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| Original file line number | Diff line number | Diff line change |
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| """Fourier features for time series with long/complex seasonality.""" | ||
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| __maintainer__ = [] | ||
| import warnings | ||
| from typing import List, Optional, Union | ||
|
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| import numpy as np | ||
| import pandas as pd | ||
|
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| from aeon.transformations.series import BaseSeriesTransformer | ||
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| class FourierFeaturesTransformer(BaseSeriesTransformer): | ||
| r"""Fourier Features for time series seasonality. | ||
| Fourier Series terms can be used as explanatory variables for the cases of multiple | ||
| seasonal periods and or complex / long seasonal periods [1]_, [2]_. For every | ||
| seasonal period, :math:`sp` and fourier term :math:`k` pair there are 2 fourier | ||
| terms sin_sp_k and cos_sp_k: | ||
| - sin_sp_k = :math:`sin(\frac{2 \pi k t}{sp})` | ||
| - cos_sp_k = :math:`cos(\frac{2 \pi k t}{sp})` | ||
| Where :math:`t` is the number of time steps elapsed from the beginning of the time | ||
| series. | ||
| The output of the trasform is a pandas DataFrame that includes the fourier terms as | ||
| additional columns with the naming convention stated above (sin_sp_k and cos_sp_k). | ||
| For instance for sp_list = [12, 3] and fourier_terms_list = [2, 1] the transformed | ||
| series will have the additional columns: | ||
| "cos_12_1", "sin_12_1", "cos_12_2", "sin_12_2", "cos_3_1", "sin_3_1" | ||
| The implementation is based on the fourier function from the R forecast package [3]_ | ||
| Parameters | ||
| ---------- | ||
| sp_list : List[Union[int, float]] | ||
| List of seasonal periods. | ||
| fourier_terms_list : List[int] | ||
| List of number of fourier terms (K) for each seasonal period. | ||
| Each K matches to the sp (seasonal period) of the sp_list. | ||
| For example, if sp_list = [7, 365] and fourier_terms_list = [3, 9], the seasonal | ||
| frequency of 7 will have 3 fourier terms and the seasonal frequency of 365 | ||
| will have 9 fourier terms. | ||
| freq : str, optional, default = None | ||
| Only used when X has a pd.DatetimeIndex without a specified frequency. | ||
| Specifies the frequency of the index of your data. The string should | ||
| match a pandas offset alias: | ||
| https://pandas.pydata.org/pandas-docs/stable/user_guide/timeseries.html#offset-aliases | ||
| keep_original_columns : boolean, default=False | ||
| Keep original columns in X passed to `.transform()`. | ||
| References | ||
| ---------- | ||
| .. [1] Hyndsight - Forecasting with long seasonal periods: | ||
| https://robjhyndman.com/hyndsight/longseasonality/ | ||
| .. [2] Hyndman, R.J., & Athanasopoulos, G. (2021) Forecasting: principles and | ||
| practice, 3rd edition, OTexts: Melbourne, Australia. OTexts.com/fpp3. | ||
| Accessed on August 14th 2022. | ||
| .. [3] https://pkg.robjhyndman.com/forecast/reference/fourier.html | ||
| Examples | ||
| -------- | ||
| >>> from aeon.transformations.fourier import FourierFeatures | ||
| >>> from aeon.datasets import load_airline | ||
| >>> y = load_airline() | ||
| >>> transformer = FourierFeatures(sp_list=[12], fourier_terms_list=[4]) | ||
| >>> y_hat = transformer.fit_transform(y) | ||
| """ | ||
|
|
||
| _tags = { | ||
| "input_data_type": "Series", | ||
| # what is the abstract type of X: Series, or Panel | ||
| "output_data_type": "Series", | ||
| # what abstract type is returned: Primitives, Series, Panel | ||
| "transform_labels": "None", | ||
| # what is the abstract type of y: None (not needed), Primitives, Series, Panel | ||
| "instancewise": True, | ||
| "capability:inverse_transform": False, | ||
| "capability:multivariate": True, | ||
| "X_inner_type": "pd.DataFrame", | ||
| "y_inner_type": "None", | ||
| "requires_y": False, # does y need to be passed in fit? | ||
| "enforce_index_type": [ | ||
| pd.PeriodIndex, | ||
| pd.DatetimeIndex, | ||
| ], # index type that needs to be enforced | ||
| # in X/y | ||
| "fit_is_empty": False, # is fit empty and can be skipped? Yes = True | ||
| "X-y-must-have-same-index": False, # can estimator handle different X/y index? | ||
| "transform-returns-same-time-index": True, | ||
| # does transform return have the same time index as input X | ||
| "skip-inverse-transform": True, # is inverse-transform skipped when called? | ||
| "capability:unequal_length": False, | ||
| # can the transformer handle unequal length time series (if passed Panel)? | ||
| "capability:unequal_length:removes": False, | ||
| # is transform result always guaranteed to be equal length (and series)? | ||
