_dist.sum();

     <span class="kw">let </span>rand = thread_rng().gen_range(<span class="number">0.0f64</span>..sum);

     <span class="kw">let </span><span class="kw-2">mut </span>tempsum = <span class="number">0.0</span>;
     <span class="kw">for </span>(i, p) <span class="kw">in </span>unnorm_dist.data().iter().enumerate() {
         tempsum += <span class="kw-2">*</span>p;

         <span class="kw">if </span>rand &lt; tempsum {
             <span class="kw">return </span>i;
         }
     }

     <span class="macro">panic!</span>(<span class="string">&quot;No random value was sampled! There may be more clusters than unique data points.&quot;</span>);
 }
 </code></pre></div>
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