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# Copyright (c) OpenMMLab. All rights reserved.
import numpy as np
def normalize_adjacent_matrix(A):
"""Normalize adjacent matrix for GCN. This code was partially adapted from
https://github.com/GXYM/DRRG licensed under the MIT license.
Args:
A (ndarray): The adjacent matrix.
returns:
G (ndarray): The normalized adjacent matrix.
"""
assert A.ndim == 2
assert A.shape[0] == A.shape[1]
A = A + np.eye(A.shape[0])
d = np.sum(A, axis=0)
d = np.clip(d, 0, None)
d_inv = np.power(d, -0.5).flatten()
d_inv[np.isinf(d_inv)] = 0.0
d_inv = np.diag(d_inv)
G = A.dot(d_inv).transpose().dot(d_inv)
return G
def euclidean_distance_matrix(A, B):
"""Calculate the Euclidean distance matrix.
Args:
A (ndarray): The point sequence.
B (ndarray): The point sequence with the same dimensions as A.
returns:
D (ndarray): The Euclidean distance matrix.
"""
assert A.ndim == 2
assert B.ndim == 2
assert A.shape[1] == B.shape[1]
m = A.shape[0]
n = B.shape[0]
A_dots = (A * A).sum(axis=1).reshape((m, 1)) * np.ones(shape=(1, n))
B_dots = (B * B).sum(axis=1) * np.ones(shape=(m, 1))
D_squared = A_dots + B_dots - 2 * A.dot(B.T)
zero_mask = np.less(D_squared, 0.0)
D_squared[zero_mask] = 0.0
D = np.sqrt(D_squared)
return D
def feature_embedding(input_feats, out_feat_len):
"""Embed features. This code was partially adapted from
https://github.com/GXYM/DRRG licensed under the MIT license.
Args:
input_feats (ndarray): The input features of shape (N, d), where N is
the number of nodes in graph, d is the input feature vector length.
out_feat_len (int): The length of output feature vector.
Returns:
embedded_feats (ndarray): The embedded features.
"""
assert input_feats.ndim == 2
assert isinstance(out_feat_len, int)
assert out_feat_len >= input_feats.shape[1]
num_nodes = input_feats.shape[0]
feat_dim = input_feats.shape[1]
feat_repeat_times = out_feat_len // feat_dim
residue_dim = out_feat_len % feat_dim
if residue_dim > 0:
embed_wave = np.array([
np.power(1000, 2.0 * (j // 2) / feat_repeat_times + 1)
for j in range(feat_repeat_times + 1)
]).reshape((feat_repeat_times + 1, 1, 1))
repeat_feats = np.repeat(
np.expand_dims(input_feats, axis=0), feat_repeat_times, axis=0)
residue_feats = np.hstack([
input_feats[:, 0:residue_dim],
np.zeros((num_nodes, feat_dim - residue_dim))
])
residue_feats = np.expand_dims(residue_feats, axis=0)
repeat_feats = np.concatenate([repeat_feats, residue_feats], axis=0)
embedded_feats = repeat_feats / embed_wave
embedded_feats[:, 0::2] = np.sin(embedded_feats[:, 0::2])
embedded_feats[:, 1::2] = np.cos(embedded_feats[:, 1::2])
embedded_feats = np.transpose(embedded_feats, (1, 0, 2)).reshape(
(num_nodes, -1))[:, 0:out_feat_len]
else:
embed_wave = np.array([
np.power(1000, 2.0 * (j // 2) / feat_repeat_times)
for j in range(feat_repeat_times)
]).reshape((feat_repeat_times, 1, 1))
repeat_feats = np.repeat(
np.expand_dims(input_feats, axis=0), feat_repeat_times, axis=0)
embedded_feats = repeat_feats / embed_wave
embedded_feats[:, 0::2] = np.sin(embedded_feats[:, 0::2])
embedded_feats[:, 1::2] = np.cos(embedded_feats[:, 1::2])
embedded_feats = np.transpose(embedded_feats, (1, 0, 2)).reshape(
(num_nodes, -1)).astype(np.float32)
return embedded_feats
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