code: def feature_space_linear_cka(features_x, features_y, debiased=False):
      """Compute CKA with a linear kernel, in feature space.
  
      This is typically faster than computing the Gram matrix when there are fewer
      features than examples.
  
      Args:
        features_x: A num_examples x num_features matrix of features.
        features_y: A num_examples x num_features matrix of features.
        debiased: Use unbiased estimator of dot product similarity. CKA may still be
          biased. Note that this estimator may be negative.
  
      Returns:
        The value of CKA between X and Y.
      """
      features_x = features_x - np.mean(features_x, 0, keepdims=True)
      features_y = features_y - np.mean(features_y, 0, keepdims=True)
  
      dot_product_similarity = (
          np.linalg.norm(features_x.T.dot(features_y)) ** 2
      )
      normalization_x = np.linalg.norm(features_x.T.dot(features_x))
      normalization_y = np.linalg.norm(features_y.T.dot(features_y))
  
      if debiased:
          n = features_x.shape[0]
          # Equivalent to np.sum(features_x ** 2, 1) but avoids an intermediate array.
          sum_squared_rows_x = np.einsum(
              "ij,ij->i", features_x, features_x
          )
          sum_squared_rows_y = np.einsum(
              "ij,ij->i", features_y, features_y
          )
          squared_norm_x = np.sum(sum_squared_rows_x)
          squared_norm_y = np.sum(sum_squared_rows_y)
  
          dot_product_similarity = (
              _debiased_dot_product_similarity_helper(
                  dot_product_similarity,
                  sum_squared_rows_x,
                  sum_squared_rows_y,
                  squared_norm_x,
                  squared_norm_y,
                  n,
              )
          )
          normalization_x = np.sqrt(
              _debiased_dot_product_similarity_helper(
                  normalization_x**2,
                  sum_squared_rows_x,
                  sum_squared_rows_x,
                  squared_norm_x,
                  squared_norm_x,
                  n,
              )
          )
          normalization_y = np.sqrt(
              _debiased_dot_product_similarity_helper(
                  normalization_y**2,
                  sum_squared_rows_y,
                  sum_squared_rows_y,
                  squared_norm_y,
                  squared_norm_y,
                  n,
              )
          )
  
      return dot_product_similarity / (
          normalization_x * normalization_y
      )
  
imports: import numpy
label_desc: Use image node_id 6 for calling a global function with example usage: feature_space_linear_cka(features_x, features_y, debiased) and returns: unknown