def objective_soft_max_old(X, W, C):
l = C.shape[0]
m = X.shape[1]
objective_value = 0
eta = find_eta(X, W)
XT_W = X.T @ W - eta
weighted_sum = sum(exp(XT_W), axis=1)
wighted_sum_matrix = diag(1 / weighted_sum)
for k in range(l):
objective_value = objective_value + C[k, :].T @ log(
wighted_sum_matrix @ exp(XT_W[:, k]))
return -objective_value / m
def objective_soft_max_gradient_W(X, W, C, WT_X=None):
m = C.shape[1]
if WT_X is None:
XT_W = X.T @ W
else:
XT_W = WT_X.T
eta = find_eta(X, W, XT_W)
XT_W -= eta
weighted_sum = sum(exp(XT_W), axis=1)
gradient = (1 / m) * X @ (divide(
exp(XT_W), weighted_sum.reshape(weighted_sum.shape[0], 1)) - C.T)
return gradient
def objective_soft_max_gradient_W_old_but_gold(X, W, C):
l = C.shape[0]
n = X.shape[0]
m = X.shape[1]
eta = find_eta(X, W)
XT_W = X.T @ W - eta
weighted_sum = sum(exp(XT_W), axis=1)
wighted_sum_matrix = np.diag(1 / weighted_sum)
grad = np.zeros((n, l))
for p in range(l):
grad[:, p] = (1 / m) * X @ (wighted_sum_matrix @ exp(XT_W[:, p]) -
C[p, :])
return grad
def objective_soft_max_gradient_W2(X, W, C):
l = C.shape[0]
n = X.shape[0]
m = X.shape[1]
eta = find_eta(X, W)
XT_W = X.T @ W - eta
weighted_sum = sum(exp(XT_W), axis=1)
grad = np.zeros((n, l))
for p in range(l):
grad[:, p] = (1 / m) * X @ (divide(exp(XT_W[:, p]), weighted_sum) -
C[p, :])
return grad
def objective_soft_max_Wj(X, W, C):
"""
:param X:
:param W: shape #features x #labels
:param C: shape #labels x #samples
:return:
"""
l = C.shape[0]
m = X.shape[1]
objective_value = 0
eta = find_eta(X, W)
XT_W = X.T @ W - eta
weighted_sum = sum(exp(XT_W), axis=1)
for k in range(l):
objective_value = objective_value + C[k, :].T @ log(
divide(exp(XT_W[:, k]), weighted_sum))
return -objective_value / m
def objective_soft_max(X, W, C, WT_X=None):
"""
:param X:
:param W: shape #features x #labels
:param C: shape #labels x #samples
:return:
"""
l, m = C.shape
objective_value = 0
if WT_X is None:
XT_W = X.T @ W
else:
XT_W = WT_X.T
eta = find_eta(X, W, XT_W)
XT_W -= eta
weighted_sum = sum(exp(XT_W), axis=1)
for k in range(l):
objective_value = objective_value + C[k, :].T @ log(
divide(exp(XT_W[:, k]), weighted_sum))
return -objective_value / m
def objective_soft_max_gradient_Wp(X, W, C, p):
m = X.shape[1]
eta = find_eta(X, W)
XT_W = X.T @ W - eta
weighted_sum = sum(exp(XT_W), axis=1)
return (1 / m) * X @ (divide(exp(XT_W[:, p]), weighted_sum) - C[p, :])
# Script 23 on page 55 from numpy.core._multiarray_umath import exp nums = [10, 20, 30, 40, 50] np_exp = exp(nums) print(np_exp)
def objective_soft_max_gradient_X(X, W, C, WT_X=None):
if WT_X is None:
WT_X = W.T @ X
m = C.shape[1]
return (1 / m) * W @ (divide(exp(WT_X), sum(exp(WT_X), axis=0)) - C)