????????K-均值聚類(K-Means)簡介可以參考：?http://blog.csdn.net/fengbingchun/article/details/79276668??

????以下是K-Means的C++實現，code參考OpenCV 3.3中的cv::kmeans函數，均值點初始化的方法僅支持KMEANS_RANDOM_CENTERS。

????????以下是從數據集MNIST中提取的40幅圖像，0,1,2,3四類各20張，如下圖：

????????關于MNIST的介紹可以參考：? http://blog.csdn.net/fengbingchun/article/details/49611549?

????? ? 實現及測試代碼如下：

????? ? kmeans.hpp:

#ifndef FBC_SRC_NN_KMEANS_HPP_
#define FBC_SRC_NN_KMEANS_HPP_#include <vector>namespace ANN {typedef enum KmeansFlags {// Select random initial centers in each attemptKMEANS_RANDOM_CENTERS = 0,// Use kmeans++ center initialization by Arthur and Vassilvitskii [Arthur2007]//KMEANS_PP_CENTERS = 2,// During the first (and possibly the only) attempt, use the//user-supplied labels instead of computing them from the initial centers. For the second and//further attempts, use the random or semi-random centers. Use one of KMEANS_\*_CENTERS flag//to specify the exact method.//KMEANS_USE_INITIAL_LABELS = 1
} KmeansFlags;template<typename T>
int kmeans(const std::vector<std::vector<T>>& data, int K, std::vector<int>& best_labels, std::vector<std::vector<T>>& centers, double& compactness_measure,int max_iter_count = 100, double epsilon = 0.001, int attempts = 3, int flags = KMEANS_RANDOM_CENTERS);} // namespace ANN#endif // FBC_SRC_NN_KMEANS_HPP_

????? ? kmeans.cpp:

