Using Weighted Average to Compute the wFM?

[LittleQuteSweetie]

Hi, thanks for sharing the code.
I have a question about the computation of wFM, which is stated to use the recursive estimator in the original paper, but it seems to become a direct weighted average of points (on the manifold) in the following code, is there anything I miss here or is this some kind of simplified way to compute the wFM?

def DCNN(x,d,W_root,mode):
   ''' 
   x is input, with shape batch * sequence_length * n_para * in_channel
   d is the number of skipped, a number
   w is the weights, with shape k * in_channel * out_channel
   mode is "SPD" or "ODF"
   '''
   W = tf.pow(W_root,2)

   batch_size = tf.shape(x)[0]#x.shape[0]
   sequence_length = x.shape[1]
   n_para = x.shape[2]
   k = W.shape[0]
   in_channel = W.shape[1]
   out_channel = W.shape[2]

   padding = (k - 1) * d
   x_pad = tf.pad(x,tf.constant([(0,0),(1,0),(0,0),(0,0)]) * padding , "REFLECT") # for the first element, we need padding
   W = tf.reshape(W,[k*in_channel,out_channel])
   W_sum = tf.reduce_sum(W,0)
   W = tf.div(W,W_sum) # constrain sum(w_k_inchannel) = 1
   if mode =="SPD":
       x_reorder = tf.transpose(x_pad,[0,2,1,3])
       x_reshape = tf.reshape(x_reorder,[batch_size*n_para,1,sequence_length+padding,in_channel])

       W = tf.reshape(W,[1,k,in_channel,out_channel])
       conv1 = tf.nn.atrous_conv2d(x_reshape,W,d,"VALID",name=None)
       conv1 = tf.reshape(conv1,[batch_size,n_para,sequence_length,out_channel])
       conv1 = tf.transpose(conv1,[0,2,1,3])
       return conv1

[zhenxingjian]

Hi,
This is the simplified way to compute the wFM on SPD only.
We tried the recursive version (see https://github.com/zhenxingjian/SPD-SRU/blob/master/matrixcell.py to have an idea about the recursive version.) of wFM on this SPD manifold and the experiment shows those two share the similar results. Thus, we only include this simplified closed-version to compute wFM.

One important notice is that for the wFM, the weights should be:

1. Non-negative (here we use $w^2\geq 0$)
2. Sum equals to $1$.

[zhenxingjian]

Feel free to reopen this Issue if you have any question.
I hope that this solves your concern.

Thanks for being interested in our work.