feat: add k-nearest neighbors algorithm (#2416)

* feat: add k-nearest neighbors, class Knn

* updating DIRECTORY.md

* clang-format and clang-tidy fixes for 8dfacfdf

* fix: comments in k-nearest neighbors

* test: add more tests for k-nearest-neighbors algorithm

* fix: description of k-nearest neighbors algorithm

* chore: apply suggestions from code review

---------

Co-authored-by: github-actions[bot] <github-actions@users.noreply.github.com>
Co-authored-by: David Leal <halfpacho@gmail.com>

DIRECTORY.md

@@ -168,6 +168,7 @@
 ## Machine Learning
   * [A Star Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/a_star_search.cpp)
   * [Adaline Learning](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/adaline_learning.cpp)
+  * [K Nearest Neighbors](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/k_nearest_neighbors.cpp)
   * [Kohonen Som Topology](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/kohonen_som_topology.cpp)
   * [Kohonen Som Trace](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/kohonen_som_trace.cpp)
   * [Neural Network](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/neural_network.cpp)

machine_learning/k_nearest_neighbors.cpp

@@ -0,0 +1,196 @@
+/**
+ * @file
+ * @brief Implementation of [K-Nearest Neighbors algorithm]
+ * (https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm).
+ * @author [Luiz Carlos Cosmi Filho](https://github.com/luizcarloscf)
+ * @details K-nearest neighbors algorithm, also known as KNN or k-NN, is a
+ * supervised learning classifier, which uses proximity to make classifications.
+ * This implementantion uses the Euclidean Distance as distance metric to find
+ * the K-nearest neighbors.
+ */
+
+#include <algorithm>      /// for std::transform and std::sort
+#include <cassert>        /// for assert
+#include <cmath>          /// for std::pow and std::sqrt
+#include <iostream>       /// for std::cout
+#include <numeric>        /// for std::accumulate
+#include <unordered_map>  /// for std::unordered_map
+#include <vector>         /// for std::vector
+
+/**
+ * @namespace machine_learning
+ * @brief Machine learning algorithms
+ */
+namespace machine_learning {
+
+/**
+ * @namespace k_nearest_neighbors
+ * @brief Functions for the [K-Nearest Neighbors algorithm]
+ * (https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm) implementation
+ */
+namespace k_nearest_neighbors {
+
+/**
+ * @brief Compute the Euclidean distance between two vectors.
+ *
+ * @tparam T typename of the vector
+ * @param a first unidimentional vector
+ * @param b second unidimentional vector
+ * @return double scalar representing the Euclidean distance between provided
+ * vectors
+ */
+template <typename T>
+double euclidean_distance(const std::vector<T>& a, const std::vector<T>& b) {
+    std::vector<double> aux;
+    std::transform(a.begin(), a.end(), b.begin(), std::back_inserter(aux),
+                   [](T x1, T x2) { return std::pow((x1 - x2), 2); });
+    aux.shrink_to_fit();
+    return std::sqrt(std::accumulate(aux.begin(), aux.end(), 0.0));
+}
+
+/**
+ * @brief K-Nearest Neighbors (Knn) class using Euclidean distance as
+ * distance metric.
+ */
+class Knn {
+ private:
+    std::vector<std::vector<double>> X_{};  ///< attributes vector
+    std::vector<int> Y_{};                  ///< labels vector
+
+ public:
+    /**
+     * @brief Construct a new Knn object.
+     * @details Using lazy-learning approch, just holds in memory the dataset.
+     * @param X attributes vector
+     * @param Y labels vector
+     */
+    explicit Knn(std::vector<std::vector<double>>& X, std::vector<int>& Y)
+        : X_(X), Y_(Y){};
+
+    /**
+     * Copy Constructor for class Knn.
+     *
+     * @param model instance of class to be copied
+     */
+    Knn(const Knn& model) = default;
+
+    /**
+     * Copy assignment operator for class Knn
+     */
+    Knn& operator=(const Knn& model) = default;
+
+    /**
+     * Move constructor for class Knn
+     */
+    Knn(Knn&&) = default;
+
+    /**
+     * Move assignment operator for class Knn
+     */
+    Knn& operator=(Knn&&) = default;