#include "kmeans.hpp"
#include <algorithm>
#include <limits>
#include<random>
#include "common.hpp"namespace ANN {namespace {template<typename T>
void generate_random_center(const std::vector<std::vector<T>>& box, std::vector<T>& center)
{std::random_device rd;std::mt19937 generator(rd());std::uniform_real_distribution<T> distribution((T)0, (T)0.0001);int dims = box.size();T margin = 1.f / dims;for (int j = 0; j < dims; j++) {center[j] = (distribution(generator) * (1. + margin * 2.) - margin) * (box[j][1] - box[j][0]) + box[j][0];}
}template<typename T>
inline T norm_L2_Sqr(const T* a, const T* b, int n)
{double s = 0.f;for (int i = 0; i < n; i++) {double v = double(a[i] - b[i]);s += v*v;}return s;
}template<typename T>
void distance_computer(std::vector<double>& distances, std::vector<int>& labels, const std::vector<std::vector<T>>& data,const std::vector<std::vector<T>>& centers, bool only_distance = false)
{const int K = centers.size();const int dims = centers[0].size();for (int i = 0; i < distances.size(); ++i) {const std::vector<T> sample = data[i];if (only_distance) {const std::vector<T> center = centers[labels[i]];distances[i] = norm_L2_Sqr(sample.data(), center.data(), dims);continue;}int k_best = 0;double min_dist = std::numeric_limits<double>::max(); // DBL_MAXfor (int k = 0; k < K; ++k) {const std::vector<T> center = centers[k];const double dist = norm_L2_Sqr(sample.data(), center.data(), dims);if (min_dist > dist) {min_dist = dist;k_best = k;}}distances[i] = min_dist;labels[i] = k_best;}
}} // namespacetemplate<typename T>
int kmeans(const std::vector<std::vector<T>>& data, int K, std::vector<int>& best_labels, std::vector<std::vector<T>>& centers, double& compactness_measure,int max_iter_count, double epsilon, int attempts, int flags)
{CHECK(flags == KMEANS_RANDOM_CENTERS);int N = data.size();CHECK(K > 0 && N >= K);int dims = data[0].size();attempts = std::max(attempts, 1);best_labels.resize(N);std::vector<int> labels(N);centers.resize(K);std::vector<std::vector<T>> centers_(K), old_centers(K);std::vector<T> temp(dims, (T)0.);for (int i = 0; i < K; ++i) {centers[i].resize(dims);centers_[i].resize(dims);old_centers[i].resize(dims);}compactness_measure = std::numeric_limits<double>::max(); // DBL_MAXdouble compactness = 0.;epsilon = std::max(epsilon, (double)0.);epsilon *= epsilon;max_iter_count = std::min(std::max(max_iter_count, 2), 100);if (K == 1) {attempts = 1;max_iter_count = 2;}std::vector<std::vector<T>> box(dims);for (int i = 0; i < dims; ++i) {box[i].resize(2);}std::vector<double> dists(N, 0.);std::vector<int> counters(K);const T* sample = data[0].data();for (int i = 0; i < dims; ++i) {box[i][0] = sample[i];box[i][1] = sample[i];}for (int i = 1; i < N; ++i) {sample = data[i].data();for (int j = 0; j < dims; ++j) {T v = sample[j];box[j][0] = std::min(box[j][0], v);box[j][1] = std::max(box[j][1], v);}}for (int a = 0; a < attempts; ++a) {double max_center_shift = std::numeric_limits<double>::max(); // DBL_MAXfor (int iter = 0;;) {centers_.swap(old_centers);if (iter == 0 && (a > 0 || true)) {for (int k = 0; k < K; ++k) {generate_random_center(box, centers_[k]);}} else {// compute centersfor (auto& center : centers_) {std::for_each(center.begin(), center.end(), [](T& v){v = (T)0; });}std::for_each(counters.begin(), counters.end(), [](int& v) {v = 0; });for (int i = 0; i < N; ++i) {sample = data[i].data();int k = labels[i];auto& center = centers_[k];for (int j = 0; j < dims; ++j) {center[j] += sample[j];}counters[k]++;}if (iter > 0) max_center_shift = 0;for (int k = 0; k < K; ++k) {if (counters[k] != 0) continue;// if some cluster appeared to be empty then://   1. find the biggest cluster//   2. find the farthest from the center point in the biggest cluster//   3. exclude the farthest point from the biggest cluster and form a new 1-point cluster.int max_k = 0;for (int k1 = 1; k1 < K; ++k1) {if (counters[max_k] < counters[k1])max_k = k1;}double max_dist = 0;int farthest_i = -1;auto& new_center = centers_[k];auto& old_center = centers_[max_k];auto& _old_center = temp; // normalizedT scale = (T)1.f / counters[max_k];for (int j = 0; j < dims; j++) {_old_center[j] = old_center[j] * scale;}for (int i = 0; i < N; ++i) {if (labels[i] != max_k)continue;sample = data[i].data();double dist = norm_L2_Sqr(sample, _old_center.data(), dims);if (max_dist <= dist) {max_dist = dist;farthest_i = i;}}counters[max_k]--;counters[k]++;labels[farthest_i] = k;sample = data[farthest_i].data();for (int j = 0; j < dims; ++j) {old_center[j] -= sample[j];new_center[j] += sample[j];}}for (int k = 0; k < K; ++k) {auto& center = centers_[k];CHECK(counters[k] != 0);T scale = (T)1.f / counters[k];for (int j = 0; j < dims; ++j) {center[j] *= scale;}if (iter > 0) {double dist = 0;const auto old_center = old_centers[k];for (int j = 0; j < dims; j++) {T t = center[j] - old_center[j];dist += t*t;}max_center_shift = std::max(max_center_shift, dist);}}}bool isLastIter = (++iter == std::max(max_iter_count, 2) || max_center_shift <= epsilon);// assign labelsstd::for_each(dists.begin(), dists.end(), [](double& v){v = 0; });distance_computer(dists, labels, data, centers_, isLastIter);std::for_each(dists.cbegin(), dists.cend(), [&compactness](double v) { compactness += v; });if (isLastIter) break;}if (compactness < compactness_measure) {compactness_measure = compactness;for (int i = 0; i < K; ++i) {memcpy(centers[i].data(), centers_[i].data(), sizeof(T)* dims);}memcpy(best_labels.data(), labels.data(), sizeof(int)* N);}}return 0;
}template int kmeans<float>(const std::vector<std::vector<float>>&, int K, std::vector<int>&, std::vector<std::vector<float>>&, double&,int max_iter_count, double epsilon, int attempts, int flags);
template int kmeans<double>(const std::vector<std::vector<double>>&, int K, std::vector<int>&, std::vector<std::vector<double>>&, double&,int max_iter_count, double epsilon, int attempts, int flags);} // namespace ANN

