To use the following operators, copy the seg_op.* files in mxnet_op to incubator-mxnet/src/operator/contrib.

• seg_sum
• seg_broadcast_add
• seg_broadcast_mul
• seg_broadcast_to
• seg_softmax
• seg_take_k_corr
• seg_weighted_pool
• seg_pool

After copying and recompiling MXNet, test the operators by running

python mxnet_op/test_seg_ops.py

Reduce the last dimension of the input based on the given segment indicators.

Inputs:

• data: Shape (batch_num, nnz)
• indptr: Shape (seg_num + 1,)

Outputs:

• ret: Shape (batch_num, seg_num)

for k = 0 to batch_num - 1
    for i = 0 to seg_num - 1
        ret[k, i] = reduce(data[k, indptr[i]], ..., data[k, indptr[i + 1] - 1])

Examples::

  out = seg_sum(data=data, indptr=indptr)

Broadcast rhs according to the segment indicators and add to lhs to get the result.

Inputs:

• lhs: Shape (batch_num, nnz)
• rhs: Shape (batch_num, seg_num)
• indptr: Shape (seg_num + 1,)

Outputs:

• ret: Shape (batch_num, nnz)

Examples::

ret = seg_broadcast_add(lhs=lhs, rhs=rhs, indptr=indptr)

Broadcast rhs according to the segment indicators and mul to lhs to get the result.

Inputs:

• lhs: Shape (batch_num, nnz)
• rhs: Shape (batch_num, seg_num)
• indptr: Shape (seg_num + 1,)

Outputs:

• ret: Shape (batch_num, nnz)

Examples::

ret = seg_broadcast_mul(lhs=lhs, rhs=rhs, indptr=indptr)

Broadcast rhs according to the segment indicators and add to lhs to get the result.

Inputs:

• data: Shape (batch_num, seg_num)
• indptr: Shape (seg_num + 1,)
• int nnz

Outputs:

• ret: Shape (batch_num, nnz)

Examples::

ret = seg_broadcast_to(data=data, indptr=indptr, nnz=nnz)

Calculate the softmax of the the input based on the given segment indicators.

Inputs:

• data: Shape (batch_num, nnz)
• indptr: Shape (seg_num + 1,)

Outputs:

• ret: Shape (batch_num, nnz)

for k = 0 to batch_num - 1
    for i = 0 to seg_num - 1
        ret[k, indptr[i]:indptr[i+1]] = softmax(data[k, indptr[i]:indptr[i+1]])

Examples::

out = seg_softmax(data=data, indptr=indptr)

For all the nodes, computes the inner product between the node and it's neighborhoods and add to dst. We assume the node_ids are 0, 1, 2, ..., node_num - 1

Inputs:

• embed1: Shape (K, node_num, feat_dim)
• embed2: Shape (K, neighbor_node_num, feat_dim)
• neighbor_ids: Shape (nnz, )
• neighbor_indptr: Shape(node_num + 1, )

Outputs:

• dst: Shape (K, nnz)

for k = 0 to K-1
    for i = 0  to node_num - 1
        for j = ind_ptr[i] to ind_ptr[i+1] - 1
            neighbor_id = neighbor_ids[j]
            dst[k, j] += InnerProduct(embed1[k, i], embed2[k, neighbor_id])

Examples::

out = seg_take_k_corr(embed1=embed1, embed2=embed2, neighbor_ids=neighbor_ids, neighbor_indptr=neighbor_indptr)

Compute weighted average of values in the segments

Inputs:

• data: Shape (batch_size, total_ind_num, feat_dim)
• weights: Shape (batch_size, nnz)
• indices: Shape (nnz, )
• indptr: Shape (seg_num + 1,)

Outputs:

• dst: Shape (batch_size, seg_num, feat_dim)

for k = 0 to K-1
    for i = 0  to node_num - 1
        for j = ind_ptr[i] to ind_ptr[i+1] - 1
            dst[k, i, :] += weights[k, j] * data[k, neighbor_ids[j], :]

Examples::

out = seg_weighted_pool(data=data, weights=weights, indices=indices, indptr=indptr)

Pooling of the values in the segments

Inputs:

• data : Shape (batch_size, total_ind_num, feat_dim)
• indices : Shape (nnz,)
• indptr : Shape (seg_num + 1,)
• pool_type : 'avg' or 'sum' or 'max'

Outputs:

• dst : Shape (batch_size, seg_num, feat_dim)

Examples::

out = seg_pool(data=data,
               indices=indices,
               indptr=indptr,
               pool_type='avg')