K-均值聚类(K-Means) C++代码实现

        K-均值聚类(K-Means)简介可以参考： http://blog.csdn.net/fengbingchun/article/details/79276668  

    以下是K-Means的C++实现，code参考OpenCV 3.3中的cv::kmeans函数，均值点初始化的方法仅支持KMEANS_RANDOM_CENTERS。

        以下是从数据集MNIST中提取的40幅图像，0,1,2,3四类各20张，如下图：

        关于MNIST的介绍可以参考：  http://blog.csdn.net/fengbingchun/article/details/49611549 

        实现及测试代码如下：

        kmeans.hpp:

#ifndef FBC_SRC_NN_KMEANS_HPP_
#define FBC_SRC_NN_KMEANS_HPP_

#include 

namespace ANN {

typedef enum KmeansFlags {
	// Select random initial centers in each attempt
	KMEANS_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
int kmeans(const std::vector>& data, int K, std::vector& best_labels, std::vector>& 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 
#include 
#include
#include "common.hpp"

namespace ANN {

namespace {

template
void generate_random_center(const std::vector>& box, std::vector& center)
{
	std::random_device rd;
	std::mt19937 generator(rd());
	std::uniform_real_distribution 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
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
void distance_computer(std::vector& distances, std::vector& labels, const std::vector>& data,
	const std::vector>& 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 sample = data[i];

		if (only_distance) {
			const std::vector 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::max(); // DBL_MAX

		for (int k = 0; k < K; ++k) {
			const std::vector 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;
	}
}

} // namespace

template
int kmeans(const std::vector>& data, int K, std::vector& best_labels, std::vector>& 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 labels(N);

	centers.resize(K);
	std::vector> centers_(K), old_centers(K);
	std::vector 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::max(); // DBL_MAX
	double 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> box(dims);
	for (int i = 0; i < dims; ++i) {
		box[i].resize(2);
	}

	std::vector dists(N, 0.);
	std::vector 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::max(); // DBL_MAX

		for (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 centers
				for (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; // normalized
					T 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 labels
			std::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(const std::vector>&, int K, std::vector&, std::vector>&, double&,
	int max_iter_count, double epsilon, int attempts, int flags);
template int kmeans(const std::vector>&, int K, std::vector&, std::vector>&, double&,
	int max_iter_count, double epsilon, int attempts, int flags);

} // namespace ANN

        main.cpp:

#include "funset.hpp"
#include 
#include 

#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(labels.data);

	for (int i = 1; i <= every_class_number; ++i) {
		static const std::vector 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> 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 best_labels;
	double compactness_measure{ 0. };
	std::vector> centers;

	ANN::kmeans(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;
}

        执行结果如下，下图中每一列表示期望是同一个label。

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