topobench.transforms.data_manipulations.hkdiag_encodings module

Heat Kernel Diagonal Structural Encoding (HKdiagSE) Transform.

class BaseTransform

Bases: ABC

An abstract base class for writing transforms.

Transforms are a general way to modify and customize Data or HeteroData objects, either by implicitly passing them as an argument to a Dataset, or by applying them explicitly to individual Data or HeteroData objects:

import torch_geometric.transforms as T
from torch_geometric.datasets import TUDataset

transform = T.Compose([T.ToUndirected(), T.AddSelfLoops()])

dataset = TUDataset(path, name='MUTAG', transform=transform)
data = dataset[0]  # Implicitly transform data on every access.

data = TUDataset(path, name='MUTAG')[0]
data = transform(data)  # Explicitly transform data.

abstractmethod forward(data)

class Data(x=None, edge_index=None, edge_attr=None, y=None, pos=None, time=None, **kwargs)

Bases: BaseData, FeatureStore, GraphStore

A data object describing a homogeneous graph. The data object can hold node-level, link-level and graph-level attributes. In general, Data tries to mimic the behavior of a regular :python:`Python` dictionary. In addition, it provides useful functionality for analyzing graph structures, and provides basic PyTorch tensor functionalities. See here for the accompanying tutorial.

from torch_geometric.data import Data

data = Data(x=x, edge_index=edge_index, ...)

# Add additional arguments to `data`:
data.train_idx = torch.tensor([...], dtype=torch.long)
data.test_mask = torch.tensor([...], dtype=torch.bool)

# Analyzing the graph structure:
data.num_nodes
>>> 23

data.is_directed()
>>> False

# PyTorch tensor functionality:
data = data.pin_memory()
data = data.to('cuda:0', non_blocking=True)

Parameters:

• x (torch.Tensor, optional) – Node feature matrix with shape [num_nodes, num_node_features]. (default: None)

• edge_index (LongTensor, optional) – Graph connectivity in COO format with shape [2, num_edges]. (default: None)

• edge_attr (torch.Tensor, optional) – Edge feature matrix with shape [num_edges, num_edge_features]. (default: None)

• y (torch.Tensor, optional) – Graph-level or node-level ground-truth labels with arbitrary shape. (default: None)

• pos (torch.Tensor, optional) – Node position matrix with shape [num_nodes, num_dimensions]. (default: None)

• time (torch.Tensor, optional) – The timestamps for each event with shape [num_edges] or [num_nodes]. (default: None)

• **kwargs (optional) – Additional attributes.

classmethod from_dict(mapping)

Creates a Data object from a dictionary.

__init__(x=None, edge_index=None, edge_attr=None, y=None, pos=None, time=None, **kwargs)

connected_components()

Extracts connected components of the graph using a union-find algorithm. The components are returned as a list of Data objects, where each object represents a connected component of the graph.

data = Data()
data.x = torch.tensor([[1.0], [2.0], [3.0], [4.0]])
data.y = torch.tensor([[1.1], [2.1], [3.1], [4.1]])
data.edge_index = torch.tensor(
    [[0, 1, 2, 3], [1, 0, 3, 2]], dtype=torch.long
)

components = data.connected_components()
print(len(components))
>>> 2

print(components[0].x)
>>> Data(x=[2, 1], y=[2, 1], edge_index=[2, 2])

Returns:

A list of disconnected components.

Return type:

List[Data]

debug()

edge_subgraph(subset)

Returns the induced subgraph given by the edge indices subset. Will currently preserve all the nodes in the graph, even if they are isolated after subgraph computation.

Parameters:

subset (LongTensor or BoolTensor) – The edges to keep.

get_all_edge_attrs()

Returns all registered edge attributes.

get_all_tensor_attrs()

Obtains all feature attributes stored in Data.

is_edge_attr(key)

Returns True if the object at key key denotes an edge-level tensor attribute.

is_node_attr(key)

Returns True if the object at key key denotes a node-level tensor attribute.

stores_as(data)

subgraph(subset)

Returns the induced subgraph given by the node indices subset.

Parameters:

subset (LongTensor or BoolTensor) – The nodes to keep.

to_dict()

Returns a dictionary of stored key/value pairs.

to_heterogeneous(node_type=None, edge_type=None, node_type_names=None, edge_type_names=None)

Converts a Data object to a heterogeneous HeteroData object. For this, node and edge attributes are splitted according to the node-level and edge-level vectors node_type and edge_type, respectively. node_type_names and edge_type_names can be used to give meaningful node and edge type names, respectively. That is, the node_type 0 is given by node_type_names[0]. If the Data object was constructed via to_homogeneous(), the object can be reconstructed without any need to pass in additional arguments.

