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  1. #include <iostream>
  2. #include <vector>
  3. #include <cassert>
  4. #include <cmath>
  5. #include <numeric>
  6. #include <stdio.h>
  7. #include <stdlib.h>
  8.  
  9. using namespace std;
  10. #define SZ(a) ((int)((a).size()))
  11.  
  12. // 注：データの次元D=2のときしか対応していません！
  13. typedef vector <double> Vec;
  14. typedef vector <Vec> Mtx;
  15.  
  16. class EMGaussianMixtures
  17. {
  18. private:
  19. 	int N; // データ個数
  20. 	int D; // データの次元
  21. 	int K; // クラスの種類数
  22. 	Mtx	m_xx;				// ｘ：正規化したデータ m_xx[N][D]
  23. 	Mtx	m_mu;				// μ：平均             m_mu[K][D]
  24. 	Vec	m_mix;				// π：混合率           m_mix[K]
  25. 	vector < Mtx >	m_sig;	// Σ：共分散           m_sig[K][D][D]
  26. 	Mtx	m_gamma_nk;			// γ：負担率			m_gamma_nk[N][K]
  27.  
  28. public:
  29.  
  30. 	// 初期化
  31. 	// データセット		dataFrame[N][D]
  32. 	// クラスの種類数	numClasses -> K
  33. 	void initialize(const Mtx& dataFrame, int numClasses)
  34. 	{
  35. 		N = SZ(dataFrame);
  36. 		D = SZ(dataFrame[0]);
  37. 		K = numClasses;
  38. 		assert(N>=1);
  39. 		assert(D==2);
  40. 		assert(K>=1);
  41.  
  42. 		// データの正規化
  43. 		m_xx = dataFrame;
  44. 		normalize(m_xx);
  45.  
  46. 		// 平均、共分散、混合率の初期値(正規乱数)
  47. 		m_mu	= Mtx(K, Vec(D));
  48.  
  49. 		for(int row=0;row<K;++row)
  50. 		{
  51. 			for(int col=0;col<D;++col)
  52. 			{
  53. 				m_mu[row][col]= getNormRand(); // たぶん、必須ではないけど、元のコードに合わせました。
  54. 			}
  55. 		}
  56.  
  57. 		m_mix = Vec(K, 1.0/K);
  58.  
  59. 		m_sig = vector < Mtx >(K, Mtx(D, Vec(D)));
  60. 		for (int k = 0; k < K; ++k)
  61. 		{
  62. 			for (int rc=0; rc<D; ++rc)
  63. 			{
  64. 				m_sig[k][rc][rc]=1.0;
  65. 			}
  66. 		}
  67. 	}
  68.  
  69. 	// E stepとM stepを1回ずつ実行
  70. 	void run()
  71. 	{
  72. 		m_gamma_nk = calcEstep(m_xx, m_mu, m_mix, m_sig);
  73.  
  74. 		Mtx	new_mu;
  75. 		Vec new_mix;
  76. 		vector < Mtx > new_sig;
  77.  
  78. 		calcMstep(new_mu, new_mix, new_sig, m_xx, m_gamma_nk);
  79.  
  80. 		m_mu = new_mu;
  81. 		m_mix = new_mix;
  82. 		m_sig = new_sig;
  83. 	}
  84.  
  85. 	void printGammaNK() const
  86. 	{
  87. 		for(int n=0;n<N;n++)
  88. 		{
  89. 			for(int k=0;k<K;k++)
  90. 			{
  91. 				printf("%.10f",m_gamma_nk[n][k]);
  92. 				if(k<K-1)
  93. 				{
  94. 					printf(", ");
  95. 				}
  96. 			}
  97. 			printf("\n");
  98. 		}
  99. 	}
  100.  
  101. private:
  102. 	// 正規化。平均0、不偏標準偏差1にする。
  103. 	void normalize( Mtx& xx ) const
  104. 	{
  105. 		for (int col=0;col<D;++col)
  106. 		{
  107. 			double mean = 0.0;	// 平均
  108. 			for (int row=0;row<N;++row)
  109. 			{
  110. 				mean += xx[row][col];
  111. 			}
  112. 			mean /= N;
  113.  
  114. 			double sd	= 0.0;	// 不偏標準偏差
  115. 			for (int row=0;row<N;++row)
  116. 			{
  117. 				const double diff = xx[row][col]-mean;
  118. 				sd += diff * diff;
  119. 			}
  120. 			sd	/= (N-1);	// 標準偏差じゃなくて不偏標準偏差なので、NじゃなくてN-1で割るのに注意。
  121. 			sd	= sqrt(sd);
  122.  
