docstr: Computes the centered kernel matrix.
  
  Parameters
  ----------
  x
      The reference data.
  
  Returns
  -------
  The centered kernel matrix.
docstr_tok: ["Computes","the","centered","kernel","matrix",".","Parameters","--","--","--","--","--","x","The","reference","data",".","Returns","--","--","--","-","The","centered","kernel","matrix","."]
code: def compute_kernel_mat(self, x: torch.Tensor) -> torch.Tensor:
      """Computes the centered kernel matrix.
  
      Parameters
      ----------
      x
          The reference data.
  
      Returns
      -------
      The centered kernel matrix.
      """
      n = len(x)
      k = self.kernel(x, x)
      self.k_col_sums = k.sum(0)
      k_row_sums = k.sum(1)
      self.k_sum = k_row_sums.sum()
      k_cen = (
          k
          - self.k_col_sums[None, :] / n
          - k_row_sums[:, None] / n
          + self.k_sum / (n**2)
      )
      return k_cen
  
imports: from typing import Optional, Callable
  import torch
  from alibi_detect.od.pytorch.base import TorchOutlierDetector
  from alibi_detect.utils._types import TorchDeviceType
label_desc: Use image node_id 4 for calling the KernelPCATorch obj's underlying member method code with example usage: obj.compute_kernel_mat(x) and returns: k_cen