assert model.node_count() == 4, "The states should include model.start, model.end, Rainy, and Sunny"
print("Great! You've finished the model.")
show_model(model, figsize=(5, 5), filename="example.png", overwrite=True, show_ends=False)
column_order = ["Example Model-start", "Sunny", "Rainy", "Example Model-end"] # Override the Pomegranate default order
column_names = [s.name for s in model.states]
order_index = [column_names.index(c) for c in column_order]
# re-order the rows/columns to match the specified column order
transitions = model.dense_transition_matrix()[:, order_index][order_index, :]
print("The state transition matrix, P(Xt|Xt-1):\n")
print(transitions)
print("\nThe transition probability from Rainy to Sunny is {:.0f}get_ipython().run_line_magic("".format(100", " * transitions[2, 1]))")
# TODO: input a sequence of 'yes'/'no' values in the list below for testing
observations = ['yes', 'no', 'yes']
assert len(observations) > 0, "You need to choose a sequence of 'yes'/'no' observations to test"
# TODO: use model.forward() to calculate the forward matrix of the observed sequence,
# and then use np.exp() to convert from log-likelihood to likelihood
forward_matrix = np.exp(model.forward(observations))
# TODO: use model.log_probability() to calculate the all-paths likelihood of the
# covs_xy[j][0] = np.exp(covs_xy[j][0]) - 1
# means_xy[j][0] = np.exp(means_xy[j][0]) - 1
single_plot = bokeh_datashader_plot(data_thr, covs=covs_xy, means=means_xy,
x_name='rateCA',
y_name='rate',
plot_width=900, plot_height=300,
pixel_width=3000, pixel_height=1000,
spread=True, color_key=color_key)
html = file_html(single_plot, CDN, "pomegranate hmm with 3 components")
Html_file.write(html)
# Html_file.write('<br><br><br><br><br><br><br><br><br><br><br><br>')
# Html_file.write('<br><br><br><br><br><br><br><br><br><br><br><br>')
# Html_file.write('<br><br><br><br><br><br><br><br><br><br><br><br>')
T = np.exp(hmm.dense_transition_matrix())[:9, :9]
plt.imshow(T, interpolation='nearest', cmap=plt.cm.Blues)
plt.colorbar()
for i, j in itertools.product(range(T.shape[0]), range(T.shape[1])):
plt.text(j, i, int(T[i, j]*100),
horizontalalignment="center",
color="white" if T[i, j] > 0.5 else "black")
plt.title('log_likelihood:%0.3f \n state order:' + str(color_key) % hmm.log_probability(X))
plt.savefig('hmm_pomegranate_files/hmm10_pomegranate_transition.png')
data_uri = open(
'hmm_pomegranate_files/hmm10_pomegranate_transition.png',
'rb').read().encode('base64').replace('\n', '')
img_tag = '<img src="data:image/png;base64,{0}">'.format(data_uri)
Html_file.write(img_tag)
data_probs['probs'+str(j)] = pd.Series(probs[:, j])
linkbru = plot_probs_bokeh_linked_brushing(data_probs, prob_names=prob_names,
color_key=color_key,
x_name='rateCA', y_name='rate',
covs=covs_xy, means=means_xy,
title='Hidden Markov Model with 3 states \n Visualization on the first 10% samples',
title2='State belonging and state probability')
html = file_html(linkbru, CDN, "pomegranate hmm with 3 components")
Html_file.write('<br><br><br><br><br><br><br><br><br><br><br><br>')
Html_file.write(html)
Html_file.write('<br><br><br><br><br><br><br><br><br><br><br><br>')
# transition matrix:
T = np.exp(hmm.dense_transition_matrix())[:3, :3]
plt.imshow(T, interpolation='nearest', cmap=plt.cm.Blues)
plt.colorbar()
for i, j in itertools.product(range(T.shape[0]), range(T.shape[1])):
plt.text(j, i, int(T[i, j]*100),
horizontalalignment="center",
color=(color_key[i] if i == j
else "white" if T[i, j] > 0.5
else "black"))
plt.title('Transition probability matrix of the HMM. \n Log likelihood value: %0.3f' % hmm.log_probability(X))
plt.savefig('hmm_pomegranate_files/hmm3_pomegranate_transition.png')
data_uri = open(
'hmm_pomegranate_files/hmm3_pomegranate_transition.png',
'rb').read().encode('base64').replace('\n', '')
img_tag = '<img src="data:image/png;base64,{0}">'.format(data_uri)
Html_file.write(img_tag)
# covs_xy[j][0] = np.exp(covs_xy[j][0]) - 1
# means_xy[j][0] = np.exp(means_xy[j][0]) - 1
single_plot = bokeh_datashader_plot(data_thr, covs=covs_xy, means=means_xy,
x_name='rateCA',
y_name='rate',
plot_width=900, plot_height=300,
pixel_width=3000, pixel_height=1000,
