Kernel Linear

linear

CLASS	DESCRIPTION
LinearKernel	Linear kernel for computing Gram matrices from feature matrices.

FUNCTION	DESCRIPTION
linear_kernel	Compute linear kernel matrix from feature matrix (functional interface).

Classes

LinearKernel(dtype: torch.dtype = torch.float32)

Bases: Kernel

Linear kernel for computing Gram matrices from feature matrices.

Computes the linear kernel (dot product kernel) as \(K = X X^\top\). Unlike distance-based kernels, this operates directly on feature matrices.

PARAMETER	DESCRIPTION
dtype	Data type for internal tensor computations. TYPE: torch.dtype, optional, by default torch.float32 DEFAULT: float32

METHOD	DESCRIPTION
get_kernel_params	Return current kernel parameters.
forward_step	Compute linear kernel matrix (Gram matrix).

Source code in spectre/kernel/linear.py

def __init__(self, dtype: torch.dtype = torch.float32) -> None:
    super().__init__(
        learnable=False, learnable_log=False, normalization=None, dtype=dtype
    )

Functions

get_kernel_params() -> dict[str, torch.Tensor]

Return current kernel parameters.

The linear kernel has no parameters.

RETURNS	DESCRIPTION
dict[str, Tensor]	Empty dictionary (no parameters).

Source code in spectre/kernel/linear.py

def get_kernel_params(self) -> dict[str, torch.Tensor]:
    """
    Return current kernel parameters.

    The linear kernel has no parameters.

    Returns
    -------
    dict[str, torch.Tensor]
        Empty dictionary (no parameters).
    """
    return {}

forward_step(X: torch.Tensor, weights: torch.Tensor | None = None, **kwargs) -> torch.Tensor

Compute linear kernel matrix (Gram matrix).

PARAMETER	DESCRIPTION
X	Feature matrix, shape (n_samples, n_features). TYPE: Tensor
weights	Sample weights (not used in this implementation). TYPE: torch.Tensor | None, optional, by default None DEFAULT: None
**kwargs	Additional keyword arguments passed to the kernel. TYPE: dict DEFAULT: {}

RETURNS	DESCRIPTION
Tensor	Linear kernel matrix, shape (n_samples, n_samples).

Source code in spectre/kernel/linear.py

def forward_step(
    self,
    X: torch.Tensor,
    weights: torch.Tensor | None = None,
    **kwargs,
) -> torch.Tensor:  # ty: ignore
    """
    Compute linear kernel matrix (Gram matrix).

    Parameters
    ----------
    X : torch.Tensor
        Feature matrix, shape (n_samples, n_features).

    weights : torch.Tensor | None, optional, by default None
        Sample weights (not used in this implementation).

    **kwargs : dict
        Additional keyword arguments passed to the kernel.

    Returns
    -------
    torch.Tensor
        Linear kernel matrix, shape (n_samples, n_samples).
    """
    return linear_kernel(X)

Functions

linear_kernel(X: torch.Tensor) -> torch.Tensor

Compute linear kernel matrix from feature matrix (functional interface).

The linear kernel is simply the Gram matrix.

PARAMETER	DESCRIPTION
X	Feature matrix, shape (n_samples, n_features). TYPE: Tensor

RETURNS	DESCRIPTION
Tensor	Linear kernel matrix, shape (n_samples, n_samples).

Source code in spectre/kernel/linear.py

def linear_kernel(X: torch.Tensor) -> torch.Tensor:
    """
    Compute linear kernel matrix from feature matrix (functional interface).

    The linear kernel is simply the Gram matrix.

    Parameters
    ----------
    X : torch.Tensor
        Feature matrix, shape (n_samples, n_features).

    Returns
    -------
    torch.Tensor
        Linear kernel matrix, shape (n_samples, n_samples).
    """
    check_2d(X)

    return X @ X.T