Convolution with full spectral domain filter

[pinkfloyd06]

Hello @mdeff

Let me thank you for this notebook showing different graph convolution implementation.

https://github.com/mdeff/cnn_graph/blob/master/trials/1_learning_filters.ipynb

l'm wondering if you have an optimized implementation of a convolution in a full spectral domain filter (instead of chebyshev expansion) ?

x ∗ G g = U.T ( diag(w_g)Ux) (link : page3 https://arxiv.org/pdf/1506.05163.pdf)
such that :
x : input
spectral multipliers w_g = ( w_1 ,...,w_N )
U : eigenvectors
U.T : transposed eigenvectors

Here is what l've tried

def graph_convolution(x,U,lambda):
       '''
       graph convolution layer on full spectral domain filter for graph classification

       x : dimension( n,z). where n is the number of nodes and z the number of features per node
      U : eignevectors dim (n,n). where n is the number of nodes
      lambda :  diagonal matrice of eigenvalues dim(n,n). where n is the number of nodes
       '''

      x1=lambda*x
      x2= U*x1
      # Let's say n=32 and z=3 then x2=[32,3]
      # convolution layer input :  32 output 100
      cl1 = nn.Linear(32,100,3) # pytorch version
      x=cl1(x2) # output x is of dim [100,3]
      
     return x

Please correct me.
Thank you,

[mdeff]

cnn_graph/lib/models.py

Lines 387 to 421 in c4d2c75

	class fgcnn2(base_model):
	"""Graph CNN with full weights, i.e. patch has the same size as input."""
	def __init__(self, L, F):
	super().__init__()
	#self.L = L # Graph Laplacian, NFEATURES x NFEATURES
	self.F = F # Number of filters
	_, self.U = graph.fourier(L)
	def _inference(self, x, dropout):
	# x: NSAMPLES x NFEATURES
	with tf.name_scope('gconv1'):
	# Transform to Fourier domain
	U = tf.constant(self.U, dtype=tf.float32)
	xf = tf.matmul(x, U)
	xf = tf.expand_dims(xf, 1) # NSAMPLES x 1 x NFEATURES
	xf = tf.transpose(xf) # NFEATURES x 1 x NSAMPLES
	# Filter
	W = self._weight_variable([NFEATURES, self.F, 1])
	yf = tf.matmul(W, xf) # for each feature
	yf = tf.transpose(yf) # NSAMPLES x NFILTERS x NFEATURES
	yf = tf.reshape(yf, [-1, NFEATURES])
	# Transform back to graph domain
	Ut = tf.transpose(U)
	y = tf.matmul(yf, Ut)
	y = tf.reshape(yf, [-1, self.F, NFEATURES])
	# Bias and non-linearity
	b = self._bias_variable([1, self.F, 1])
	# b = self._bias_variable([1, self.F, NFEATURES])
	y += b # NSAMPLES x NFILTERS x NFEATURES
	y = tf.nn.relu(y)
	with tf.name_scope('fc1'):
	W = self._weight_variable([self.F*NFEATURES, NCLASSES])
	b = self._bias_variable([NCLASSES])
	y = tf.reshape(y, [-1, self.F*NFEATURES])
	y = tf.matmul(y, W) + b
	return y