spread=True, color_key=color_key)
html = file_html(single_plot, CDN, "pomegranate hmm with 3 components")
Html_file.write(html)
# Html_file.write('<br><br><br><br><br><br><br><br><br><br><br><br>')
# Html_file.write('<br><br><br><br><br><br><br><br><br><br><br><br>')
# Html_file.write('<br><br><br><br><br><br><br><br><br><br><br><br>')
T = np.exp(hmm.dense_transition_matrix())[:18, :18]
plt.imshow(T, interpolation='nearest', cmap=plt.cm.Blues)
plt.colorbar()
for i, j in itertools.product(range(T.shape[0]), range(T.shape[1])):
plt.text(j, i, int(T[i, j]*100),
horizontalalignment="center",
color="white" if T[i, j] > 0.5 else "black")
plt.title('log_likelihood:%0.3f' % hmm.log_probability(X))
plt.savefig('hmm_pomegranate_files/hmm18_pomegranate_transition.png')
data_uri = open(
'hmm_pomegranate_files/hmm18_pomegranate_transition.png',
'rb').read().encode('base64').replace('\n', '')
img_tag = '<img src="data:image/png;base64,{0}">'.format(data_uri)
Html_file.write(img_tag)
class RealTimeHMM():
def __init__(self, n_trials=3, leave_one_out=1):
"""Variable initialization"""
self.patient = rospy.get_param("gait_phase_det/patient")
self.verbose = rospy.get_param("gait_phase_det/verbose")
self.n_trials = n_trials
self.n_features = 2 # Raw data and 1st-derivative
self.leave_one_out = leave_one_out
self.rec_data = 0.0 # Number of recorded IMU data
self.proc_data = 0.0 # Number of extracted features
self.win_size = 3
self.raw_win = [None] * self.win_size
# self.fder_win = [0] * self.win_size
self.ff = [[] for x in range(self.n_trials)] # Training and test dataset
self.labels = [[] for x in range(self.n_trials)] # Reference labels from local data
self.first_eval = True
self.model_loaded = False
algorithm = rospy.get_param("gait_phase_det/algorithm")
rospy.loginfo('Decoding algorithm: {}'.format(algorithm))
if algorithm not in DECODER_ALGORITHMS:
raise ValueError("Unknown decoder {!r}".format(algorithm))
self.decode = {
"fov": self._run_fov,
"bvsw": self._run_bvsw
}[algorithm]
self.imu_callback = {
"fov": self._fov_callback,
"bvsw": self._bvsw_callback
}[algorithm]
"""HMM variables"""
''' State list:
s1: Heel Strike (HS)
s2: Flat Foot (FF)
s3: Heel Off (HO)
s4: Swing Phase (SP)'''
self.model_name = "Gait"
self.has_model = False
self.must_train = False
self.states = ['s1', 's2', 's3', 's4']
self.n_states = len(self.states)
self.state2phase = {"s1": "hs", "s2": "ff", "s3": "ho", "s4": "sp"}
self.train_data = []
self.mgds = {}
self.dis_means = [[] for x in range(self.n_states)]
self.dis_covars = [[] for x in range(self.n_states)]
self.start_prob = [1.0/self.n_states]*self.n_states
self.trans_mat = np.array([(0.9, 0.1, 0, 0), (0, 0.9, 0.1, 0), (0, 0, 0.9, 0.1), (0.1, 0, 0, 0.9)]) # Left-right model
# self.trans_mat = np.array([0.8, 0.1, 0, 0.1], [0.1, 0.8, 0.1, 0], [0, 0.1, 0.8, 0.1], [0.1, 0, 0.1, 0.8]) # Left-right-left model
self.log_startprob = []
self.log_transmat = np.empty((self.n_states, self.n_states))
self.max_win_len = 11 # ms (120 ms: mean IC duration for healthy subjects walking at comfortable speed)
self.viterbi_path = np.empty((self.max_win_len+1, self.n_states))
self.backtrack = [[None for x in range(self.n_states)] for y in range(self.max_win_len+1)]
self.global_path = []
self.work_buffer = np.empty(self.n_states)
self.boundary = 1
self.buff_len = 0
self.states_pos = {}
for i in range(len(self.states)):
self.states_pos[self.states[i]] = i
self.last_state = -1
self.curr_state = -1
self.conv_point = 0
self.conv_found = False
self.smp_freq = 100.0 # Hz
self.fp_thresh = 1/self.smp_freq*4 # Threshold corresponds to 8 samples
self.time_passed = 0.0
self.obs = [[None for x in range(self.n_features)] for y in range(self.max_win_len)]
self.model = HMM(name=self.model_name)
"""ROS init"""
rospy.init_node('real_time_HMM', anonymous=True)
rospack = rospkg.RosPack()
self.packpath = rospack.get_path('hmm_gait_phase_classifier')
self.init_subs()
self.init_pubs()
"""HMM-training (if no model exists)"""
try:
'''HMM-model loading'''
with open(self.packpath+'/log/HMM_models/'+self.patient+'.txt') as infile:
json_model = json.load(infile)
self.model = HMM.from_json(json_model)
rospy.logwarn(self.patient + "'s HMM model was loaded.")
