class_docstr: Piecewise Aggregate Approximation Transformer (PAA).
  
  (PAA) Piecewise Aggregate Approximation Transformer, as described in
  Eamonn Keogh, Kaushik Chakrabarti, Michael Pazzani, and Sharad Mehrotra.
  Dimensionality reduction for fast similarity search in large time series
  databases.
  Knowledge and information Systems, 3(3), 263-286, 2001.
  For each series reduce the dimensionality to num_intervals, where each
  value is the mean of values in
  the interval.
  
  TO DO: pythonise it to make it more efficient. Maybe check vs this version
          http://vigne.sh/posts/piecewise-aggregate-approx/
  Could have: Tune the interval size in fit somehow?
  
  Parameters
  ----------
  num_intervals   : int, dimension of the transformed data (default 8)
docstr: Transform data.
  
  Parameters
  ----------
  X : nested pandas DataFrame of shape [n_instances, n_dims]
      Nested dataframe with multivariate time-series in cells.
  
  Returns
  -------
  dims: Pandas data frame with first dimension in column zero,
        second in column one etc.
code: def _transform(self, X, y=None):
      """Transform data.
  
      Parameters
      ----------
      X : nested pandas DataFrame of shape [n_instances, n_dims]
          Nested dataframe with multivariate time-series in cells.
  
      Returns
      -------
      dims: Pandas data frame with first dimension in column zero,
            second in column one etc.
      """
      # Get information about the dataframe
      num_atts = len(X.iloc[0, 0])
      col_names = X.columns
  
      # Check the parameters are appropriate
      self._check_parameters(num_atts)
  
      # On each dimension, perform PAA
      dataFrames = []
      for x in col_names:
          dataFrames.append(
              self._perform_paa_along_dim(pd.DataFrame(X[x]))
          )
  
      # Combine the dimensions together
      result = pd.concat(dataFrames, axis=1, sort=False)
      result.columns = col_names
  
      return result
  
file_path: sktime/sktime/transformations/panel/dictionary_based/_paa.py
imports: import pandas
  from sktime.datatypes._panel._convert import from_nested_to_2d_array
  from sktime.transformations.base import BaseTransformer
label_desc: Use image node_id 3 for calling the PAA obj's underlying member method code with example usage: obj._transform(X, y) and returns: result