Viterbi Algorithm for HMM, https://tinyurl.com/y8xt2lcf

Author: WuLC

python/Viterbi.py

@@ -0,0 +1,61 @@
+# -*- coding: utf-8 -*-
+# @Author: WuLC
+# @Date:   2017-04-02 08:52:24
+# @Last Modified by:   WuLC
+# @Last Modified time: 2017-04-02 09:50:31
+
+###########################################################################################################
+# Viterbi Algorithm for HMM
+# dynamic programming, time complexity O(mn^2), m is the length of sequence of observation, n is the number of hidden states
+# more details can be obtained from: https://tinyurl.com/y8xt2lcf
+##########################################################################################################
+
+
+# five elements for HMM
+states = ('Healthy', 'Fever')
+ 
+observations = ('normal', 'cold', 'dizzy')
+ 
+start_probability = {'Healthy': 0.6, 'Fever': 0.4}
+ 
+transition_probability = {
+   'Healthy' : {'Healthy': 0.7, 'Fever': 0.3},
+   'Fever' :   {'Healthy': 0.4, 'Fever': 0.6},
+   }
+ 
+emission_probability = {
+   'Healthy' : {'normal': 0.5, 'cold': 0.4, 'dizzy': 0.1},
+   'Fever'   : {'normal': 0.1, 'cold': 0.3, 'dizzy': 0.6},
+   }
+
+
+
+def Viterbit(obs, states, s_pro, t_pro, e_pro):
+	path = { s:[] for s in states} # init path: path[s] represents the path ends with s
+	curr_pro = {}
+	for s in states:
+		curr_pro[s] = s_pro[s]*e_pro[s][obs[0]]
+	for i in xrange(1, len(obs)):
+		last_pro = curr_pro
+		curr_pro = {}
+		for curr_state in states:
+			max_pro, last_sta = max(((last_pro[last_state]*t_pro[last_state][curr_state]*e_pro[curr_state][obs[i]], last_state) 
+				                       for last_state in states))
+			curr_pro[curr_state] = max_pro
+			path[curr_state].append(last_sta)
+
+	# find the final largest probability
+	max_pro = -1
+	max_path = None
+	for s in states:
+		path[s].append(s)
+		if curr_pro[s] > max_pro:
+			max_path = path[s]
+			max_pro = curr_pro[s]
+		# print '%s: %s'%(curr_pro[s], path[s]) # different path and their probability
+	return max_path
+
+
+if __name__ == '__main__':
+	obs = ['normal', 'cold', 'dizzy']
+	print Viterbit(obs, states, start_probability, transition_probability, emission_probability)