self.has_model = True
except IOError:
if os.path.isfile(self.packpath + "/log/mat_files/" + self.patient + "_proc_data1.mat"):
"""Training with data collected with FSR-based reference system"""
self.data_ext = 'mat'
self.must_train = True
elif os.path.isfile(self.packpath + "/log/IMU_data/" + self.patient + "_labels.csv"):
"""Training with data collected with offline threshold-based gait phase detection method"""
self.data_ext = 'csv'
self.must_train = True
else:
rospy.logerr("Please collect data for training ({})!".format(self.patient))
if self.must_train:
rospy.logwarn("HMM model not trained yet for {}!".format(self.patient))
rospy.logwarn("Training HMM with local data...")
self.load_data()
self.init_hmm()
self.train_hmm()
self.has_model = True
if self.has_model:
try:
'''MGDs loading if model exists'''
for st in self.states:
with open(self.packpath+'/log/HMM_models/'+self.patient+'_'+self.state2phase[st]+'.txt') as infile:
yaml_dis = yaml.safe_load(infile)
dis = MGD.from_yaml(yaml_dis)
self.mgds[st] = dis
rospy.logwarn(self.patient +"'s " + self.state2phase[st] + " MGC was loaded.")
'''Loading means and covariance matrix'''
self.dis_means[self.states_pos[st]] = self.mgds[st].parameters[0]
self.dis_covars[self.states_pos[st]] = self.mgds[st].parameters[1]
except yaml.YAMLError as exc:
rospy.logwarn("Not able to load distributions: " + exc)
"""Transition and initial (log) probabilities matrices upon training"""
trans_mat = self.model.dense_transition_matrix()[:self.n_states,:self.n_states]
if self.verbose: print '**TRANSITION MATRIX (post-training)**\n'+ str(trans_mat)
for i in range(self.n_states):
self.log_startprob.append(ln(self.start_prob[i]))
for j in range(self.n_states):
self.log_transmat[i,j] = ln(trans_mat[i][j])
self.model_loaded = True
"""Init ROS publishers"""
def init_pubs(self):
self.phase_pub = rospy.Publisher('/gait_phase', Int8, queue_size=100)
"""Init ROS subcribers"""
def init_subs(self):
rospy.Subscriber('/imu_data', Imu, self.imu_callback)
"""Callback function upon arrival of IMU data for forward-only decoding"""
def _fov_callback(self, data):
self.rec_data += 1.0
self.raw_win.append(data.angular_velocity.y)
self.raw_win.pop(0) # Drop first element
if self.rec_data >= self.win_size and self.model_loaded: # At least one previous and one subsequent data should have been received
"""Extract feature and append it to test dataset"""
fder = (self.raw_win[self.win_size/2 + 1] - self.raw_win[self.win_size/2 - 1])/2
# peak_detector = self.raw_win[self.win_size/2]/max(self.raw_win)
# self.fder_win.append(fder)
# self.fder_win.pop(0)
# sder = (self.fder_win[2] - self.fder_win[0])/2
# test_set = [self.raw_win[self.win_size/2], self.raw_win[self.win_size/2 - 2], self.raw_win[self.win_size/2 - 1], self.raw_win[self.win_size/2 + 1], self.raw_win[self.win_size/2 + 2]] # Temporally proximal features
test_set = [self.raw_win[self.win_size/2], fder] # Temporally proximal features
'''Forward-only decoding approach'''
state = self.decode(test_set)
# rospy.loginfo("Decoded phase: {}".format(state))
self.time_passed += 1/self.smp_freq
if self.last_state == state:
if (self.time_passed >= self.fp_thresh) and (self.curr_state == 3 and state == 0) or (state == self.curr_state + 1):
self.curr_state = state
self.phase_pub.publish(state)
else:
# rospy.loginfo("Current phase: {}".format(self.state2phase[self.states[self.curr_state]]))
# self.phase_pub.publish((self.curr_state-1)%4)
self.phase_pub.publish(self.curr_state)
else:
self.last_state = state
self.time_passed = 1/self.smp_freq
# rospy.logwarn("Detected phase: {}".format(self.state2phase[self.states[self.last_state]]))
"""Callback function upon arrival of IMU data for BVSW"""
def _bvsw_callback(self, data):
self.rec_data += 1.0
self.raw_win.append(data.angular_velocity.y)
