README.md

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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

Ensure that at least PyTorch 0.4.1 is installed and verify that `cuda/bin` and `cuda/install` are in your `$PATH` and `$CPATH` respectively, *e.g.*:

```
$ python -c "import torch; print(torch.__version__)"
>>> 0.4.1

$ echo $PATH
>>> /usr/local/cuda/bin:...

$ echo $CPATH
>>> /usr/local/cuda/install:...
```

Then run:

```
pip install torch-spline-conv
```

If you are running into any installation problems, please create an [issue](https://github.com/rusty1s/pytorch_spline_conv/issues).

## Usage

```python
from torch_spline_conv import SplineConv

out = SplineConv.apply(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
<p align="center">
  <img width="50%" src="https://user-images.githubusercontent.com/6945922/38684093-36d9c52e-3e6f-11e8-9021-db054223c6b9.png" />
</p>
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.

<p align="center">
  <img width="45%" src="https://user-images.githubusercontent.com/6945922/38685443-3a2a0c68-3e72-11e8-8e13-9ce9ad8fe43e.png" />
  <img width="45%" src="https://user-images.githubusercontent.com/6945922/38685459-42b2bcae-3e72-11e8-88cc-4b61e41dbd93.png" />
</p>

### 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 SplineConv

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 = SplineConv.apply(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
```