code: def initialize_decomposition(
      tensor_slices,
      rank,
      init="random",
      svd="truncated_svd",
      random_state=None,
  ):
      r"""Initiate a random PARAFAC2 decomposition given rank and tensor slices.
  
      The SVD-based initialization is based on concatenation of all the tensor slices.
      This concatenated matrix is used to derive the factor matrix corresponding to the
      :math:`k` mode for an :math:`X_{ijk}` tensor. However, concatenating these slices
      requires a new copy of the tensor. For tensors where the sum of the :math:`j` mode
      along each slice is on average larger than the :math:`k` mode, an alternative
      strategy is adding together the cross-product matrix of each slice:
  
      .. math::
  
          K = X_{1}^T X_{1} + X_{2}^T X_{2} + ...
  
      The eigenvectors of this symmetric matrix are then equal to the right eigenvectors
      of the concatenation matrix. This function automatically chooses between
      concatenating or forming the cross-product, depending on which resulting matrix
      is smaller.
  
      Parameters
      ----------
      tensor_slices : Iterable of ndarray
      rank : int
      init : {'random', 'svd', CPTensor, Parafac2Tensor}, optional
      random_state : `np.random.RandomState`
  
      Returns
      -------
      parafac2_tensor : Parafac2Tensor
          List of initialized factors of the CP decomposition where element `i`
          is of shape (tensor.shape[i], rank)
      """
      context = tl.context(tensor_slices[0])
      shapes = [m.shape for m in tensor_slices]
      concat_shape = sum(shape[0] for shape in shapes)
  
      if init == "random":
          return random_parafac2(
              shapes,
              rank,
              full=False,
              random_state=random_state,
              **context,
          )
      elif init == "svd":
          if shapes[0][1] < rank:
              raise ValueError(
                  f"Cannot perform SVD init if rank ({rank}) is greater than the number of columns in each tensor slice ({shapes[0][1]})"
              )
  
          A = tl.ones((len(tensor_slices), rank), **context)
  
          if concat_shape > shapes[0][1]:
              # If the concatenated matrix would be larger than the cross-product, use the latter
              unfolded_mode_2 = (
                  tl.transpose(tensor_slices[0]) @ tensor_slices[0]
              )
  
              for slice in tensor_slices[1:]:
                  unfolded_mode_2 += tl.matmul(
                      tl.transpose(slice), slice
                  )
          else:
              unfolded_mode_2 = tl.transpose(
                  tl.concatenate(list(tensor_slices), axis=0)
              )
  
          C = svd_interface(
              unfolded_mode_2, n_eigenvecs=rank, method=svd
          )[0]
  
          B = tl.eye(rank, **context)
          projections = _compute_projections(
              tensor_slices, (A, B, C), svd
          )
          return Parafac2Tensor((None, [A, B, C], projections))
  
      elif isinstance(init, (tuple, list, Parafac2Tensor, CPTensor)):
          try:
              decomposition = Parafac2Tensor.from_CPTensor(
                  init, parafac2_tensor_ok=True
              )
          except ValueError:
              raise ValueError(
                  "If initialization method is a mapping, then it must "
                  "be possible to convert it to a Parafac2Tensor instance"
              )
          if decomposition.rank != rank:
              raise ValueError(
                  "Cannot init with a decomposition of different rank"
              )
          return decomposition
      raise ValueError(f'Initialization method "{init}" not recognized')
  
imports: from warnings import warn
  from typing import Iterable
  import tensorly
  from ._base_decomposition import DecompositionMixin
  from tensorly.random import random_parafac2
  from tensorly import backend
  from .None import parafac, non_negative_parafac_hals
  from ..parafac2_tensor import Parafac2Tensor, _validate_parafac2_tensor
  from ..cp_tensor import CPTensor, cp_normalize
  from ..tenalg.svd import svd_interface
label_desc: Use image node_id 1 for calling a global function with example usage: initialize_decomposition(tensor_slices, rank, init, svd, random_state) and returns: random_parafac2, Parafac2Tensor, decomposition