self.raw_win.pop(0) # Drop first element
if self.rec_data >= 3 and self.model_loaded: # At least one previous and one subsequent data should have been received
"""Extract feature and append it to test dataset"""
test_set = [self.raw_win[1], (self.raw_win[0]+self.raw_win[2])/2] # First-derivate of angular velocity
'''Bounded sliding window decoding approach'''
self.obs.append(test_set)
self.obs.pop(0) # This way, -1 element corresponds to last received features
states = self.decode(test_set)
if len(states) != 0:
for st in states:
self.phase_pub.publish(st)
if self.curr_state != st:
rospy.logwarn("Detected phase: {}".format(self.state2phase[self.states[st]]))
self.curr_state = st
self.proc_data += 1.0 # One gyro data has been processed
"""Local data loading from mat file and feature extraction"""
def load_data(self):
"""Data loading"""
'''Load mat file (Data processed offline in Matlab)'''
if self.data_ext == 'mat':
rospy.logwarn("Initializing parameters via FSR-based reference system")
# subs = ['daniel', 'erika', 'felipe', 'jonathan', 'luis', 'nathalia', 'paula', 'pedro', 'tatiana'] # Healthy subjects
# subs = ['carmen', 'carolina', 'catalina', 'claudia', 'emmanuel', 'fabian', 'gustavo'] # Pathological subjects
# subs = ['daniel'] # Single subject
datapath = self.packpath + "/log/mat_files/"
gyro_y = [[] for x in range(self.n_trials)]
time_array = [[] for x in range(self.n_trials)]
# for patient in subs:
for i in range(self.n_trials):
data = scio.loadmat(datapath + self.patient + "_proc_data" + str(i+1) + ".mat")
# data = scio.loadmat(datapath + patient + "_proc_data" + str(i+1) + ".mat")
gyro_y[i] = data["gyro_y"][0]
# gyro_y[i] += list(data["gyro_y"][0])
time_array[i] = data["time"][0]
# time_array[i] += list(data["time"][0])
self.labels[i] = data["labels"][0]
# self.labels[i] += list(data["labels"][0])
"""Feature extraction"""
'''First derivative'''
fder_gyro_y = []
for i in range(self.n_trials):
der = []
der.append(gyro_y[i][0])
for j in range(1,len(gyro_y[i])-1):
der.append((gyro_y[i][j+1]-gyro_y[i][j-1])/2)
der.append(gyro_y[i][-1])
fder_gyro_y.append(der)
'''Second derivative'''
# sder_gyro_y = []
# for i in range(self.n_trials):
# der = []
# der.append(fder_gyro_y[i][0])
# for j in range(1,len(fder_gyro_y[i])-1):
# der.append((fder_gyro_y[i][j+1]-fder_gyro_y[i][j-1])/2)
# der.append(fder_gyro_y[i][-1])
# sder_gyro_y.append(der)
'''Peak detector'''
# peak_detector = []
# for i in range(self.n_trials):
# win = []
# for j in range(len(gyro_y[i])):
# if (j - self.win_size/2) < 0:
# win.append(gyro_y[i][j] / self._max(gyro_y[i][0:j + self.win_size/2]))
# elif (j + self.win_size/2) > (len(gyro_y[i])-1):
# win.append(gyro_y[i][j] / self._max(gyro_y[i][j - self.win_size/2:len(gyro_y[i])-1]))
# else:
# win.append(gyro_y[i][j] / self._max(gyro_y[i][j - self.win_size/2:j + self.win_size/2]))
# peak_detector.append(win)
"""Create training data"""
for j in range(self.n_trials):
# for k in range(self.win_size/2,len(gyro_y[j])-1-self.win_size/2):
for k in range(len(gyro_y[j])):
f_ = []
f_.append(gyro_y[j][k])
'''Approximate differentials'''
f_.append(fder_gyro_y[j][k])
# f_.append(sder_gyro_y[j][k])
'''Temporally proximal feature'''
# f_.append(gyro_y[j][k-1])
# f_.append(gyro_y[j][k-2])
# f_.append(gyro_y[j][k+1])
# f_.append(gyro_y[j][k+2])
'''Peak detector'''
# f_.append(peak_detector[j][k])
self.ff[j].append(f_)
self.ff = np.array(self.ff)
self.n_features = len(self.ff[0][0])
for i in range(len(self.ff[self.leave_one_out-1])):
self.train_data.append(self.ff[self.leave_one_out-1][i])
for i in range(len(self.ff[(self.leave_one_out+1) % self.n_trials])):
self.train_data.append(self.ff[(self.leave_one_out+1) % self.n_trials][i])
self.train_data = [self.train_data] # Keep this line or training won't work
"""Parameter initialization"""
'''Kmeans clustering'''
