def build_LDF_model(num_class, x_train, y_train):
""" LDF model
First call QDF model to caculate the mean, cov_matirx
"""
prior, mean, cov_matrix = build_QDF_model(num_class, x_train, y_train)
#print_cov_matrix(cov_matrix)
# cacualte the shared covariance matirx
avg_cov = np.matlib.zeros(cov_matrix[0].shape)
for i in range(num_class):
avg_cov += (prior[i] * cov_matrix[i])
inverse_cov = avg_cov.getI() # get the inverse covariance matrix
num_feature = x_train.shape[1]
# each column for weight[i]
weight = np.matrix([0] * num_feature).T
w0 = []
for i in range(num_class):
wi = 2 * inverse_cov.T * mean[i]
weight = np.hstack((weight, wi))
wi0 = 2 * math.log(prior[i]) - (mean[i].T * inverse_cov * mean[i])[0,0]
w0.append(wi0)
return inverse_cov, weight[:, 1:], w0
def build_RDA_model(num_class, x_train, y_train, beta, gamma):
""" First call QDF model to caculate the mean, cov_matirx
beta, gamma: hyper-parameters, range: 0~1
"""
prior, mean, cov_matrix = build_QDF_model(num_class, x_train, y_train)
# cacualte the shared covariance matirx
avg_cov = np.matlib.zeros(cov_matrix[0].shape)
for i in range(num_class):
avg_cov += (prior[i] * cov_matrix[i])
num_feature = len(x_train[0])
for i in range(num_class):
# the following formula is from PPT
tmp = cov_matrix[i]
dev = tmp.trace()[0,0] * 1.0 / num_feature
cov_matrix[i] = (1-gamma) * ((1-beta)*tmp + beta*avg_cov) + gamma * dev * np.matlib.eye(num_feature)
"""
# refer to Statistical Pattern Recognition, page 43
tmp = cov_matrix[i]
tmp = (1-beta) * prior[i] * tmp + beta * avg_cov
dev = tmp.trace()[0,0] * 1.0 / num_feature
cov_matrix[i] = (1-gamma) * tmp + gamma * dev * np.matlib.eye(num_feature)
"""
return prior, mean, cov_matrix
def build_MQDF_model(num_class, x_train, y_train, k, delta0):
""" MQDF model
@k and @delta are hyper-parameters
Note: There are three possible ways to set @delta:
1) @delta is a hyper-parameter, set by cross validation
2) @delta can be estimated via ML estimation, in which case, this delta
is no longer a hyper-parameter
3) @delta can be set close to $\sigma_{i,k}$ or $\sigma_{i,k+1}$, in which case,
this delta is also not a hyper-parameter
"""
d = len(x_train[0]) # number of features
assert(k<d and k>0)
prior, mean, cov_matrix = build_QDF_model(num_class, x_train, y_train)
eigenvalue = [] # store the first largest k eigenvalues of each class
eigenvector = [] # the first largest k eigenvectors, column-wise of each class
delta = [0] * num_class # deltas for each class
for i in range(num_class):
cov = cov_matrix[i]
eig_values, eig_vectors = linalg.eigh(cov)
# sort the eigvalues
idx = eig_values.argsort()
idx = idx[::-1] # reverse the array
eig_values = eig_values[idx]
eig_vectors = eig_vectors[:,idx]
eigenvector.append(eig_vectors[:, 0:k])
eigenvalue.append(eig_values[:k])
# delta via ML estimation
#delta[i] = (cov.trace() - sum(eigenvalue[i])) * 1.0 / (d-k)
# delta close to $\sigma_{i,k-1}$ or $\sigma_{i,k}$
#delta[i] = (eig_values[k-1] + eig_values[k])/2
#print 'Suggestd delta[%d]: %f' % (i, (eig_values[k] + eig_values[k+1])/2)
# delta as the mean of minor values
delta[i] = sum(eig_values[k:]) / len(eig_values[k:])
#delta = [delta0] * num_class
return prior, mean, eigenvalue, eigenvector, delta
