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Perform Independent Slow Feature Analysis on the input data. Internal variables of interest: self.RP -- the global rotation-permutation matrix. This is the filter applied on input_data to get output_data self.RPC -- the *complete* global rotation-permutation matrix. This is a matrix of dimension input_dim x input_dim (the 'outer space' is retained) self.covs -- A mdp.utils.MultipleCovarianceMatrices instance containing the current time-delayed covariance matrices of the input_data. After convergence the uppermost output_dim x output_dim submatrices should be almost diagonal. self.covs[n-1] is the covariance matrix relative to the n-th time-lag Note: they are not cleared after convergence. If you need to free some memory, you can safely delete them with >>> del self.covs self.initial_contrast -- a dictionary with the starting contrast and the SFA and ICA parts of it. self.final_contrast -- like the above but after convergence. Note: If you intend to use this node for large datasets please have a look at the stop_training method documentation for speeding things up. References: Blaschke, T. , Zito, T., and Wiskott, L. (2007). Independent Slow Feature Analysis and Nonlinear Blind Source Separation. Neural Computation 19(4):994-1021 (2007) http://itb.biologie.hu-berlin.de/~wiskott/Publications/BlasZitoWisk2007-ISFA-NeurComp.pdf
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__metaclass__ This Metaclass is meant to overwrite doc strings of methods like execute, stop_training, inverse with the ones defined in the corresponding private methods _execute, _stop_training, _inverse, etc... |
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_train_seq List of tuples: [(training-phase1, stop-training-phase1), (training-phase2, stop_training-phase2), ... |
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dtype dtype |
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input_dim Input dimensions |
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output_dim Output dimensions |
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supported_dtypes Supported dtypes |
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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. Keyword arguments: 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.
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Return the list of dtypes supported by this node.
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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.
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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.
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