def optimize(self, E, iterations):
M = self.M
W, H = utils.init_wh(M, self.k)
V, U = utils.init_wh(M, self.k)
for i in range(iterations):
print(i, utils.objective(M, W, H, E))
H, _ = admm_H_update(M, W, H, U, E, self.k)
W, _ = admm_W_update(M, W, H, V, E, self.k)
return W, H
def optimize(self, E, iterations):
M = self.M
W, H = utils.init_wh(M, self.k)
for j in range(self.k):
W[:, j] = W[:, j] / torch.norm(W[:, j])
H[j, :] = H[j, :] / torch.norm(H[j, :])
for i in range(iterations):
print(i, utils.objective(M, W, H, E))
Dif = E * (M - W.mm(H))
for j in range(self.k):
uj = W[:, j]
vj = H[j, :]
Dif = Dif + uj.reshape(-1, 1).mm(vj.reshape(1, -1))
u_nom = Dif.t().mv(uj).clamp_min(0)
if torch.norm(u_nom) > 1e-18:
vj = u_nom / (torch.norm(uj)**2)
else:
vj = torch.zeros_like(vj)
v_nom = Dif.mv(vj).clamp_min(0)
if torch.norm(v_nom) > 1e-18:
uj = v_nom / (torch.norm(vj)**2)
else:
uj = torch.zeros_like(uj)
W[:, j] = uj
H[j, :] = vj
Dif = Dif - uj.reshape(-1, 1).mm(vj.reshape(1, -1))
return W, H
def optimize(self, E, iterations):
M = self.M
W, H = utils.init_wh(M, self.k)
for i in range(iterations):
print(i, utils.objective(M, W, H, E))
pH = H
H = H + self.step * (W.T.mm(E * (M - W.mm(H))))
H = utils.proj(H, pH, self.sticky)
pW = W
W = W + self.step * ((E * (M - W.mm(H))).mm(H.T))
W = utils.proj(W, pW, self.sticky)
return W, H
def optimize(self, E, iterations):
M = self.M
W, H = utils.init_wh(M, self.k)
for i in range(iterations):
print(i, utils.objective(M, W, H, E))
# M_aux = (M - W.mm(H)) * E + W.mm(H)
h_denom = W.t().mm(E * W.mm(H))
H = H * torch.where(h_denom < 1e-10, eps, W.t().mm(M) / h_denom) # TODO
# M_aux = (M - W.mm(H)) * E + W.mm(H)
w_denom = (E * W.mm(H)).mm(H.t())
W = W * torch.where(w_denom < 1e-10, eps, (M).mm(H.t()) / w_denom) # TODO
return W, H
def optimize(self, E: Tensor, iterations):
M = self.M
W, H = utils.init_wh(M, self.k)
mW, mH = 0, 0
for i in range(iterations):
print(i, utils.objective(M, W, H, E))
prevW, prevH = W, H
W = W + (1 - self.momentum) * mW
H = H + (1 - self.momentum) * mH
(gW, gH) = self.grad(M, W, H, E)
# nW = np.random.normal(0, 0.01 * self.step, (n, self.k))
# nH = np.random.normal(0, 0.01 * self.step, (self.k, m))
W = utils.proj(W - self.step * gW, W, self.sticky)
H = utils.proj(H - self.step * gH, H, self.sticky)
mW = W - prevW
mH = H - prevH
return W, H
def optimize(self, iterations):
M = self.M
w, h = utils.init_wh(M, self.k)
distance_type = self.distance_type
w_aux = w.copy()
h_aux = h.copy()
# init dual variables for w, h, y
dual_w = np.zeros_like(w)
dual_h = np.zeros_like(h)
v_aux = np.zeros_like(M)
dual_v = np.zeros_like(M)
reg_w = (0, 'nn')
reg_h = (0, 'l2n')
rho = 1
for i in range(iterations):
print(i, utils.objective(M, w, h))
if distance_type == 'eu':
h_aux = aux_update(h, dual_h, w_aux, M, None, rho,
distance_type)
w_aux = aux_update(w.T, dual_w.T, h_aux.T, M.T, None, rho,
distance_type)
w_aux = w_aux.T
h = prox(reg_h[1], h_aux, dual_h, rho=rho, lambda_=reg_h[0])
w = prox(reg_w[1],
w_aux.T,
dual_w.T,
rho=rho,
lambda_=reg_w[0])
w = w.T
elif distance_type == 'kl':
h_aux = aux_update(h, dual_h, w_aux, v_aux, dual_v, rho,
distance_type)
w_aux = aux_update(w.T, dual_w.T, h_aux.T, v_aux.T, dual_v.T,
rho, distance_type)
w_aux = w_aux.T
h = prox(reg_h[1], h_aux, dual_h, rho=rho, lambda_=reg_h[0])
w = prox(reg_w[1],
w_aux.T,
dual_w.T,
rho=rho,
lambda_=reg_w[0])
w = w.T
v_bar = w_aux @ h_aux - dual_v
v_aux = 1 / 2 * ((v_bar - 1) + np.sqrt((v_bar - 1)**2 + 4 * M))
dual_v = dual_v + v_aux - w_aux @ h_aux
else:
raise TypeError('Unknown loss type.')
dual_h = dual_h + h - h_aux
dual_w = dual_w + w - w_aux
return w, h