pyagc.clusters.MinCutClusterHead

class MinCutClusterHead(n_clusters: int, n_features: int, temperature: float = 1.0)

Bases: BaseClusterHead

MinCut Clustering Head proposed in “Spectral Clustering in Graph Neural Networks for Graph Pooling” (Bianchi et al., ICML 2019).

This layer learns a soft cluster assignment matrix \(\mathbf{S}\) by projecting node embeddings \(\mathbf{Z}\) into \(K\) clusters. It jointly optimizes two objectives:

(1) MinCut loss:

\[\mathcal{L}_{\text{mincut}} = - \frac{\mathrm{Tr}(\mathbf{S}^\top \mathbf{A} \mathbf{S})} {\mathrm{Tr}(\mathbf{S}^\top \mathbf{D} \mathbf{S})}\]

where \(\mathbf{D}\) is the degree matrix.

(2) Orthogonality loss:

\[\mathcal{L}_{\text{ortho}} = \left\| \frac{\mathbf{S}^\top \mathbf{S}}{\|\mathbf{S}^\top \mathbf{S}\|_F} - \frac{\mathbf{I}_K}{\sqrt{K}} \right\|_F\]

which encourages near-orthogonal cluster assignments.

Parameters:

• n_clusters (int) – Number of clusters \(K\).

• n_features (int) – Feature dimension of node embeddings \(F\).

• temperature (float, optional) – Softmax temperature. (default: 1.0)

__init__(n_clusters: int, n_features: int, temperature: float = 1.0)

Initialize internal Module state, shared by both nn.Module and ScriptModule.

Methods

__init__(n_clusters, n_features[, temperature])	Initialize internal Module state, shared by both nn.Module and ScriptModule.
add_module(name, module)	Add a child module to the current module.
apply(fn)	Apply fn recursively to every submodule (as returned by .children()) as well as self.
bfloat16()	Casts all floating point parameters and buffers to bfloat16 datatype.
buffers([recurse])	Return an iterator over module buffers.
children()	Return an iterator over immediate children modules.
cluster(z[, soft])	Predict cluster assignments.
compile(*args, **kwargs)	Compile this Module's forward using torch.compile().
cpu()	Move all model parameters and buffers to the CPU.
cuda([device])	Move all model parameters and buffers to the GPU.
double()	Casts all floating point parameters and buffers to double datatype.
eval()	Set the module in evaluation mode.
extra_repr()	Return the extra representation of the module.
float()	Casts all floating point parameters and buffers to float datatype.
forward(z, edge_index)	Compute MinCut and Orthogonality losses given node embeddings and graph structure.
get_buffer(target)	Return the buffer given by target if it exists, otherwise throw an error.
get_extra_state()	Return any extra state to include in the module's state_dict.
get_parameter(target)	Return the parameter given by target if it exists, otherwise throw an error.
get_submodule(target)	Return the submodule given by target if it exists, otherwise throw an error.
half()	Casts all floating point parameters and buffers to half datatype.
ipu([device])	Move all model parameters and buffers to the IPU.
load_state_dict(state_dict[, strict, assign])	Copy parameters and buffers from state_dict into this module and its descendants.
modules()	Return an iterator over all modules in the network.
mtia([device])	Move all model parameters and buffers to the MTIA.
named_buffers([prefix, recurse, ...])	Return an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.
named_children()	Return an iterator over immediate children modules, yielding both the name of the module as well as the module itself.
named_modules([memo, prefix, remove_duplicate])	Return an iterator over all modules in the network, yielding both the name of the module as well as the module itself.
named_parameters([prefix, recurse, ...])	Return an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.
parameters([recurse])	Return an iterator over module parameters.
register_backward_hook(hook)	Register a backward hook on the module.
register_buffer(name, tensor[, persistent])	Add a buffer to the module.
register_forward_hook(hook, *[, prepend, ...])	Register a forward hook on the module.
register_forward_pre_hook(hook, *[, ...])	Register a forward pre-hook on the module.
register_full_backward_hook(hook[, prepend])	Register a backward hook on the module.
register_full_backward_pre_hook(hook[, prepend])	Register a backward pre-hook on the module.
register_load_state_dict_post_hook(hook)	Register a post-hook to be run after module's load_state_dict() is called.
register_load_state_dict_pre_hook(hook)	Register a pre-hook to be run before module's load_state_dict() is called.
register_module(name, module)	Alias for add_module().
register_parameter(name, param)	Add a parameter to the module.
register_state_dict_post_hook(hook)	Register a post-hook for the state_dict() method.
register_state_dict_pre_hook(hook)	Register a pre-hook for the state_dict() method.
requires_grad_([requires_grad])	Change if autograd should record operations on parameters in this module.
reset_cluster_centers([cluster_centers])	Manually sets the cluster centers.
set_extra_state(state)	Set extra state contained in the loaded state_dict.
set_submodule(target, module[, strict])	Set the submodule given by target if it exists, otherwise throw an error.
share_memory()	See torch.Tensor.share_memory_().
state_dict(*args[, destination, prefix, ...])	Return a dictionary containing references to the whole state of the module.
to(*args, **kwargs)	Move and/or cast the parameters and buffers.
to_empty(*, device[, recurse])	Move the parameters and buffers to the specified device without copying storage.
train([mode])	Set the module in training mode.
type(dst_type)	Casts all parameters and buffers to dst_type.
xpu([device])	Move all model parameters and buffers to the XPU.
zero_grad([set_to_none])	Reset gradients of all model parameters.

Attributes

T_destination	alias of TypeVar('T_destination', bound=dict[str, Any])
call_super_init
dump_patches
predict	Alias for cluster().

reset_cluster_centers(cluster_centers: Optional[Tensor] = None) → None

Manually sets the cluster centers.

Parameters:

cluster_centers (torch.Tensor, optional) – Tensor of shape (n_clusters, n_features) to initialize the cluster centers. If None, use Xavier uniform initialization.

Return type:

None

forward(z: Tensor, edge_index: Tensor) → Tuple[Tensor, Tensor]

Compute MinCut and Orthogonality losses given node embeddings and graph structure.

Parameters:

• z (torch.Tensor) – Node embeddings \((N, F)\).

• edge_index (torch.Tensor) – Edge indices \((2, E)\).

Returns:

mincut_loss and ortho_loss

Return type:

Tuple[torch.Tensor, torch.Tensor]

cluster(z: Tensor, soft: bool = False) → Tensor

Predict cluster assignments.

Parameters:

• z (torch.Tensor) – Node embeddings of shape (N, F).

• soft (bool, optional) – If True, return soft assignment probabilities.

Returns:

Hard cluster indices or soft assignment matrix.

Return type:

torch.Tensor