Class SFANode

Parameters:

• input_dim (int) - The input dimensionality.
• output_dim (int) - The output dimensionality.
• dtype (numpy.dtype or str) - The datatype.

• include_last_sample (bool) - If False the train method discards the last sample in every chunk during training when calculating the covariance matrix. The last sample is in this case only used for calculating the covariance matrix of the derivatives. The switch should be set to False if you plan to train with several small chunks. For example we can split a sequence (index is time):

  x_1 x_2 x_3 x_4
  

  in smaller parts like this:

  x_1 x_2
  x_2 x_3
  x_3 x_4
  

  The SFANode will see 3 derivatives for the temporal covariance matrix, and the first 3 points for the spatial covariance matrix. Of course you will need to use a generator that connects the small chunks (the last sample needs to be sent again in the next chunk). If include_last_sample was True, depending on the generator you use, you would either get:

  x_1 x_2
  x_2 x_3
  x_3 x_4
  

  in which case the last sample of every chunk would be used twice when calculating the covariance matrix, or:

  x_1 x_2
  x_3 x_4
  

  in which case you loose the derivative between x_3 and x_2.

  If you plan to train with a single big chunk leave include_last_sample to the default value, i.e. True.

  You can even change this behaviour during training. Just set the corresponding switch in the train method.

• rank_deficit_method (str) - Possible values: 'none' (default), 'reg', 'pca', 'svd', 'auto' If not 'none', the stop_train method solves the SFA eigenvalue problem in a way that is robust against linear redundancies in the input data. This would otherwise lead to rank deficit in the covariance matrix, which usually yields a SymeigException ('Covariance matrices may be singular'). There are several solving methods implemented:

  reg - works by regularization pca - works by PCA svd - works by SVD ldl - works by LDL decomposition (requires SciPy >= 1.0)

  auto - (Will be: selects the best-benchmarked method of the above)

  Currently it simply selects pca.

  Note: If you already received an exception SymeigException ('Covariance matrices may be singular') you can manually set the solving method for an existing node:

  sfa.set_rank_deficit_method('pca')
  

  That means,:

  sfa = SFANode(rank_deficit='pca')
  

  is equivalent to:

  sfa = SFANode()
  sfa.set_rank_deficit_method('pca')
  

  After such an adjustment you can run stop_training() again, which would save a potentially time-consuming rerun of all train() calls.

Overrides: object.__init__

Parameters:

• x (numpy.ndarray) - The time series data.
• n (int) - The number of slowest components. If 'n' is an integer, then use the first 'n' slowest components.

Returns: numpy.ndarray

The output of the slowest functions.

Overrides: Node.execute

Return the eta values of the slow components learned during the training phase. If the training phase has not been completed yet, call stop_training.

The delta value of a signal is a measure of its temporal variation, and is defined as the mean of the derivative squared, i.e. delta(x) = mean(dx/dt(t)^2). delta(x) is zero if x is a constant signal, and increases if the temporal variation of the signal is bigger.

The eta value is a more intuitive measure of temporal variation, defined as eta(x) = t/(2*pi) * sqrt(delta(x)) If x is a signal of length 't' which consists of a sine function that accomplishes exactly N oscillations, then eta(x)=N.

Parameters:

• t - Sampling frequency in Hz.

  The original definition in (Wiskott and Sejnowski, 2002) is obtained for t = number of training data points, while for t=1 (default), this corresponds to the beta-value defined in (Berkes and Wiskott, 2005).

Returns:

The eta values of the slow components learned during the training phase.

Invert y.

If the node is invertible, compute the input x such that y = execute(x).

By default, subclasses should overwrite _inverse to implement their inverse function. The docstring of the inverse method overwrites this docstring.

Overrides: Node.inverse

Stop the training phase.

By default, subclasses should overwrite _stop_training to implement this functionality. The docstring of the _stop_training method overwrites this docstring.

Overrides: Node.stop_training

Parameters:

• x (numpy.ndarray) - The time series data.

Returns: numpy.ndarray

Piecewise linear approximation of the time derivative.

Parameters:

• x (numpy.ndarray) - The time series data.
• include_last_sample (bool) - For the include_last_sample switch have a look at the SFANode.__init__ docstring.

Overrides: Node.train

avg

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