+
+    /**
+     * @brief Destroy the Knn object
+     */
+    ~Knn() = default;
+
+    /**
+     * @brief Classify sample.
+     * @param sample sample
+     * @param k number of neighbors
+     * @return int label of most frequent neighbors
+     */
+    int predict(std::vector<double>& sample, int k) {
+        std::vector<int> neighbors;
+        std::vector<std::pair<double, int>> distances;
+        for (size_t i = 0; i < this->X_.size(); ++i) {
+            auto current = this->X_.at(i);
+            auto label = this->Y_.at(i);
+            auto distance = euclidean_distance(current, sample);
+            distances.emplace_back(distance, label);
+        }
+        std::sort(distances.begin(), distances.end());
+        for (int i = 0; i < k; i++) {
+            auto label = distances.at(i).second;
+            neighbors.push_back(label);
+        }
+        std::unordered_map<int, int> frequency;
+        for (auto neighbor : neighbors) {
+            ++frequency[neighbor];
+        }
+        std::pair<int, int> predicted;
+        predicted.first = -1;
+        predicted.second = -1;
+        for (auto& kv : frequency) {
+            if (kv.second > predicted.second) {
+                predicted.second = kv.second;
+                predicted.first = kv.first;
+            }
+        }
+        return predicted.first;
+    }
+};
+}  // namespace k_nearest_neighbors
+}  // namespace machine_learning
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    std::cout << "------- Test 1 -------" << std::endl;
+    std::vector<std::vector<double>> X1 = {{0.0, 0.0}, {0.25, 0.25},
+                                           {0.0, 0.5}, {0.5, 0.5},
+                                           {1.0, 0.5}, {1.0, 1.0}};
+    std::vector<int> Y1 = {1, 1, 1, 1, 2, 2};
+    auto model1 = machine_learning::k_nearest_neighbors::Knn(X1, Y1);
+    std::vector<double> sample1 = {1.2, 1.2};
+    std::vector<double> sample2 = {0.1, 0.1};
+    std::vector<double> sample3 = {0.1, 0.5};
+    std::vector<double> sample4 = {1.0, 0.75};
+    assert(model1.predict(sample1, 2) == 2);
+    assert(model1.predict(sample2, 2) == 1);
+    assert(model1.predict(sample3, 2) == 1);
+    assert(model1.predict(sample4, 2) == 2);
+    std::cout << "... Passed" << std::endl;
+    std::cout << "------- Test 2 -------" << std::endl;
+    std::vector<std::vector<double>> X2 = {
+        {0.0, 0.0, 0.0}, {0.25, 0.25, 0.0}, {0.0, 0.5, 0.0}, {0.5, 0.5, 0.0},
+        {1.0, 0.5, 0.0}, {1.0, 1.0, 0.0},   {1.0, 1.0, 1.0}, {1.5, 1.5, 1.0}};
+    std::vector<int> Y2 = {1, 1, 1, 1, 2, 2, 3, 3};
+    auto model2 = machine_learning::k_nearest_neighbors::Knn(X2, Y2);
+    std::vector<double> sample5 = {1.2, 1.2, 0.0};
+    std::vector<double> sample6 = {0.1, 0.1, 0.0};
+    std::vector<double> sample7 = {0.1, 0.5, 0.0};
+    std::vector<double> sample8 = {1.0, 0.75, 1.0};
+    assert(model2.predict(sample5, 2) == 2);
+    assert(model2.predict(sample6, 2) == 1);
+    assert(model2.predict(sample7, 2) == 1);
+    assert(model2.predict(sample8, 2) == 3);
+    std::cout << "... Passed" << std::endl;
+    std::cout << "------- Test 3 -------" << std::endl;
+    std::vector<std::vector<double>> X3 = {{0.0}, {1.0}, {2.0}, {3.0},
+                                           {4.0}, {5.0}, {6.0}, {7.0}};
+    std::vector<int> Y3 = {1, 1, 1, 1, 2, 2, 2, 2};
+    auto model3 = machine_learning::k_nearest_neighbors::Knn(X3, Y3);
+    std::vector<double> sample9 = {0.5};
+    std::vector<double> sample10 = {2.9};
+    std::vector<double> sample11 = {5.5};
+    std::vector<double> sample12 = {7.5};
+    assert(model3.predict(sample9, 3) == 1);
+    assert(model3.predict(sample10, 3) == 1);
+    assert(model3.predict(sample11, 3) == 2);
+    assert(model3.predict(sample12, 3) == 2);
+    std::cout << "... Passed" << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @param argc commandline argument count (ignored)
+ * @param argv commandline array of arguments (ignored)
+ * @return int 0 on exit
+ */
+int main(int argc, char* argv[]) {
+    test();  // run self-test implementations
+    return 0;
+}