# n_components = 4 # No. components of MGD
# init = 'kmeans++' # "kmeans||", "first-k", "random"
# n_init = 1
# weights = None
# max_kmeans_iterations = 1
# batch_size = None
# batches_per_epoch = None
#
# X_concat = x_train
#
# # X_concat = numpy.concatenate(x_train)
# # if X_concat.ndim == 1:
# # X_concat = X_concat.reshape(X_concat.shape[0], 1)
# # n, d = X_concat.shape
#
# rospy.logwarn("K-means clustering...")
# clf = Kmeans(n_components, init=init, n_init=n_init)
# clf.fit(X_concat, weights, max_iterations=max_kmeans_iterations,
# batch_size=batch_size, batches_per_epoch=batches_per_epoch)
# y = clf.predict(X_concat)
#
# rospy.logwarn("Creating distributions...")
# class_data = [[] for x in range(self.n_states)]
# for i in range(len(x_train)):
# class_data[y[i]].append(x_train[i])
# if self.verbose:
# sum = 0
# print "Kmeans clusters:"
# for i in range(self.n_states):
# temp = len(class_data[i])
# sum += temp
# print temp
# print sum, len(x_train)
"""Offline threshold-based classification"""
if self.data_ext == 'csv':
rospy.logwarn("Initializing parameters via threshold-based gait phase detection method")
self.leave_one_out = 0
gyro_y = []
datapath = self.packpath + '/log/IMU_data/'
with open(datapath+'{}.csv'.format(self.patient), 'r') as imu_file:
reader = csv.DictReader(imu_file)
for row in reader:
gyro_y.append(float(dict(row)['gyro_y']))
'''Feature extraction: 1st derivative'''
for i in range(1, len(gyro_y)-1):
feature_vect = [gyro_y[i], (gyro_y[i+1]-gyro_y[i-1])/2]
self.train_data.append(feature_vect)
self.ff[self.leave_one_out].append(feature_vect)
'''Reference labels'''
with open(datapath+'{}_labels.csv'.format(self.patient), 'r') as labels_file:
reader = csv.reader(labels_file)
for row in reader:
self.labels[self.leave_one_out].append(int(row[0]))
self.train_data = [self.train_data]
"""Init HMM if no previous training"""
def init_hmm(self):
if self.data_ext == 'mat':
rospy.logwarn("-------Leaving trial {} out-------".format(self.leave_one_out+1))
"""Transition matrix (A)"""
'''Transition matrix from reference labels'''
# prev = -1
# for i in range(len(self.labels[self.leave_one_out])):
# if prev == -1:
# prev = self.labels[self.leave_one_out][i]
# self.trans_mat[prev][self.labels[self.leave_one_out][i]] += 1.0
# prev = self.labels[self.leave_one_out][i]
# self.trans_mat = normalize(self.trans_mat, axis=1, norm='l1')
if self.verbose: rospy.logwarn("**TRANSITION MATRIX (pre-training)**\n" + str(self.trans_mat) + '\nMatrix type: {}'.format(type(self.trans_mat)))
class_data = [[] for x in range(self.n_states)]
for i in range(len(self.ff[self.leave_one_out])):
class_data[self.labels[self.leave_one_out][i]].append(self.ff[self.leave_one_out][i])
"""Multivariate Gaussian Distributions for each hidden state"""
class_means = [[[] for x in range(self.n_features)] for i in range(self.n_states)]
# class_vars = [[[] for x in range(self.n_features)] for i in range(self.n_states)]
# class_std = [[[] for x in range(self.n_features)] for i in range(self.n_states)]
class_cov = []
for i in range(self.n_states):
cov = np.ma.cov(np.array(class_data[i]), rowvar=False)
class_cov.append(cov)
for j in range(self.n_features):
class_means[i][j] = np.array(class_data[i][:])[:, [j]].mean(axis=0)
# class_vars[i][j] = np.array(class_data[i][:])[:, [j]].var(axis=0)
# class_std[i][j] = np.array(class_data[i][:])[:, [j]].std(axis=0)
"""Classifier initialization"""
distros = []
hmm_states = []
for i in range(self.n_states):
dis = MGD(np.array(class_means[i]).flatten(), np.array(class_cov[i]))
st = State(dis, name=self.states[i])
distros.append(dis)
hmm_states.append(st)
self.model.add_states(hmm_states)
'''Initial transitions'''
for i in range(self.n_states):
self.model.add_transition(self.model.start, hmm_states[i], self.start_prob[i])
'''Left-right model'''
for i in range(self.n_states):
for j in range(self.n_states):
self.model.add_transition(hmm_states[i], hmm_states[j], self.trans_mat[i][j])
'''Finish model setup'''
self.model.bake()
"""Train initialized model"""
def train_hmm(self):
rospy.logwarn("Training initialized model...")
