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utils.py
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utils.py
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from annoy import AnnoyIndex
import copy
import numpy as np
import random
from scipy.optimize import curve_fit
BOXMIN = np.array([10, 2])
TOLERANCE = 1e-5
MAX_GRAD = 4.0
MIN_DIST_SCALE = 1e-3
def embed_graph(
knn,
n_vertices,
n_components,
initial_alpha, # self.learning_rate
a,
b,
gamma, # repulsive strength
negative_sample_rate,
n_epochs=0,
init='random'
):
if n_epochs <= 0:
# For smaller datasets we can use more epochs
if n_vertices <= 10000:
n_epochs = 500
else:
n_epochs = 200
# TODO: implement spectral?
if init == 'random':
embedding = np.random.uniform(0, 4, size=(n_vertices, n_components))
else:
raise NotImplementedError('Only random initialization of embedding is implemented')
embedding = optimize_layout(
embedding,
knn,
n_epochs,
knn.shape[1] // 4,
n_vertices,
a, b,
gamma,
initial_alpha,
negative_sample_rate
)
return embedding
def optimize_layout(
embedding,
knn,
n_epochs,
minibatch,
n_vertices,
a, b,
gamma=1,
initial_alpha=1,
negative_sample_rate=5,
):
def batch(knn, k=minibatch):
ir = np.random.choice(knn.shape[1], k)
return knn[:, ir]
ir = minibatch * 2
def neg_samples(k):
nonlocal ir
next = np.arange(ir, ir + k)
ir += k
while ir >= n_vertices:
next[next >= n_vertices] -= n_vertices
ir -= n_vertices
return next
alpha = initial_alpha
n_eff = n_epochs * knn.shape[1] // minibatch
da = alpha / n_eff
for _ in range(n_eff):
js, kpos, weight = batch(knn)
keep = random.random() <= weight
kpos = kpos[keep].astype(int)
if len(kpos) == 0:
continue
js = js[keep].astype(int)
dpos = dpos_dy(embedding[js], embedding[kpos], a, b)
embedding[kpos, :] += -alpha * dpos
for _ in range(negative_sample_rate):
kneg = neg_samples(len(kpos))
while True:
drop = (kneg == js) | (kneg == kpos)
if ~np.any(drop):
break
kneg[drop] = neg_samples(np.sum(drop))
dneg = dneg_dy(embedding[js], embedding[kneg], gamma, a, b)
dpos += dneg
embedding[kneg] += -alpha * dneg
embedding[js, :] += alpha * (dpos + dneg)
alpha -= da
return embedding
def clip(val):
return np.minimum(MAX_GRAD, np.maximum(-MAX_GRAD, val))
def dpos_dy(current, others, a, b, boxmin=BOXMIN):
del_x = current - others
d_sq = dist(del_x)
if boxmin is not None:
d = np.sqrt(d_sq)
hat_x = del_x / d
case = np.argmin(boxmin * hat_x, axis=1)
dbox = boxmin[case] - np.abs(del_x[np.arange(len(case)), case])
ob = dbox > 0
grad_coeff = -2.0 * a * b * (np.power(d_sq, b - 1.0)
/ (a * np.power(d_sq, b) + 1.0))
grad = clip(grad_coeff * del_x)
if boxmin is not None:
grad[ob, case[ob]] = -np.sign(grad[ob, case[ob]]) * dbox[ob]
return grad
def dneg_dy(current, others, gamma, a, b, boxmin=BOXMIN):
del_x = current - others
d_sq = dist(del_x)
if boxmin is not None:
d = np.sqrt(d_sq)
hat_x = del_x / d
case = np.argmin(boxmin * hat_x, axis=1)
dbox = boxmin[case] - np.abs(del_x[np.arange(len(case)), case])
ob = dbox > 0
grad_coeff = 2.0 * b * gamma / (
(0.001 + d_sq) * (a * np.power(d_sq, b) + 1))
grad_coeff[d_sq <= 0] = 0
grad_d = clip(grad_coeff * del_x)
grad_d[grad_coeff[:, 0] <= 0, :] = MAX_GRAD
if boxmin is not None:
grad_d[ob, case[ob]] = np.sign(grad_d[ob, case[ob]]) * dbox[ob]
return grad_d
def build_graph_nocoo(X, n_neighbors, counts=None):
