def get_weights(self, ctx): weights = nd.dot( self.w_p.data(ctx), nd.dot( (self.w_l.data(ctx) * self.l_mask.data(ctx) + self.l_eye.data(ctx)), ((self.w_u.data(ctx) * self.u_mask.data(ctx)) + nd.diag(self.s_sign.data(ctx) * nd.exp(self.w_s.data(ctx)))))) weights = weights.reshape(0, 0, 1, 1) # expand dims return weights
def forward(self, adj, feat, lambda_max=None): r""" Description ----------- Compute (Dense) Chebyshev Spectral Graph Convolution layer. Parameters ---------- adj : mxnet.NDArray The adjacency matrix of the graph to apply Graph Convolution on, should be of shape :math:`(N, N)`, where a row represents the destination and a column represents the source. feat : mxnet.NDArray The input feature of shape :math:`(N, D_{in})` where :math:`D_{in}` is size of input feature, :math:`N` is the number of nodes. lambda_max : float or None, optional A float value indicates the largest eigenvalue of given graph. Default: None. Returns ------- mxnet.NDArray The output feature of shape :math:`(N, D_{out})` where :math:`D_{out}` is size of output feature. """ A = adj.astype(feat.dtype).as_in_context(feat.context) num_nodes = A.shape[0] in_degree = 1. / nd.clip(A.sum(axis=1), 1, float('inf')).sqrt() D_invsqrt = nd.diag(in_degree) I = nd.eye(num_nodes, ctx=A.context) L = I - nd.dot(D_invsqrt, nd.dot(A, D_invsqrt)) if lambda_max is None: # NOTE(zihao): this only works for directed graph. lambda_max = (nd.linalg.syevd(L)[1]).max() L_hat = 2 * L / lambda_max - I Z = [nd.eye(num_nodes, ctx=A.context)] Zh = self.fc[0](feat) for i in range(1, self._k): if i == 1: Z.append(L_hat) else: Z.append(2 * nd.dot(L_hat, Z[-1]) - Z[-2]) Zh = Zh + nd.dot(Z[i], self.fc[i](feat)) if self.bias is not None: Zh = Zh + self.bias.data(feat.context) return Zh
def cos_mat(vecs): ## dot product divided by the norms xtx = nd.dot(vecs, vecs.T) nmx = nd.sqrt(nd.diag(xtx)).reshape((-1, 1)) cnm = nd.dot(nmx, nmx.T) return xtx / cnm