def get_armijos_step_size(kernel_matrices,
d,
y_mat,
alpha0,
box_constraints,
gamma0,
Jd,
D,
dJ,
c=0.5,
T=0.5):
#m = D' * dJ, should be negative
#Loop until f(x + gamma * p <= f(x) + gamma*c*m)
# J(d + gamma * D) <= J(d) + gamma * c * m
gamma = gamma0
m = D.T.dot(dJ)
while True:
combined_kernel_matrix = k_helpers.get_combined_kernel(
kernel_matrices, d + gamma * D)
alpha, new_J, info = compute_J(combined_kernel_matrix, y_mat, alpha0,
box_constraints)
if new_J <= Jd + gamma * c * m:
return gamma
else:
#Update gamma
gamma = gamma * T
return gamma / 2
def get_armijos_step_size(kernel_matrices, d, y_mat, alpha0, box_constraints, gamma0, Jd, D, dJ, c=0.5, T=0.5):
#m = D' * dJ, should be negative
#Loop until f(x + gamma * p <= f(x) + gamma*c*m)
# J(d + gamma * D) <= J(d) + gamma * c * m
gamma = gamma0
m = D.T.dot(dJ)
while True:
combined_kernel_matrix = k_helpers.get_combined_kernel(kernel_matrices, d + gamma * D)
alpha, new_J, info = compute_J(combined_kernel_matrix, y_mat, alpha0, box_constraints)
if new_J <= Jd + gamma * c * m:
return gamma
else:
#Update gamma
gamma = gamma * T
return gamma / 2
def find_kernel_weights(X, y, kernel_functions):
# The number of kernels
M = len(kernel_functions)
#The number of examples
n = len(y)
#The weights of each kernel
#Initialized to 1/M
d = np.ones(M) / M
D = np.ones(M)
#Just a placeholder for something that gets updated later
dJ = '-20'
#Stores all the individual kernel matrices
kernel_matrices = k_helpers.get_all_kernels(X, kernel_functions)
#Creates y matrix for use in SVM later
#y's should be -1, 1 before doing this.
y_mat = np.outer(y, y)
#Gets constraints for running SVM
box_constraints = helpers.get_box_constraints(n, 1.0)
#Gets starting value for SVM
alpha0 = np.zeros(n)
iteration = 0
#Loops until stopping criterion reached
while (max(D) != 0 and not helpers.stopping_criterion(dJ, d, 0.01)):
iteration += 1
print "iteration and weights:", iteration, d
combined_kernel_matrix = k_helpers.get_combined_kernel(kernel_matrices, d)
combined_kernel_func = k_helpers.get_combined_kernel_function(kernel_functions, d)
#Gets J, also calculates the optimal values for alpha
alpha, J, info = helpers.compute_J(combined_kernel_matrix, y_mat, alpha0, box_constraints)
J *= -1
#Gradient of J w.r.t d (weights)
dJ = helpers.compute_dJ(kernel_matrices, y_mat, alpha)
#The index of the largest component of d
mu = d.argmax()
#Descent direction
#Basically, we are calculating -1 * reduced gradient of J w.r.t d,
#using the index of the largest component of d as our "mu"
#in the reduced gradient calculation
D = helpers.compute_descent_direction(d, dJ, mu)
D = helpers.fix_precision_of_vector(D, 0)
J_cross = 0
d_cross = d.copy()
D_cross = D.copy()
sub_iteration = 0
#Get maximum admissible step size in direction D
while (J_cross < J):
sub_iteration += 1
d = d_cross.copy()
D = D_cross.copy()
print ' J:', J, '| J_cross:', J_cross
print ' d cross', d_cross
print ' d cross sum', sum(d_cross)
print ' D cross', D_cross
print ' D cross sum', sum(D_cross)
combined_kernel_matrix = k_helpers.get_combined_kernel(kernel_matrices, d)
alpha, J, info = helpers.compute_J(combined_kernel_matrix, y_mat, alpha, box_constraints)
J *= -1
#Maximum admissible step size
gamma_max = 123456
#argmax of above
v = -0.123456
#Find gamma_max and v
for m in range(M):
if D[m] < 0:
d_D_quotient = -1 * d[m] / D[m]
if d_D_quotient < gamma_max:
gamma_max = d_D_quotient
v = m
d_cross = d + gamma_max * D
#Not strictly necessary, but helps avoid precision errors
d_cross[v] = 0
D_cross[mu] = D[mu] + D[v]
D_cross[v] = 0
d_cross = helpers.fix_precision_of_vector(d_cross, 1)
D_cross = helpers.fix_precision_of_vector(D_cross, 0)
combined_kernel_matrix_cross = k_helpers.get_combined_kernel(kernel_matrices, d_cross)
alpha_cross, J_cross, cross_info = helpers.compute_J(combined_kernel_matrix_cross, y_mat, alpha, box_constraints)
J_cross *= -1
print ' new J cross', J_cross
#Line search along D for gamma (step) in [0, gamma_max]
# gamma = helpers.get_armijos_step_size()
gamma = helpers.get_armijos_step_size(kernel_matrices, d, y_mat, alpha,
box_constraints, gamma_max, J_cross,
D, dJ)
print 'gamma:', gamma
print 'D:', D
d += gamma * D
d = helpers.fix_precision_of_vector(d, 1)
#Return final weights
return d