self.model.fit(self.train_data, algorithm='baum-welch', verbose=self.verbose)
self.model.freeze_distributions() # Freeze all model distributions, preventing update from ocurring
if self.verbose: print "**HMM model:\n{}**".format(self.model)
"""Save Multivariate Gaussian Distributions into yaml file"""
for st in self.model.states:
if st.name != self.model_name+"-start" and st.name != self.model_name+"-end":
dis = st.distribution
dis_yaml = dis.to_yaml()
try:
with open(self.packpath+'/log/HMM_models/'+self.patient+'_'+self.state2phase[st.name]+'.txt', 'w') as outfile:
yaml.dump(dis_yaml, outfile, default_flow_style=False)
rospy.logwarn(self.patient+"'s "+self.state2phase[st.name]+" distribution was saved.")
except IOError:
rospy.logwarn('It was not possible to write GMM distribution.')
"""Save model (json script) into txt file"""
model_json = self.model.to_json()
try:
with open(self.packpath+'/log/HMM_models/'+self.patient+'.txt', 'w') as outfile:
json.dump(model_json, outfile)
rospy.logwarn(self.patient+"'s HMM model was saved.")
except IOError:
rospy.logwarn('It was not possible to write HMM model.')
"""Compute the log probability under a multivariate Gaussian distribution.
Parameters
----------
X : array_like, shape (n_samples, n_features)
List of n_features-dimensional data points. Each row corresponds to a
single data point.
means : array_like, shape (n_components, n_features)
List of n_features-dimensional mean vectors for n_components Gaussians.
Each row corresponds to a single mean vector.
covars : array_like
List of n_components covariance parameters for each Gaussian. The shape
is (n_components, n_features, n_features) if 'full'
Returns
----------
lpr : array_like, shape (n_samples, n_components)
Array containing the log probabilities of each data point in
X under each of the n_components multivariate Gaussian distributions."""
def log_multivariate_normal_density(self, X, min_covar=1.e-7):
"""Log probability for full covariance matrices."""
n_samples, n_dim = X.shape
nmix = len(self.dis_means)
log_prob = np.empty((n_samples, nmix))
for c, (mu, cv) in enumerate(zip(self.dis_means, self.dis_covars)):
try:
cv_chol = linalg.cholesky(cv, lower=True)
except linalg.LinAlgError:
# The model is most probably stuck in a component with too
# few observations, we need to reinitialize this components
try:
cv_chol = linalg.cholesky(cv + min_covar * np.eye(n_dim),
lower=True)
except linalg.LinAlgError:
raise ValueError("'covars' must be symmetric, "
"positive-definite")
cv_log_det = 2 * np.sum(np.log(np.diagonal(cv_chol)))
cv_sol = linalg.solve_triangular(cv_chol, (X - mu).T, lower=True).T
log_prob[:, c] = - .5 * (np.sum(cv_sol ** 2, axis=1) +
n_dim * np.log(2 * np.pi) + cv_log_det)
return log_prob
"""Find argument (pos) that has the maximum value in array-like object"""
def _argmax(self, X):
X_max = float("-inf")
pos = 0
for i in range(X.shape[0]):
if X[i] > X_max:
X_max = X[i]
pos = i
return pos
"""Find max value in array-like object"""
def _max(self, X):
return X[self._argmax(X)]
"""Backtracking process to decode most-likely state sequence"""
def _optim_backtrack(self, k):
opt = []
self.last_state = where_from = self._argmax(self.viterbi_path[k])
opt.append(where_from)
for lp in range(k-1, -1, -1):
opt.insert(0, self.backtrack[lp + 1][where_from])
where_from = self.backtrack[lp + 1][where_from]
self.global_path.extend(opt)
return opt
'''Forward-only decoding approach'''
def _run_fov(self, test_set):
# Probability distribution of state given observation
framelogprob = self.log_multivariate_normal_density(np.array([test_set]))
if self.first_eval:
for i in range(self.n_states):
self.viterbi_path[0, i] = self.log_startprob[i] + framelogprob[0, i]
self.first_eval = False
return self._argmax(self.viterbi_path[0])
else: # Recursion
for i in range(self.n_states):
for j in range(self.n_states):