num_iters = max(0, 3 - int(np.log10(X.shape[0])))
knn_d = nearer_neighbours(X, n_neighbors, num_iters=num_iters)
sigmas, rhos = smooth_knn_dist(knn_d, n_neighbors)
knn_w = compute_graph_weights(np.array(knn_d), sigmas, rhos)
if counts is not None:
knn_w[:, 1, :] *= counts[:, np.newaxis] / np.max(counts)
knn_list = []
for i in range(knn_w.shape[0]):
new, new_w = np.where(knn_w[:, 0, :] == i)
dup = np.isin(new, knn_w[i, 0, :])
for ii, j in enumerate(knn_w[i, 0, :]):
if j not in new[dup]:
continue
jj = np.where(j == new[dup])[0][0]
knn_w[i, 1, ii] = knn_w[i, 1, ii] + knn_w[j.astype(int), 1, jj] - knn_w[i, 1, ii]*knn_w[j.astype(int), 1, jj]
knn_w[j.astype(int), 1, jj] = 0
knn_list.append(np.concatenate(
[knn_w[i, :, :], np.row_stack([new[~dup], knn_w[new[~dup], 1, new_w[~dup]]])], axis=1))
knn_list[-1] = np.concatenate([i*np.ones((1, knn_list[-1].shape[1])), knn_list[-1]], axis=0)
knn_m = np.concatenate(knn_list, axis=1)
return knn_m, sigmas, rhos
def random_nn_trees(X, num_trees):
t = AnnoyIndex(X.shape[1], 'euclidean')
for i in range(X.shape[0]):
t.add_item(i, X[i, :])
t.build(num_trees)
return t
def nearer_neighbours(X, k, num_trees=5, num_iters=0):
r_forest = random_nn_trees(X, num_trees)
knn = [r_forest.get_nns_by_item(i, k, include_distances=True) for i in range(X.shape[0])]
for i in range(X.shape[0]):
knn[i] = (np.array(knn[i][0][1:]), np.array(knn[i][1][1:]))
for _ in range(num_iters):
old_knn = copy.deepcopy(knn)
for i in range(X.shape[0]):
ind, d = old_knn[i]
nn_ind = np.unique([k for j in ind for k in old_knn[j][0]
if (k != i) and (k not in ind)])
ind = np.append(ind, nn_ind)
d = np.append(d, dist(X[[i], :] - X[nn_ind, :]))
keep = np.argsort(d)[:k]
knn[i] = (ind[keep], d[keep])
return knn
def dist(x_y, metric='sqeuclidean'):
d_sq = np.sum(np.square(x_y), axis=1, keepdims=True)
if metric == 'euclidean':
return np.sqrt(d_sq)
return d_sq
# return cdist(x, y, metric=metric)
def binary_search(f, target, lo=0., mid=1., hi=np.inf, n_iter=64):
for _ in range(n_iter):
f_mid = f(mid)
if np.abs(f_mid - target) < TOLERANCE:
break
if f_mid > target:
hi = mid
mid = 0.5 * (lo + hi)
else:
lo = mid
mid = mid*2 if np.isinf(hi) else 0.5 *(lo + hi)
return mid
def smooth_knn_dist(knn, k, bandwidth=1):
target = np.log2(k) * bandwidth
rho = np.zeros(len(knn))
sigmas = np.zeros(len(knn))
means = []
for i, (_, dist) in enumerate(knn):
rho[i] = np.min(dist[dist > 0])
d = dist - rho[i]
psum = lambda sigma: np.sum(np.exp(-d / sigma))
sigmas[i] = binary_search(psum, target)
means.append(np.mean(dist))
if rho[i] == 0:
sigmas[i] = np.max(MIN_DIST_SCALE * means[-1], sigmas[i])
mean_distance = np.mean(means)
rho_0 = rho == 0
if np.any(rho_0):
sigmas[rho_0] = np.max(MIN_DIST_SCALE * mean_distance, sigmas[rho_0])
return sigmas, rho
def compute_graph_weights(knn, sigmas, rhos):
rho_m = rhos[:, np.newaxis]
sig_m = sigmas[:, np.newaxis]
vals = np.exp(- (knn[:, 1, :] - rho_m) / sig_m)
ok = (knn[:, 1, :] - rho_m > 0.0) & (sig_m > 0.0)
vals[~ok] = 1
knn[:, 1, :] = vals
return knn
def find_ab_params(spread, min_dist):
def curve(x, a, b):
return 1.0 / (1.0 + a * x ** (2 * b))
xv = np.linspace(0, spread * 3, 300)
yv = np.zeros(xv.shape)
yv[xv < min_dist] = 1.0
yv[xv >= min_dist] = np.exp(-(xv[xv >= min_dist] - min_dist) / spread)
params, covar = curve_fit(curve, xv, yv)
return params[0], params[1]