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Compute the eta values of the normalized training data. 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``. ``EtaComputerNode`` normalizes the training data to have unit variance, such that it is possible to compare the temporal variation of two signals independently from their scaling. Reference: Wiskott, L. and Sejnowski, T.J. (2002). Slow Feature Analysis: Unsupervised Learning of Invariances, Neural Computation, 14(4):715-770. Important: if a data chunk is tlen data points long, this node is going to consider only the first tlen-1 points together with their derivatives. This means in particular that the variance of the signal is not computed on all data points. This behavior is compatible with that of ``SFANode``. This is an analysis node, i.e. the data is analyzed during training and the results are stored internally. Use the method ``get_eta`` to access them.
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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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If the input dimension and the output dimension are unspecified, they will be set when the `train` or `execute` method is called for the first time. If dtype is unspecified, it will be inherited from the data it receives at the first call of `train` or `execute`. Every subclass must take care of up- or down-casting the internal structures to match this argument (use `_refcast` private method when possible).
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Return the eta values of the data received during the training phase. If the training phase has not been completed yet, call stop_training. :Arguments: t Sampling frequency in Hz. The original definition in (Wiskott and Sejnowski, 2002) is obtained for ``t=self._tlen``, while for ``t=1`` (default), this corresponds to the beta-value defined in (Berkes and Wiskott, 2005). |
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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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.
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