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# Spline-Based Convolution Operator of SplineCNN
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This is a PyTorch implementation of the spline-based convolution operator of SplineCNN, as described in our paper:
Matthias Fey, Jan Eric Lenssen, Frank Weichert, Heinrich Müller: [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://arxiv.org/abs/1711.08920) (CVPR 2018)
The operator works on all floating point data types and is implemented both for CPU and GPU.
## Installation
### Binaries
We provide pip wheels for all major OS/PyTorch/CUDA combinations, see [here](https://pytorch-geometric.com/whl).
To install the binaries for PyTorch 1.4.0, simply run
```
pip install torch-spline-conv==latest+${CUDA} -f https://pytorch-geometric.com/whl/torch-1.4.0.html
```
where `${CUDA}` should be replaced by either `cpu`, `cu92`, `cu100` or `cu101` depending on your PyTorch installation.
| | `cpu` | `cu92` | `cu100` | `cu101` |
|-------------|-------|--------|---------|---------|
| **Linux** | ✅ | ✅ | ✅ | ✅ |
| **Windows** | ✅ | ❌ | ❌ | ✅ |
| **macOS** | ✅ | | | |
### From source
Ensure that at least PyTorch 1.4.0 is installed and verify that `cuda/bin` and `cuda/include` are in your `$PATH` and `$CPATH` respectively, *e.g.*:
```
$ python -c "import torch; print(torch.__version__)"
>>> 1.4.0
$ echo $PATH
>>> /usr/local/cuda/bin:...
$ echo $CPATH
>>> /usr/local/cuda/include:...
```
Then run:
```
pip install torch-spline-conv
```
When running in a docker container without NVIDIA driver, PyTorch needs to evaluate the compute capabilities and may fail.
In this case, ensure that the compute capabilities are set via `TORCH_CUDA_ARCH_LIST`, *e.g.*:
```
export TORCH_CUDA_ARCH_LIST = "6.0 6.1 7.2+PTX 7.5+PTX"
```
## Usage
```python
from torch_spline_conv import spline_conv
out = spline_conv(x,
edge_index,
pseudo,
weight,
kernel_size,
is_open_spline,
degree=1,
norm=True,
root_weight=None,
bias=None)
```
Applies the spline-based convolution operator
over several node features of an input graph.
The kernel function is defined over the weighted B-spline tensor product basis, as shown below for different B-spline degrees.
### Parameters
* **x** *(Tensor)* - Input node features of shape `(number_of_nodes x in_channels)`.
* **edge_index** *(LongTensor)* - Graph edges, given by source and target indices, of shape `(2 x number_of_edges)`.
* **pseudo** *(Tensor)* - Edge attributes, ie. pseudo coordinates, of shape `(number_of_edges x number_of_edge_attributes)` in the fixed interval [0, 1].
* **weight** *(Tensor)* - Trainable weight parameters of shape `(kernel_size x in_channels x out_channels)`.
* **kernel_size** *(LongTensor)* - Number of trainable weight parameters in each edge dimension.
* **is_open_spline** *(ByteTensor)* - Whether to use open or closed B-spline bases for each dimension.
* **degree** *(int, optional)* - B-spline basis degree. (default: `1`)
* **norm** *(bool, optional)*: Whether to normalize output by node degree. (default: `True`)
* **root_weight** *(Tensor, optional)* - Additional shared trainable parameters for each feature of the root node of shape `(in_channels x out_channels)`. (default: `None`)
* **bias** *(Tensor, optional)* - Optional bias of shape `(out_channels)`. (default: `None`)
### Returns
* **out** *(Tensor)* - Out node features of shape `(number_of_nodes x out_channels)`.
### Example
```python
import torch
from torch_spline_conv import spline_conv
x = torch.rand((4, 2), dtype=torch.float) # 4 nodes with 2 features each
edge_index = torch.tensor([[0, 1, 1, 2, 2, 3], [1, 0, 2, 1, 3, 2]]) # 6 edges
pseudo = torch.rand((6, 2), dtype=torch.float) # two-dimensional edge attributes
weight = torch.rand((25, 2, 4), dtype=torch.float) # 25 parameters for in_channels x out_channels
kernel_size = torch.tensor([5, 5]) # 5 parameters in each edge dimension
is_open_spline = torch.tensor([1, 1], dtype=torch.uint8) # only use open B-splines
degree = 1 # B-spline degree of 1
norm = True # Normalize output by node degree.
root_weight = torch.rand((2, 4), dtype=torch.float) # separately weight root nodes
bias = None # do not apply an additional bias
out = spline_conv(x, edge_index, pseudo, weight, kernel_size,
is_open_spline, degree, norm, root_weight, bias)
print(out.size())
torch.Size([4, 4]) # 4 nodes with 4 features each
```
## Cite
Please cite our paper if you use this code in your own work:
```
@inproceedings{Fey/etal/2018,
title={{SplineCNN}: Fast Geometric Deep Learning with Continuous {B}-Spline Kernels},
author={Fey, Matthias and Lenssen, Jan Eric and Weichert, Frank and M{\"u}ller, Heinrich},
booktitle={IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
year={2018},
}
```
## Running tests
```
python setup.py test
```