  123. 			// 平均を引いた後に、不偏標準偏差で割る。
  124. 			for (int row=0;row<N;++row)
  125. 			{
  126. 				xx[row][col] = (xx[row][col]-mean)/sd;
  127. 			}
  128. 		}
  129. 	}
  130.  
  131. 	// 行列と行列の積
  132. 	inline Mtx mul(const Mtx& a, const Mtx& b) const
  133. 	{
  134. 		vector <vector <double> > c(SZ(a), vector<double>(SZ(b[0])));
  135. 		for (int i = 0; i < SZ(a); i++)
  136. 		{
  137. 			for (int k = 0; k < SZ(b); k++)
  138. 			{
  139. 				for (int j = 0; j < SZ(b[0]); j++)
  140. 				{
  141. 					c[i][j] += a[i][k]*b[k][j];
  142. 				}
  143. 			}
  144. 		}
  145. 		return c;
  146. 	}
  147.  
  148. 	// スカラーと行列の積
  149. 	inline Mtx mulScalar(const Mtx& a, const double scalar) const
  150. 	{
  151. 		Mtx ret(a);
  152. 		for (int i = 0; i < SZ(ret); i++)
  153. 		{
  154. 			for (int k = 0; k < SZ(ret[0]); k++)
  155. 			{
  156. 				ret[i][k] *= scalar;
  157. 			}
  158. 		}
  159. 		return ret;
  160. 	}
  161.  
  162. 	// スカラーとベクトルの積
  163. 	inline Vec mulScalar(const Vec& a, const double scalar) const
  164. 	{
  165. 		Vec ret(a);
  166. 		for (int i = 0; i < SZ(ret); i++)
  167. 		{
  168. 			ret[i] *= scalar;
  169. 		}
  170. 		return ret;
  171. 	}
  172.  
  173. 	// 行列の転置
  174. 	inline Mtx transpose( const Mtx& vs ) const
  175. 	{
  176. 		const int H = SZ(vs);
  177. 		const int W = SZ(vs[0]);
  178.  
  179. 		Mtx ret(W, Vec(H) );
  180. 		for (int y = 0; y < W; y++)
  181. 		{
  182. 			for (int x = 0; x < H; x++)
  183. 			{
  184. 				ret[y][x] = vs[x][y];
  185. 			}
  186. 		}
  187.  
  188. 		return ret;
  189. 	}
  190.  
  191. 	// 2*2の行列式を求める
  192. 	inline double det(const Mtx& m) const
  193. 	{
  194. 		return m[0][0]*m[1][1]-m[0][1]*m[1][0];
  195. 	}
  196.  
  197. 	// 2*2の逆行列を求める
  198. 	inline Mtx solve(const Mtx& m ) const
  199. 	{
  200. 		vector < vector <double> > ret(m);
  201. 		swap(ret[0][0],ret[1][1]);
  202. 		ret[0][1] = -ret[0][1];
  203. 		ret[1][0] = -ret[1][0];
  204. 		ret = mulScalar(ret,1.0/abs(det(m)));
  205. 		return ret;
  206. 	}
  207.  
  208. 	// 多次元正規分布密度関数を求める
  209. 	double getDMNorm(const Vec& x, const Vec& mu, const Mtx& sig) const
  210. 	{
  211. 		Vec x_mu(x);	// x - mu
  212. 		for (int i = 0; i < SZ(x_mu); i++)
  213. 		{
  214. 			x_mu[i] -= mu[i];
  215. 		}
  216.  
  217. 		const Mtx inv = solve(sig);
  218.  
  219. 		// D=2決め打ちなので、mul(mul(transpose(x_mu),solve(sig)),x_mu)の部分を展開し、Cとした。
  220. 		const double C = x_mu[0]*(x_mu[0]*inv[0][0]+x_mu[1]*inv[1][0]) + x_mu[1]*(x_mu[0]*inv[0][1]+x_mu[1]*inv[1][1]);
  221.  
  222. 		double ret = 1/(sqrt(pow(2.0*M_PI,D) * det(sig))) * exp( -0.5 * C );
  223.  
  224. 		return ret;
  225. 	}
  226.  
  227. 	// Eステップ。返り値は gamma_nk[N][K]
  228. 	Mtx calcEstep( const Mtx& xx, const Mtx& mu, const Vec& mix, const vector < Mtx >& sig) const
  229. 	{
  230. 		Mtx ret;
  231.  