????? ? main.cpp:

#include "funset.hpp"
#include <iostream>
#include <opencv2/opencv.hpp>#include "perceptron.hpp"
#include "BP.hpp""
#include "CNN.hpp"
#include "linear_regression.hpp"
#include "naive_bayes_classifier.hpp"
#include "logistic_regression.hpp"
#include "common.hpp"
#include "knn.hpp"
#include "decision_tree.hpp"
#include "pca.hpp"
#include "logistic_regression2.hpp"
#include "single_hidden_layer.hpp"
#include "kmeans.hpp"// ================================= K-Means ===============================
int test_kmeans()
{const std::string image_path{ "E:/GitCode/NN_Test/data/images/digit/handwriting_0_and_1/" };cv::Mat tmp = cv::imread(image_path + "0_1.jpg", 0);CHECK(tmp.data != nullptr && tmp.channels() == 1);const int samples_number{ 80 }, every_class_number{ 20 }, categories_number{ samples_number / every_class_number };cv::Mat samples_data(samples_number, tmp.rows * tmp.cols, CV_32FC1);cv::Mat labels(samples_number, 1, CV_32FC1);float* p1 = reinterpret_cast<float*>(labels.data);for (int i = 1; i <= every_class_number; ++i) {static const std::vector<std::string> digit{ "0_", "1_", "2_", "3_" };CHECK(digit.size() == categories_number);static const std::string suffix{ ".jpg" };for (int j = 0; j < categories_number; ++j) {std::string image_name = image_path + digit[j] + std::to_string(i) + suffix;cv::Mat image = cv::imread(image_name, 0);CHECK(!image.empty() && image.channels() == 1);image.convertTo(image, CV_32FC1);image = image.reshape(0, 1);tmp = samples_data.rowRange((i - 1) * categories_number + j, (i - 1) * categories_number + j + 1);image.copyTo(tmp);p1[(i - 1) * categories_number + j] = j;}}std::vector<std::vector<float>> data(samples_data.rows);for (int i = 0; i < samples_data.rows; ++i) {data[i].resize(samples_data.cols);const float* p = (const float*)samples_data.ptr(i);memcpy(data[i].data(), p, sizeof(float)* samples_data.cols);}const int K{ 4 }, attemps{ 100 }, max_iter_count{ 100 };const double epsilon{ 0.001 };const int flags = ANN::KMEANS_RANDOM_CENTERS;std::vector<int> best_labels;double compactness_measure{ 0. };std::vector<std::vector<float>> centers;ANN::kmeans<float>(data, K, best_labels, centers, compactness_measure, max_iter_count, epsilon, attemps, flags);fprintf(stdout, "K = %d, attemps = %d, iter count = %d, compactness measure =  %f\n",K, attemps, max_iter_count, compactness_measure);CHECK(best_labels.size() == samples_number);const auto* p2 = best_labels.data();for (int i = 1; i <= every_class_number; ++i) {for (int j = 0; j < categories_number; ++j) {fprintf(stdout, "  %d  ", *p2++);}fprintf(stdout, "\n");}return 0;
}

????? ? 執行結果如下，下圖中每一列表示期望是同一個label。

????? ? GitHub：?https://github.com/fengbingchun/NN_Test?

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