Class ISFANode

Perform Independent Slow Feature Analysis.

The notation is the same used in the paper by Blaschke et al. Please refer to the paper for more information.

Parameters:

• lags - list of time-lags to generate the time-delayed covariance matrices (in the paper this is the set of au). If lags is an integer, time-lags 1,2,...,'lags' are used. Note that time-lag == 0 (instantaneous correlation) is always implicitly used.
• sfa_ica_coeff - a list of float with two entries, which defines the weights of the SFA and ICA part of the objective function. They are called b_{SFA} and b_{ICA} in the paper.
• sfaweights - weighting factors for the covariance matrices relative to the SFA part of the objective function (called kappa_{SFA}^{ au} in the paper). Default is [1., 0., ..., 0.] For possible values see the description of icaweights.

• icaweights - weighting factors for the cov matrices relative to the ICA part of the objective function (called kappa_{ICA}^{ au} in the paper). Default is 1. Possible values are:

  • an integer n: all matrices are weighted the same (note that it does not make sense to have n != 1)
  • a list or array of floats of len == len(lags): each element of the list is used for weighting the corresponding matrix
  • None: use the default values.
• whitened - True if input data is already white, False otherwise (the data will be whitened internally).
• white_comp - If whitened is false, you can set white_comp to the number of whitened components to keep during the calculation (i.e., the input dimensions are reduced to white_comp by keeping the components of largest variance).
• white_parm - a dictionary with additional parameters for whitening. It is passed directly to the WhiteningNode constructor. Ex: white_parm = { 'svd' : True }
• eps_contrast - Convergence is achieved when the relative improvement in the contrast is below this threshold. Values in the range [1E-4, 1E-10] are usually reasonable.
• max_iter - If the algorithms does not achieve convergence within max_iter iterations raise an Exception. Should be larger than 100.
• RP - Starting rotation-permutation matrix. It is an input_dim x input_dim matrix used to initially rotate the input components. If not set, the identity matrix is used. In the paper this is used to start the algorithm at the SFA solution (which is often quite near to the optimum).
• verbose - print progress information during convergence. This can slow down the algorithm, but it's the only way to see the rate of improvement and immediately spot if something is going wrong.
• output_dim - sets the number of independent components that have to be extracted. Note that if this is not smaller than input_dim, the problem is solved linearly and SFA would give the same solution only much faster.

Overrides: object.__init__

Process the data contained in x.

If the object is still in the training phase, the function stop_training will be called. x is a matrix having different variables on different columns and observations on the rows.

By default, subclasses should overwrite _execute to implement their execution phase. The docstring of the _execute method overwrites this docstring.

Overrides: Node.execute

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.

If the node is used on large datasets it may be wise to first learn the covariance matrices, and then tune the parameters until a suitable parameter set has been found (learning the covariance matrices is the slowest part in this case). This could be done for example in the following way (assuming the data is already white):

>>> covs=[mdp.utils.DelayCovarianceMatrix(dt, dtype=dtype)
...       for dt in lags]
>>> for block in data:
...     [covs[i].update(block) for i in range(len(lags))]

You can then initialize the ISFANode with the desired parameters, do a fake training with some random data to set the internal node structure and then call stop_training with the stored covariance matrices. For example:

>>> isfa = ISFANode(lags, .....)
>>> x = mdp.numx_rand.random((100, input_dim)).astype(dtype)
>>> isfa.train(x)
>>> isfa.stop_training(covs=covs)

This trick has been used in the paper to apply ISFA to surrogate matrices, i.e. covariance matrices that were not learnt on a real dataset.

Overrides: Node.stop_training

Update the internal structures according to the input data x.

x is a matrix having different variables on different columns and observations on the rows.

By default, subclasses should overwrite _train to implement their training phase. The docstring of the _train method overwrites this docstring.

Note: a subclass supporting multiple training phases should implement the same signature for all the training phases and document the meaning of the arguments in the _train method doc-string. Having consistent signatures is a requirement to use the node in a flow.

Overrides: Node.train