隐马尔可夫模型中的Viterbi算法的C++实现
#include <iostream> #include <vector> #include <map> #include <string> using namespace std; typedef vector< string > VecStr; typedef map< string, double > MapStrDou; typedef map< string, map< string, double > > MapStrMap; typedef vector< string > :: iterator VecStrI; typedef map< string, double > :: iterator MapStrDouI; typedef map< string, map< string, double > > :: iterator MapStrMapI; typedef struct DSD { double d1; string s; double d2; }DSD; typedef map< string, DSD > MapStrDSD; #define RAINY "Rainy" #define SUNNY "Sunny" #define WALK "walk" #define SHOP "shop" #define CLEAN "clean" DSD forward_viterbi(VecStr& obs, VecStr& states, MapStrDou& start_p, MapStrMap& trans_p, MapStrMap& emit_p); int main(void) { VecStr states; VecStr observations; MapStrDou start_probability; MapStrMap transition_probability; MapStrMap emission_probability; states.push_back(RAINY); states.push_back(SUNNY); observations.push_back(WALK); observations.push_back(SHOP); observations.push_back(CLEAN); start_probability[RAINY] = 0.6; start_probability[SUNNY] = 0.4; MapStrDou t1; t1[RAINY] = 0.7; t1[SUNNY] = 0.3; MapStrDou t2; t2[RAINY] = 0.4; t2[SUNNY] = 0.6; transition_probability[RAINY] = t1; transition_probability[SUNNY] = t2; MapStrDou e1; e1[WALK] = 0.1; e1[SHOP] = 0.4; e1[CLEAN] = 0.5; MapStrDou e2; e2[WALK] = 0.6; e2[SHOP] = 0.3; e2[CLEAN] = 0.1; emission_probability[RAINY] = e1; emission_probability[SUNNY] = e2; DSD ret = forward_viterbi(observations, states, start_probability, transition_probability, emission_probability); cout << ret.d1 <<endl; cout << ret.s << endl; cout << ret.d2 << endl; return 0; } DSD forward_viterbi(VecStr& obs, VecStr& states, MapStrDou& start_p, MapStrMap& trans_p, MapStrMap& emit_p) { MapStrDSD T; VecStrI VS_i, VS_j, VS_k; DSD DSD_tmp; for(VS_i = states.begin(); VS_i != states.end(); VS_i++) { DSD_tmp.d1 = start_p[*VS_i]; DSD_tmp.s = *VS_i; DSD_tmp.d2 = start_p[*VS_i]; T[*VS_i] = DSD_tmp; } for(VS_i = obs.begin(); VS_i != obs.end(); VS_i++) { MapStrDSD U; for(VS_j = states.begin(); VS_j != states.end(); VS_j++) { double total = 0.0; string argmax = ""; double valmax = 0.0; double prob = 1.0; string v_path = ""; double v_prob = 1.0; for(VS_k = states.begin(); VS_k != states.end(); VS_k++) { DSD objs = T[*VS_k]; prob = objs.d1; v_path = objs.s; v_prob = objs.d2; double p = (emit_p[*VS_k])[*VS_i] * (trans_p[*VS_k])[*VS_j]; prob *= p; v_prob *= p; total += prob; if(v_prob > valmax) { argmax = v_path + "," + *VS_j; valmax = v_prob; } /** test */ cout << "obs = " << *VS_i << endl; cout << "/tnext_state = " << *VS_j << endl; cout << "/t/tstate = " << *VS_k << endl; cout << "/t/t/tp = " << p << " = " << (emit_p[*VS_k])[*VS_i] << " * " << (trans_p[*VS_k])[*VS_j] << endl; cout << "/t/t/t{prob, v_path, v_prob} = {" << prob << ", " << v_path << ", " << v_prob << "}" << endl; cout << "/t/t/t{total, argmax, valmax} = {" << total << ", " << argmax << ", " << valmax << "}" << endl; /** end of test */ } DSD_tmp.d1 = total; DSD_tmp.s = argmax; DSD_tmp.d2 = valmax; U[*VS_j] = DSD_tmp; } T = U; } double total = 0.0; string argmax = ""; double valmax = 0.0; double prob = 1.0; string v_path = ""; double v_prob = 1.0; for(VS_i = states.begin(); VS_i != states.end(); VS_i++) { DSD objs = T[*VS_i]; prob = objs.d1; v_path = objs.s; v_prob = objs.d2; total += prob; if(v_prob > valmax) { argmax = v_path; valmax = v_prob; } } DSD_tmp.d1 = total; DSD_tmp.s = argmax; DSD_tmp.d2 = valmax; return DSD_tmp; }
执行结果：
obs = walk
next_state = Rainy
state = Rainy
p = 0.07 = 0.1 * 0.7
{prob, v_path, v_prob} = {0.042, Rainy, 0.042}
{total, argmax, valmax} = {0.042, Rainy,Rainy, 0.042}
obs = walk
next_state = Rainy
state = Sunny
p = 0.24 = 0.6 * 0.4
{prob, v_path, v_prob} = {0.096, Sunny, 0.096}
{total, argmax, valmax} = {0.138, Sunny,Rainy, 0.096}
obs = walk
next_state = Sunny
state = Rainy
p = 0.03 = 0.1 * 0.3
{prob, v_path, v_prob} = {0.018, Rainy, 0.018}
{total, argmax, valmax} = {0.018, Rainy,Sunny, 0.018}
obs = walk
next_state = Sunny
state = Sunny
p = 0.36 = 0.6 * 0.6
{prob, v_path, v_prob} = {0.144, Sunny, 0.144}
{total, argmax, valmax} = {0.162, Sunny,Sunny, 0.144}
obs = shop
next_state = Rainy
state = Rainy
p = 0.28 = 0.4 * 0.7
{prob, v_path, v_prob} = {0.03864, Sunny,Rainy, 0.02688}
{total, argmax, valmax} = {0.03864, Sunny,Rainy,Rainy, 0.02688}
obs = shop
next_state = Rainy
state = Sunny
p = 0.12 = 0.3 * 0.4
{prob, v_path, v_prob} = {0.01944, Sunny,Sunny, 0.01728}
{total, argmax, valmax} = {0.05808, Sunny,Rainy,Rainy, 0.02688}
obs = shop
next_state = Sunny
state = Rainy
p = 0.12 = 0.4 * 0.3
{prob, v_path, v_prob} = {0.01656, Sunny,Rainy, 0.01152}
{total, argmax, valmax} = {0.01656, Sunny,Rainy,Sunny, 0.01152}
obs = shop
next_state = Sunny
state = Sunny
p = 0.18 = 0.3 * 0.6
{prob, v_path, v_prob} = {0.02916, Sunny,Sunny, 0.02592}
{total, argmax, valmax} = {0.04572, Sunny,Sunny,Sunny, 0.02592}
obs = clean
next_state = Rainy
state = Rainy
p = 0.35 = 0.5 * 0.7
{prob, v_path, v_prob} = {0.020328, Sunny,Rainy,Rainy, 0.009408}
{total, argmax, valmax} = {0.020328, Sunny,Rainy,Rainy,Rainy, 0.009408}
obs = clean
next_state = Rainy
state = Sunny
p = 0.04 = 0.1 * 0.4
{prob, v_path, v_prob} = {0.0018288, Sunny,Sunny,Sunny, 0.0010368}
{total, argmax, valmax} = {0.0221568, Sunny,Rainy,Rainy,Rainy, 0.009408}
obs = clean
next_state = Sunny
state = Rainy
p = 0.15 = 0.5 * 0.3
{prob, v_path, v_prob} = {0.008712, Sunny,Rainy,Rainy, 0.004032}
{total, argmax, valmax} = {0.008712, Sunny,Rainy,Rainy,Sunny, 0.004032}
obs = clean
next_state = Sunny
state = Sunny
p = 0.06 = 0.1 * 0.6
{prob, v_path, v_prob} = {0.0027432, Sunny,Sunny,Sunny, 0.0015552}
{total, argmax, valmax} = {0.0114552, Sunny,Rainy,Rainy,Sunny, 0.004032}
0.033612
Sunny,Rainy,Rainy,Rainy
0.009408
参考文献：
http://en.wikipedia.org/wiki/Viterbi_algorithm
http://hi.baidu.com/liqinghuisi/blog/item/a11cd4f54394f22fbc3109cf.html