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Extract the slowly varying components from the input data. More information about Slow Feature Analysis can be found in Wiskott, L. and Sejnowski, T.J., Slow Feature Analysis: Unsupervised Learning of Invariances, Neural Computation, 14(4):715-770 (2002). **Instance variables of interest** ``self.avg`` Mean of the input data (available after training) ``self.sf`` Matrix of the SFA filters (available after training) ``self.d`` Delta values corresponding to the SFA components (generalized eigenvalues). [See the docs of the ``get_eta_values`` method for more information] **Special arguments for constructor** ``include_last_sample`` 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.
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_train_seq List of tuples:: |
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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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For the ``include_last_sample`` switch have a look at the SFANode class docstring.
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Compute the output of the slowest functions. If 'n' is an integer, then use the first 'n' slowest components.
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For the ``include_last_sample`` switch have a look at the SFANode class docstring.
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Compute the output of the slowest functions. If 'n' is an integer, then use the first 'n' slowest components.
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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). |
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.
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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.
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Compute the linear approximation of the time derivative. |
For the ``include_last_sample`` switch have a look at the SFANode class docstring.
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