def power(A, v, it):
u = v
for i in range(it):
v = pnp.dot(A, u)
l = pnp.dot(pnp.transpose(v), u) * myreciprocal(pnp.dot(pnp.transpose(u), u))
u = v * myreciprocal(l.flatten()[0])
return u, l
def jaccard_sim_po(mat):
intersect = pnp.dot(mat, pnp.transpose(mat))
union = pnp.sum(mat, axis = 1)
union = pnp.reshape(pnp.tile(union, len(mat)), (len(mat), len(mat)))
union = union + pnp.transpose(union) - intersect + 0.0
sim = intersect * myreciprocal(union,0.0)
for i in range(sim.shape[0]):
sim[i, i] = pp.sfixed(1.0)
return sim
def backward_dropout(network, expected):
n_layer = len(network)
for i in reversed(range(n_layer)):
layer = network[i]
if i == n_layer - 1: # linear, outputs_before_act == outputs
exp_size = pnp.ravel(expected).shape[0]
layer['delta'] = (layer['outputs_before_act'] - expected) / (exp_size + 0.0)
layer['gradient'] = pnp.dot(pnp.transpose(layer['inputs']), layer['delta'])
layer['bias_gradient'] = pnp.dot(pnp.ones((1, layer['inputs'].shape[0])), layer['delta'])
else:
nrow = layer['outputs_before_act'].shape[0]
next = network[i + 1]
layer['delta'] = pnp.dot(next['delta'], pnp.transpose(next['weight'])) * relu_derivative(layer['outputs_before_act']) * pnp.dot(pnp.ones((nrow, 1)), layer['mask'])
layer['gradient'] = pnp.dot(pnp.transpose(layer['inputs']), layer['delta'])
layer['bias_gradient'] = pnp.dot(pnp.ones((1, layer['inputs'].shape[0])), layer['delta'])
def grad_full(X, W, H, Y, l):
'''
The symbol in this function is consistent with the symbol in paper Large-scale Multi-label Learning with Missing Labels
X: real matrix: 708 * (350 or lower) (private)/ 1512 * (800 or lower) (public)
W: real matrix: (350/800 or lower) * 125 (private)
H: real matrix: 708/1512 * 125 (private)
Y: bin matrix: 708 * 1512 (private, dense)
l: (lamb) 1
A = X * W * H^T
D = A - Y
ans = X^T * D * H
'''
ans = multi_dot([pnp.transpose(X), X, W, pnp.transpose(H), H]) - multi_dot([pnp.transpose(X), Y, H]) + l * W
return ans
def dice_sim_matrix_po(X):
sumX = pnp.sum(X, axis = 1)
sumX = pnp.reshape(pnp.tile(sumX, len(X)), (len(X), len(X)))
sumX = sumX + pnp.transpose(sumX)
cmpX = pnp.zeros((len(X), len(X)))
for i in range(len(X)):
cmpX[i] = pnp.sum(X * pnp.reshape(pnp.tile(X[i], len(X)), (len(X), len(X[0]))), axis = 1)
result = 2 * cmpX * myreciprocal(sumX * sumX, 0.0)
result = sumX * result
return result
def DCA_po(networks, dim, rsp, maxiter, pmiter, log_iter):
def log_po(x, times):
tmp = x - 1
sgn = 1
result = 0
for k in range(times):
result += 1. / (k+1) * sgn * tmp
tmp *= x - 1
sgn *= -1
return result
def power(A, v, it):
u = v
for i in range(it):
v = pnp.dot(A, u)
l = pnp.dot(pnp.transpose(v), u) * myreciprocal(pnp.dot(pnp.transpose(u), u))
u = v * myreciprocal(l.flatten()[0])
return u, l
def hhmul(v, w):
return v - 2 * pnp.transpose(w).dot(v).flatten()[0]* w
def hhupdate(A, w):
wA = 2 * pnp.dot(w, pnp.dot(pnp.transpose(w), A))
wAw = 2 * pnp.dot(pnp.dot(wA, w), pnp.transpose(w))
A = A - wA - pnp.transpose(wA) + wAw
return A[1:, 1:]
def pmPCA_po(A, dim, it):
results = []
ws = []
ls = []
for i in range(dim):
v = pnp.ones((A.shape[0], 1))
v, l = power(A, v, it)
# Prepare a vector w
w = pnp.zeros(v.shape)
w[0] = pnp.norm(v)
w += v
w = w * myreciprocal(pnp.norm(w))
# Reduce the matrix dimension
A = hhupdate(A, w)