Parameters:

• node_type (torch.Tensor, optional) – A node-level vector denoting the type of each node. (default: None)

• edge_type (torch.Tensor, optional) – An edge-level vector denoting the type of each edge. (default: None)

• node_type_names (List[str], optional) – The names of node types. (default: None)

• edge_type_names (List[Tuple[str, str, str]], optional) – The names of edge types. (default: None)

to_namedtuple()

Returns a NamedTuple of stored key/value pairs.

update(data)

Updates the data object with the elements from another data object. Added elements will override existing ones (in case of duplicates).

validate(raise_on_error=True)

Validates the correctness of the data.

property batch: Tensor | None

!! processed by numpydoc !!

property edge_attr: Tensor | None

!! processed by numpydoc !!

property edge_index: Tensor | None

!! processed by numpydoc !!

property edge_stores: List[EdgeStorage]

!! processed by numpydoc !!

property edge_weight: Tensor | None

!! processed by numpydoc !!

property face: Tensor | None

!! processed by numpydoc !!

property node_stores: List[NodeStorage]

!! processed by numpydoc !!

property num_edge_features: int

Returns the number of features per edge in the graph.

property num_edge_types: int

Returns the number of edge types in the graph.

property num_faces: int | None

Returns the number of faces in the mesh.

property num_features: int

Returns the number of features per node in the graph. Alias for num_node_features.

property num_node_features: int

Returns the number of features per node in the graph.

property num_node_types: int

Returns the number of node types in the graph.

property num_nodes: int | None

Returns the number of nodes in the graph.

Note

The number of nodes in the data object is automatically inferred in case node-level attributes are present, e.g., data.x. In some cases, however, a graph may only be given without any node-level attributes. :pyg:`PyG` then guesses the number of nodes according to edge_index.max().item() + 1. However, in case there exists isolated nodes, this number does not have to be correct which can result in unexpected behavior. Thus, we recommend to set the number of nodes in your data object explicitly via data.num_nodes = .... You will be given a warning that requests you to do so.

property pos: Tensor | None

!! processed by numpydoc !!

property stores: List[BaseStorage]

!! processed by numpydoc !!

property time: Tensor | None

!! processed by numpydoc !!

property x: Tensor | None

!! processed by numpydoc !!

property y: Tensor | int | float | None

!! processed by numpydoc !!

class HKdiagSE(kernel_param_HKdiagSE, space_dim=0, include_eigenvalues=False, include_first=False, concat_to_x=True, method='fast', debug=False, **kwargs)

Bases: BaseTransform

Heat Kernel Diagonal Structural Encoding (HKdiagSE) transform.

Parameters:

kernel_param_HKdiagSEtuple of int

Tuple specifying the start and end diffusion times for the heat kernel.

space_dimint, optional

Estimated dimensionality of the space. Used to correct the diffusion diagonal by a factor t^(space_dim/2). Default is 0 (no correction).

include_eigenvaluesbool, optional

If True, concatenates eigenvalues alongside eigenvectors. Default is False.

include_firstbool, optional

If False, removes eigenvectors corresponding to (near-)zero eigenvalues. Default is False.

concat_to_xbool, optional

If True, concatenates the encodings with existing node features. Default is True.

methodstr, optional

Computation method: “exact” (CPU NumPy + loop) or “fast” (GPU PyTorch + vectorized). Default is “fast”.

debugbool, optional

If True, runs both methods and prints error/timing metrics. Default is False.

**kwargsdict

Additional arguments (not used).

__init__(kernel_param_HKdiagSE, space_dim=0, include_eigenvalues=False, include_first=False, concat_to_x=True, method='fast', debug=False, **kwargs)

forward(data)

Compute the Heat Kernel Diagonal Structural Encodings for the input graph.

Parameters:

datatorch_geometric.data.Data

Input graph data object.

Returns:

torch_geometric.data.Data

Graph data object with HKdiagSE positional encodings added.

get_laplacian(edge_index, edge_weight=None, normalization=None, dtype=None, num_nodes=None)

Computes the graph Laplacian of the graph given by edge_index and optional edge_weight.

Parameters:

• edge_index (LongTensor) – The edge indices.

• edge_weight (Tensor, optional) – One-dimensional edge weights. (default: None)

• normalization (str, optional) –

  The normalization scheme for the graph Laplacian (default: None):

  1. None: No normalization \(\mathbf{L} = \mathbf{D} - \mathbf{A}\)

  2. "sym": Symmetric normalization \(\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1/2} \mathbf{A} \mathbf{D}^{-1/2}\)

  3. "rw": Random-walk normalization \(\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1} \mathbf{A}\)

• dtype (torch.dtype, optional) – The desired data type of returned tensor in case edge_weight=None. (default: None)

• num_nodes (int, optional) – The number of nodes, i.e. max_val + 1 of edge_index. (default: None)

Examples

>>> edge_index = torch.tensor([[0, 1, 1, 2],
...                            [1, 0, 2, 1]])
>>> edge_weight = torch.tensor([1., 2., 2., 4.])

>>> # No normalization
>>> lap = get_laplacian(edge_index, edge_weight)

>>> # Symmetric normalization
>>> lap_sym = get_laplacian(edge_index, edge_weight,
                            normalization='sym')

>>> # Random-walk normalization
>>> lap_rw = get_laplacian(edge_index, edge_weight, normalization='rw')

remove_self_loops(edge_index, edge_attr=None)

Removes every self-loop in the graph given by edge_index, so that \((i,i) \not\in \mathcal{E}\) for every \(i \in \mathcal{V}\).

Parameters:

• edge_index (LongTensor) – The edge indices.

• edge_attr (Tensor, optional) – Edge weights or multi-dimensional edge features. (default: None)

Return type:

(LongTensor, Tensor)

Example

>>> edge_index = torch.tensor([[0, 1, 0],
...                            [1, 0, 0]])
>>> edge_attr = [[1, 2], [3, 4], [5, 6]]
>>> edge_attr = torch.tensor(edge_attr)
>>> remove_self_loops(edge_index, edge_attr)
(tensor([[0, 1],
        [1, 0]]),
tensor([[1, 2],
        [3, 4]]))