Class TDSEPNode

Input arguments:

lags -- list of time-lags to generate the time-delayed covariance

matrices. If lags is an integer, time-lags 1,2,...,'lags' are used. Note that time-lag == 0 (instantaneous correlation) is always implicitly used.

whitened -- Set whitened is True if input data are already whitened.

Otherwise the node will whiten the data itself.

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 }

limit -- convergence threshold.

max_iter -- If the algorithms does not achieve convergence within

max_iter iterations raise an Exception. Should be larger than 100.

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__

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