class_docstr: Maximum independence domain adaptation
  Args:
      n_components (int): Number of components to keep.
      kernel (str): "linear", "rbf", or "poly". Kernel to use for MIDA. Defaults to "linear".
      mu (float): Hyperparameter of the l2 penalty. Defaults to 1.0.
      eta (float): Hyperparameter of the label dependence. Defaults to 1.0.
      augmentation (bool): Whether using covariates as augment features. Defaults to False.
      kernel_params (dict or None): Parameters for the kernel. Defaults to None.
  
  References:
      [1] Yan, K., Kou, L. and Zhang, D., 2018. Learning domain-invariant subspace using domain features and
          independence maximization. IEEE transactions on cybernetics, 48(1), pp.288-299.
docstr: solve MIDA
  
  Args:
      kernel_x: array-like, kernel matrix of input data x, shape (n_samples, n_samples)
      y: array-like. Labels, shape (nl_samples,)
      covariates: array-like. Domain co-variates, shape (n_samples, n_covariates)
  
  Returns:
      self
docstr_tok: ["solve","MIDA","Args",":","kernel_x",":","array-like",",","kernel","matrix","of","input","data","x",",","shape","(","n_samples",",","n_samples",")","y",":","array-like",".","Labels",",","shape","(","nl_samples",",",")","covariates",":","array-like",".","Domain","co-variates",",","shape","(","n_samples",",","n_covariates",")","Returns",":","self"]
code: def _fit(self, kernel_x, y, covariates=None):
      """solve MIDA
  
      Args:
          kernel_x: array-like, kernel matrix of input data x, shape (n_samples, n_samples)
          y: array-like. Labels, shape (nl_samples,)
          covariates: array-like. Domain co-variates, shape (n_samples, n_covariates)
  
      Returns:
          self
      """
      n_samples = kernel_x.shape[0]
      # Identity (unit) matrix
      unit_mat = np.eye(n_samples)
      # Centering matrix
      ctr_mat = unit_mat - 1.0 / n_samples * np.ones(
          (n_samples, n_samples)
      )
  
      kernel_x = self._centerer.fit_transform(kernel_x)
      if isinstance(covariates, np.ndarray):
          kernel_c = np.dot(covariates, covariates.T)
      else:
          kernel_c = np.zeros((n_samples, n_samples))
  
      if y is not None:
          n_labeled = y.shape[0]
          if n_labeled > n_samples:
              raise ValueError(
                  "Number of labels exceeds number of samples"
              )
          y_mat_ = self._label_binarizer.fit_transform(y)
          y_mat = np.zeros((n_samples, y_mat_.shape[1]))
          y_mat[:n_labeled, :] = y_mat_
          ker_y = np.dot(y_mat, y_mat.T)
          obj = multi_dot(
              [
                  kernel_x,
                  self.mu * ctr_mat
                  + self.eta * multi_dot([ctr_mat, ker_y, ctr_mat])
                  - multi_dot([ctr_mat, kernel_c, ctr_mat]),
                  kernel_x.T,
              ]
          )
      else:
          obj = multi_dot(
              [
                  kernel_x,
                  self.mu * ctr_mat
                  - multi_dot([ctr_mat, kernel_c, ctr_mat]),
                  kernel_x.T,
              ]
          )
  
      eig_values, eig_vectors = linalg.eigh(
          obj,
          subset_by_index=[
              n_samples - self.n_components,
              n_samples - 1,
          ],
      )
      idx_sorted = eig_values.argsort()[::-1]
  
      self.eig_values_ = eig_values[idx_sorted]
      self.U = eig_vectors[:, idx_sorted]
      self.U = np.asarray(self.U, dtype=np.float64)
  
      return self
  
imports: import logging
  import warnings
  import numpy
  from numpy.linalg import multi_dot
  from scipy import linalg
  from sklearn.base import BaseEstimator, TransformerMixin
  from sklearn.metrics.pairwise import pairwise_kernels
  from sklearn.preprocessing import KernelCenterer, LabelBinarizer
  from sklearn.utils.validation import check_is_fitted
  from tensorly.base import fold, unfold
  from tensorly.tenalg import multi_mode_dot
label_desc: Use image node_id 4 for calling the MIDA obj's underlying member method code with example usage: obj._fit(kernel_x, y, covariates) and returns: self