  232. 		for(int row=0;row<N;++row)
  233. 		{
  234. 			Vec numer(K);
  235. 			for(int k=0;k<K;k++)
  236. 			{
  237. 				numer[k]=mix[k]*getDMNorm(xx[row], mu[k], sig[k]);
  238. 			}
  239. 			const double sum_numer = accumulate(numer.begin(),numer.end(),0.0);
  240.  
  241. 			for (int k=0; k < K; k++)
  242. 			{
  243. 				numer[k]/=sum_numer;
  244. 			}
  245.  
  246. 			ret.push_back(numer);
  247. 		}
  248.  
  249. 		return ret;
  250. 	}
  251.  
  252. 	// Mステップ。次のステップのmu,mix,sigを求める。
  253. 	void calcMstep(	Mtx& new_mu, Vec& new_mix, vector < Mtx >& new_sig, const Mtx& xx, const Mtx& gamma_nk) const	
  254. 	{
  255. 		new_mu.clear();
  256. 		new_mix.clear();
  257. 		new_sig.clear();
  258.  
  259. 		Vec N_k(K);
  260. 		for(int n=0;n<N;n++)
  261. 		{
  262. 			for (int k = 0; k < K; k++)
  263. 			{
  264. 				N_k[k] += gamma_nk[n][k];
  265. 			}
  266. 		}
  267.  
  268. 		new_mix = N_k;
  269. 		for (int k = 0; k < K; k++)
  270. 		{
  271. 			new_mix[k] /= N;
  272. 		}
  273.  
  274. 		new_mu = mul(transpose(gamma_nk),xx);
  275. 		for (int k = 0; k < K; k++)
  276. 		{
  277. 			new_mu[k] = mulScalar(new_mu[k], 1.0/N_k[k]);
  278. 		}
  279.  
  280. 		new_sig = vector < Mtx >(K, Mtx(D, Vec(D)));
  281. 		for(int k=0;k<K;++k)
  282. 		{
  283. 			for(int n=0;n<N;++n)
  284. 			{
  285. 				Vec x_newmu(xx[n]);	// x - new_mu
  286. 				for (int i = 0; i < SZ(x_newmu); i++)
  287. 				{
  288. 					x_newmu[i] -= new_mu[k][i];
  289. 				}
  290.  
  291. 				// D=2きめうち
  292. 				new_sig[k][0][0] += gamma_nk[n][k] * x_newmu[0] * x_newmu[0];
  293. 				new_sig[k][0][1] += gamma_nk[n][k] * x_newmu[0] * x_newmu[1];
  294. 				new_sig[k][1][0] += gamma_nk[n][k] * x_newmu[1] * x_newmu[0];
  295. 				new_sig[k][1][1] += gamma_nk[n][k] * x_newmu[1] * x_newmu[1];
  296. 			}
  297.  
  298. 			new_sig[k] = mulScalar(new_sig[k], 1.0/ N_k[k]);
  299. 		}
  300. 	}
  301.  
  302. 	// おおよその標準正規乱数（平均0、分散1）
  303. 	double getNormRand() const
  304. 	{
  305. 		double ret = 0.0;
  306. 		for( int i = 0; i < 12;i++ ){
  307. 			ret += (double)rand()/RAND_MAX;
  308. 		}
  309. 		return ret-6.0;
  310. 	}
  311. };
  312.  
  313. int main()
  314. {
  315. 	EMGaussianMixtures	*em = new EMGaussianMixtures();
  316.  
  317. 	// 入力
  318. 	Mtx dataFrame;
  319. 	Vec pos(2);
  320. 	while (scanf("%lf %lf",&pos[0],&pos[1])!=EOF)
  321. 	{
  322. 		dataFrame.push_back(pos);
  323. 	}
  324.  
  325. 	// 初期化
  326. 	const int numLoops	 = 20;
  327. 	const int numClasses =  3;
  328. 	em->initialize(dataFrame, numClasses);
  329.  
  330. 	// 実行
  331. 	for (int i = 0; i < numLoops; i++)
  332. 	{
  333. 		em->run();
  334. 	}
  335.  
  336. 	// 出力
  337. 	em->printGammaNK();
  338.  
  339. 	delete em;
  340.  
  341. 	return 0;
  342. }
  343.  
Success #stdin #stdout 0.02s 3452KB
comments (?)
stdin 
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stdout 
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https://ideone.com/LXH8vi
language:
C++ (gcc 8.3)
created:
10 years ago
visibility:
public

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