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Perform Independent Component Analysis using the FastICA algorithm. Note that FastICA is a batch-algorithm. This means that it needs all input data before it can start and compute the ICs. The algorithm is here given as a Node for convenience, but it actually accumulates all inputs it receives. Remember that to avoid running out of memory when you have many components and many time samples. FastICA does not support the telescope mode (the convergence criterium is not robust in telescope mode). Reference: Aapo Hyvarinen (1999). Fast and Robust Fixed-Point Algorithms for Independent Component Analysis IEEE Transactions on Neural Networks, 10(3):626-634. Internal variables of interest: self.white -- the whitening node used for preprocessing. self.filters -- the ICA filters matrix (this is the transposed of the projection matrix after whitening). self.convergence -- the value of the convergence threshold. History: - 1.4.1998 created for Matlab by Jarmo Hurri, Hugo Gavert, Jaakko Sarela, and Aapo Hyvarinen - 7.3.2003 modified for Python by Thomas Wendler - 3.6.2004 rewritten and adapted for scipy and MDP by MDP's authors - 25.5.2005 now independent from scipy. Requires Numeric or numarray - 26.6.2006 converted to numpy - 14.9.2007 updated to Matlab version 2.5
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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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Input arguments: General: whitened -- Set whitened == True if input data are already whitened. Otherwise the node will whiten the data itself white_comp -- If whitened == 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. Specific for FastICA: approach -- Approach to use. Possible values are: 'defl' --> deflation 'symm' --> symmetric g -- Nonlinearity to use. Possible values are: 'pow3' --> x^3 'tanh' --> tanh(fine_tanh*x) 'gaus' --> x*exp(-fine_gaus*x^2/2) 'skew' --> x^2 (for skewed signals) fine_g -- Nonlinearity for fine tuning. Possible values are the same as for 'g'. Set it to None to disable fine tuning. mu -- Step size stabilization -- Enable stabilization procedure: the value of mu can momentarily be halved if the algorithm is stuck between two points (this is called a stroke). Also if there is no convergence before half of the maximum number of iterations has been reached then mu will be halved for the rest of the rounds. sample_size -- Percentage of samples used in one iteration. If sample_size < 1, samples are chosen in random order. fine_tanh -- parameter for 'tanh' nonlinearity fine_gaus -- parameter for 'gaus' nonlinearity guess -- initial guess for the mixing matrix (ignored if None) max_it -- maximum number of iterations max_it_fine -- maximum number of iterations for fine tuning failures -- maximum number of failures to allow in deflation mode
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This is the core routine of the ICANode. Each subclass must define this function to return the achieved convergence value. This function is also responsible for setting the ICA filters matrix self.filters. Note that the matrix self.filters is applied to the right of the matrix containing input data. This is the transposed of the matrix defining the linear transformation.
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