Documentation for Basis Functions
¶
Fourier
¶
Build Fourier basis function. Generate a new feature matrix consisting of all Fourier features with respect to the number of harmonics.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
degree | int(max_degree), default | The maximum degree of the polynomial features. | 1 |
Notes¶
Be aware that the number of features in the output array scales significantly as the number of inputs, the max lag of the input and output.
Source code in sysidentpy\basis_function\_basis_function.py
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fit(data, max_lag, predefined_regressors=None)
¶
Build the Polynomial information matrix.
Each columns of the information matrix represents a candidate regressor. The set of candidate regressors are based on xlag, ylag, and degree defined by the user.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
data | ndarray of floats | The lagged matrix built with respect to each lag and column. | required |
max_lag | int | Target data used on training phase. | required |
predefined_regressors | ndarray of int | The index of the selected regressors by the Model Structure Selection algorithm. | None |
Returns:
Type | Description |
---|---|
psi | The lagged matrix built in respect with each lag and column. |
Source code in sysidentpy\basis_function\_basis_function.py
Polynomial
¶
Bases: InformationMatrix
Build polynomial basis function. Generate a new feature matrix consisting of all polynomial combinations of the features with degree less than or equal to the specified degree.
..math: y_k = \sum_{i=1}^{p}\Theta_i imes \prod_{j=0}{n_x}u_{k-j}\prod_{l=1}{n_e}e_{k-l}\prod_{m=1}{n_y}y_{k-m} \label{eq5:narx}
where :math:p
is the number of regressors, :math:\Theta_i
are the model parameters, and :math:a_i, m, b_i, j
and :math:d_i, l \in \mathbb{N}
are the exponents of the output, input and noise terms, respectively.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
degree | int(max_degree), default | The maximum degree of the polynomial features. | 2 |
Notes¶
Be aware that the number of features in the output array scales significantly as the number of inputs, the max lag of the input and output, and degree increases. High degrees can cause overfitting.
Source code in sysidentpy\basis_function\_basis_function.py
fit(data, max_lag, predefined_regressors=None)
¶
Build the Polynomial information matrix.
Each columns of the information matrix represents a candidate regressor. The set of candidate regressors are based on xlag, ylag, and degree defined by the user.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
data | ndarray of floats | The lagged matrix built with respect to each lag and column. | required |
max_lag | int | Target data used on training phase. | required |
predefined_regressors | ndarray of int | The index of the selected regressors by the Model Structure Selection algorithm. | None |
Returns:
Type | Description |
---|---|
psi | The lagged matrix built in respect with each lag and column. |