self.work_buffer[j] = (self.log_transmat[j, i] + self.viterbi_path[0, j])
self.viterbi_path[1, i] = self._max(self.work_buffer) + framelogprob[0, i]
self.viterbi_path[0] = self.viterbi_path[1] # Prepare for next feature vector
return self._argmax(self.viterbi_path[1])
'''Bounded sliding variable window approach'''
def _run_bvsw(self, test_set):
framelogprob = self.log_multivariate_normal_density(np.array([test_set]))
if self.first_eval:
for i in range(self.n_states):
self.viterbi_path[0,i] = self.log_startprob[i] + framelogprob[0,i]
self.backtrack[0][i] = None
self.first_eval = False
return []
else:
'''Find likelihood probability and backpointer'''
for j in range(self.n_states):
for i in range(self.n_states):
self.work_buffer[i] = self.viterbi_path[self.boundary - 1][i] + self.log_transmat[i, j]
self.viterbi_path[self.boundary][j] = self._max(self.work_buffer) + framelogprob[0][j]
self.backtrack[self.boundary][j] = self._argmax(self.work_buffer)
'''Backtracking local paths'''
local_paths = [[] for x in range(self.n_states)]
for j in range(self.n_states):
where_from = j
for smp in range(self.boundary-1, -1, -1):
local_paths[j].insert(0, self.backtrack[smp+1][where_from])
where_from = self.backtrack[smp+1][where_from]
# if self.verbose:
# print "\n{}, {}".format(t, b)
# for path in local_paths:
# print path
'''Given all local paths, find fusion point'''
tmp = [None] * self.n_states
for k in range(len(local_paths[0])-1, 0, -1):
for st in range(self.n_states):
tmp[st] = local_paths[st][k]
if tmp.count(tmp[0]) == len(tmp): # All local paths point to only one state?
self.conv_found = True
self.conv_point = k
# if self.verbose: print "Found, {}".format(k)
break
'''Find local path if fusion point was found'''
if self.boundary < self.max_win_len and self.conv_found:
self.buff_len += self.conv_point
opt = self._optim_backtrack(self.conv_point)
self.conv_found = False
# if self.verbose: print "\nOpt1: " + str(opt) + ", {}".format(len(self.global_path))
'''Reinitialize local variables'''
for i in range(self.n_states):
if i == self.last_state:
self.log_startprob[i] = ln(1.0)
else:
self.log_startprob[i] = ln(0.0)
self.viterbi_path[0][i] = self.log_startprob[i] + framelogprob[0][i]
self.backtrack[0][i] = None
for smp in range(1, self.boundary-self.conv_point+1):
for j in range(self.n_states):
for i in range(self.n_states):
self.work_buffer[i] = self.viterbi_path[smp - 1][i] + self.log_transmat[i, j]
self.viterbi_path[smp][j] = self._max(self.work_buffer) + self.log_multivariate_normal_density(np.array([self.obs[self.conv_point-self.boundary+smp-1]]))[0,j]
self.backtrack[smp][j] = self._argmax(self.work_buffer)
self.boundary -= self.conv_point-1
return opt
elif self.boundary >= self.max_win_len:
'''Bounding threshold was exceeded'''
self.buff_len += self.max_win_len
opt = self._optim_backtrack(self.boundary-1)
# if self.verbose: print "\nOpt2: " + str(opt) + ", {}".format(len(self.global_path))
'''Reinitialize local variables'''
self.boundary = 1
for i in range(self.n_states):
if i == self.last_state:
self.log_startprob[i] = ln(1.0)
else:
self.log_startprob[i] = ln(0.0)
self.viterbi_path[0][i] = self.log_startprob[i] + framelogprob[0][i]
self.backtrack[0][i] = None
return opt
else:
self.boundary += 1
return []
data_probs['probs'+str(j)] = pd.Series(probs[:, j])
linkbru = plot_probs_bokeh_linked_brushing(data_probs, prob_names=prob_names,
color_key=color_key,
x_name='rateCA', y_name='rate',
covs=covs_xy, means=means_xy,
title='Hidden Markov Model with 5 states. \n Visualization on the first 10% samples',
title2='State belonging and state probability')
html = file_html(linkbru, CDN, "pomegranate hmm with 5 components")
Html_file.write('<br><br><br><br><br><br><br><br><br><br><br><br>')
Html_file.write(html)
Html_file.write('<br><br><br><br><br><br><br><br><br><br><br><br>')
# transition matrix:
T = np.exp(hmm.dense_transition_matrix())[:5, :5]