# Reconstruct the eigenvector of original matrix from the current one
for wp in ws:
v = pnp.concatenate((pp.farr([[0]]), v))
v = hhmul(v, wp)
v = v * myreciprocal(pnp.norm(v))
results.append(v)
ws.insert(0, w)
ls.append(pp.sfixed(l.flatten()[0]))
return pnp.concatenate(results, axis=1), pp.farr(ls)
P = pp.farr([])
for net in networks:
tQ = RWR_po(net, maxiter, rsp)
if P.shape[0] == 0:
P = pnp.zeros((tQ.shape[0], 0))
# concatenate network
P = pnp.hstack((P, tQ))
alpha = 0.01
P = log_po(P + alpha, log_iter) - pnp.log(alpha) # 0 < p <ln(n+1)
P = pnp.dot(P, pnp.transpose(P)) # 0 < p < n * ln^2(n+1)
vecs, lambdas = pmPCA_po(P, dim, pmiter)
sigd = pnp.dot(pnp.eye(dim), pnp.diag(lambdas))
sigd_sqsq = pnp.sqrt(pnp.sqrt(sigd))
flag = pnp.abs(sigd)<1e-6
sigd_sqsq = flag*pnp.zeros(sigd.shape)+(1-flag)*sigd_sqsq
X = pnp.dot(vecs, sigd_sqsq)
return X
def hess_full(X, W, S, H, Y, l):
'''
Only works under square loss function
'''
ans = multi_dot([pnp.transpose(X), X, S, pnp.transpose(H), H]) + l * S
return ans
def IMC_po(Y, D, P, k, lamb, maxiter, gciter):
'''
D: real matrix: 708 * (350 or lower) (private)
P: real matrix: 1512 * (800 or lower) (public)
Y: bin matrix: 708 * 1512 (private)
'''
def multi_dot(arr):
ans = arr[-1]
for ii in range(len(arr)-2,-1,-1):
ans = pp.farr(arr[ii]).dot(ans)
return ans
## require MPC version <-
def grad_full(X, W, H, Y, l):
'''
The symbol in this function is consistent with the symbol in paper Large-scale Multi-label Learning with Missing Labels
X: real matrix: 708 * (350 or lower) (private)/ 1512 * (800 or lower) (public)
W: real matrix: (350/800 or lower) * 125 (private)
H: real matrix: 708/1512 * 125 (private)
Y: bin matrix: 708 * 1512 (private, dense)
l: (lamb) 1
A = X * W * H^T
D = A - Y
ans = X^T * D * H
'''
ans = multi_dot([pnp.transpose(X), X, W, pnp.transpose(H), H]) - multi_dot([pnp.transpose(X), Y, H]) + l * W
return ans
def hess_full(X, W, S, H, Y, l):
'''
Only works under square loss function
'''
ans = multi_dot([pnp.transpose(X), X, S, pnp.transpose(H), H]) + l * S
return ans
def fdot(A, B):
# flatten dot. Regard A and B as long vector
A = pp.farr(A)
B = pp.farr(B)
A = A * (1.0/A.shape[0])
B = B * (1.0/B.shape[0])
return pnp.sum(A * B)
def GC(X, W, H, Y, l, iters):
grad_solver = lambda W: grad_full(X, W, H, Y, l)
hess_solver = lambda W, S: hess_full(X, W, S, H, Y, l)
R = - grad_solver(W) + 0.0
D = R
oldR2 = fdot(R, R)
for t in range(iters):
hessD = hess_solver(W, D)
a = oldR2 * pp.reciprocal(fdot(D, hessD)+1e-8)
W += a * D
R -= a * hessD
newR2 = fdot(R, R)
b = newR2 * pp.reciprocal(oldR2+1e-8)
D = R + b * D
oldR2 = newR2
return W
W = pnp.eye(D.shape[1],k)*0.3
H = pnp.eye(P.shape[1],k)*0.3
updateW = lambda W, H, it: GC(D, W, pnp.dot(P, H), Y, lamb, it)
updateH = lambda W, H, it: GC(P, H, pnp.dot(D, W), pnp.transpose(Y), lamb, it)
for i in range(maxiter):
W = updateW(W, H, gciter)
H = updateH(W, H, gciter)
if True: # log
Yhat = multi_dot([D, W, pnp.transpose(H), pnp.transpose(P)])
loss = pnp.norm(Y - Yhat)
Yhat = multi_dot((D, W, pnp.transpose(H), pnp.transpose(P)))
return Yhat
def hhupdate(A, w):
wA = 2 * pnp.dot(w, pnp.dot(pnp.transpose(w), A))
wAw = 2 * pnp.dot(pnp.dot(wA, w), pnp.transpose(w))
A = A - wA - pnp.transpose(wA) + wAw
return A[1:, 1:]
def hhmul(v, w):
return v - 2 * pnp.transpose(w).dot(v).flatten()[0]* w