plt.imshow(T, interpolation='nearest', cmap=plt.cm.Blues)
plt.colorbar()
for i, j in itertools.product(range(T.shape[0]), range(T.shape[1])):
plt.text(j, i, int(T[i, j]*100),
horizontalalignment="center",
color=(color_key[i] if i == j
else "white" if T[i, j] > 0.5
else "black"))
plt.title('Transition probability matrix of the HMM. \n Log likelihood value: %0.3f' % hmm.log_probability(X))
plt.savefig('hmm_pomegranate_files/hmm5_pomegranate_transition.png')
data_uri = open(
'hmm_pomegranate_files/hmm5_pomegranate_transition.png',
'rb').read().encode('base64').replace('\n', '')
img_tag = '<img src="data:image/png;base64,{0}">'.format(data_uri)
Html_file.write(img_tag)
sunny_emissions = DiscreteDistribution({"yes": 0.1, "no": 0.9})
sunny_state = State(sunny_emissions, name="Sunny")
rainy_emissions = DiscreteDistribution({"yes": 0.8, "no": 0.2})
rainy_state = State(rainy_emissions, name="Rainy")
model.add_states(sunny_state, rainy_state)
# create edges for each possible state transition in the model
# equal probability of a sequence starting on either a rainy or sunny day
model.add_transition(model.start, sunny_state, 0.5)
model.add_transition(model.start, rainy_state, 0.5)
# Sunny Rainy
#Sunny 0.80 0.20
#Rainy 0.40 0.60
model.add_transition(sunny_state, sunny_state, 0.8) # 80% sunny->sunny
model.add_transition(sunny_state, rainy_state, 0.2) # 20% sunny->rainy
model.add_transition(rainy_state, sunny_state, 0.4) # 40% rainy->sunny
model.add_transition(rainy_state, rainy_state, 0.6) # 60% rainy->rainy
model.bake()
assert model.edge_count() == 6, "There should be two edges from model.start, two from Rainy, and two from Sunny"
assert model.node_count() == 4, "The states should include model.start, model.end, Rainy, and Sunny"
print("Great! You've finished the model.")
print(model.dense_transition_matrix())
from pomegranate import HiddenMarkovModel, DiscreteDistribution, State
import numpy as np
model = HiddenMarkovModel(name='weather')
sunny_emissions = DiscreteDistribution({'yes': 0.1, 'no': 0.9})
sunny_state = State(sunny_emissions, name='sunny')
rainy_emissions = DiscreteDistribution({'yes': 0.8, 'no': 0.2})
rainy_state = State(rainy_emissions, name='rainy')
model.add_states(sunny_state, rainy_state)
model.add_transition(model.start, sunny_state, 0.5)
model.add_transition(model.start, rainy_state, 0.5)
model.add_transition(sunny_state, rainy_state, 0.2)
model.add_transition(sunny_state, sunny_state, 0.8)
model.add_transition(rainy_state, rainy_state, 0.6)
model.add_transition(rainy_state, sunny_state, 0.4)
model.bake()
states = np.array([s.name for s in model.states])
print('{} states: {}'.format(model.node_count(), states))
transitions = model.dense_transition_matrix()
print('{} transitions probabilities between states \n{}'.format(
model.edge_count(), transitions))
# for j in range(len(covs)):
# covs_xy[j][0] = np.exp(covs_xy[j][0]) - 1
# means_xy[j][0] = np.exp(means_xy[j][0]) - 1
single_plot = bokeh_datashader_plot(data_thr, covs=covs_xy, means=means_xy,
x_name='rateCA',
y_name='rate',
plot_width=900, plot_height=300,
pixel_width=3000, pixel_height=1000,
spread=True, color_key=color_key)
html = file_html(single_plot, CDN, "pomegranate hmm with 3 components")
Html_file.write('<br><br><br><br><br>')
Html_file.write(html)
T = np.exp(hmm.dense_transition_matrix())[:4, :4]
plt.imshow(T, interpolation='nearest', cmap=plt.cm.Blues)
plt.colorbar()
for i, j in itertools.product(range(T.shape[0]), range(T.shape[1])):
plt.text(j, i, int(T[i, j]*100),
horizontalalignment="center",
color="white" if T[i, j] > 0.5 else "black")
plt.title('log_likelihood:%0.3f' % hmm.log_probability(X))
plt.savefig('hmm_pomegranate_files/hmm4_pomegranate_transition.png')
data_uri = open(
'hmm_pomegranate_files/hmm4_pomegranate_transition.png',
'rb').read().encode('base64').replace('\n', '')
img_tag = '<img src="data:image/png;base64,{0}">'.format(data_uri)
Html_file.write(img_tag)