| # not relevant for transformers that return Primitives in transform-output | ||
| "capability:missing_values": False, # can estimator handle missing data? | ||
| "capability:missing_values:removes": False, | ||
| # is transform result always guaranteed to contain no missing values? | ||
| "python_version": None, # PEP 440 python version specifier to limit versions | ||
| } | ||
|
|
||
| def __init__( | ||
| self, | ||
| sp_list: List[Union[int, float]], | ||
| fourier_terms_list: List[int], | ||
| freq: Optional[str] = None, | ||
| keep_original_columns: Optional[bool] = True, | ||
| ): | ||
| self.sp_list = sp_list | ||
| self.fourier_terms_list = fourier_terms_list | ||
| self.freq = freq | ||
| self.keep_original_columns = keep_original_columns | ||
| if len(self.sp_list) != len(self.fourier_terms_list): | ||
| raise ValueError( | ||
| "In FourierFeatures the length of the sp_list needs to be equal " | ||
| "to the length of fourier_terms_list." | ||
| ) | ||
|
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||
| if np.any(np.array(self.sp_list) / np.array(self.fourier_terms_list) < 1): | ||
| raise ValueError( | ||
| "In FourierFeatures the number of each element of fourier_terms_list" | ||
| "needs to be lower from the corresponding element of the sp_list" | ||
| ) | ||
|
|
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| super().__init__() | ||
|
|
||
| def _fit(self, X, y=None): | ||
| """Fit transformer to X and y. | ||
| private _fit containing the core logic, called from fit | ||
| Parameters | ||
| ---------- | ||
| X: data structure of type X_inner_type | ||
| If X_inner_type is list, _fit must support all types in it | ||
| Data to fit transform to. | ||
| y : data structure of type y_inner_type, default=None | ||
| Additional data, e.g., labels for transformation. | ||
| freq : str, optional, default = None | ||
| Only used when X has a pd.DatetimeIndex without a specified frequency. | ||
| Specifies the frequency of the index of your data. The string should | ||
| match a pandas offset alias. | ||
| https://pandas.pydata.org/pandas-docs/stable/user_guide/timeseries.html#offset-aliases | ||
| Returns | ||
| ------- | ||
| self: reference to self | ||
| """ | ||
| # Create the sp, k pairs | ||
| # Don't add pairs where the coefficient k/sp already exists | ||
| self.sp_k_pairs_list_ = [] | ||
| coefficient_list = [] | ||
| for i, sp in enumerate(self.sp_list): | ||
| for k in range(1, self.fourier_terms_list[i] + 1): | ||
| coef = k / sp | ||
| if coef not in coefficient_list: | ||
| coefficient_list.append(coef) | ||
| self.sp_k_pairs_list_.append((sp, k)) | ||
| else: | ||
| warnings.warn( | ||
| f"The terms sin_{sp}_{k} and cos_{sp}_{k} from FourierFeatures " | ||
| "will be skipped because the resulting coefficient already " | ||
| "exists from other seasonal period, fourier term pairs.", | ||
| stacklevel=2, | ||
| ) | ||
|
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| time_index = X.index | ||
|
|
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| if isinstance(time_index, pd.DatetimeIndex): | ||
| # Chooses first non None value | ||
| self.freq_ = time_index.freq or self.freq or pd.infer_freq(time_index) | ||
| if self.freq_ is None: | ||
| ValueError("X has no known frequency and none is supplied") | ||
| if self.freq_ == time_index.freq and self.freq_ != self.freq: | ||
| warnings.warn( | ||
| f"Using frequency from index: {time_index.freq}, which \ | ||
| does not match the frequency given:{self.freq}.", | ||
| stacklevel=2, | ||
| ) | ||
| time_index = time_index.to_period(self.freq_) | ||
| # this is used to make sure that time t is calculated with reference to | ||
| # the data passed on fit | ||
| # store the integer form of the minimum date in the prediod index | ||
| self.min_t_ = np.min(time_index.astype("int64")) | ||
|
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| return self | ||
|
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| def _transform(self, X, y=None): | ||
| """Transform X and return a transformed version. | ||
| private _transform containing core logic, called from transform | ||
| Parameters | ||
| ---------- | ||
| X: data structure of type X_inner_type | ||
| If X_inner_type is list, _transform must support all types in it | ||
| Data to be transformed. | ||
| y : data structure of type y_inner_type, default=None | ||
| Additional data, e.g., labels for transformation. | ||
| Returns | ||
| ------- | ||
| transformed version of X. | ||
| """ | ||
| X_transformed = pd.DataFrame(index=X.index) | ||
| time_index = X.index | ||
|
|
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| if isinstance(time_index, pd.DatetimeIndex): | ||
| time_index = time_index.to_period(self.freq_) | ||
|
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| # get the integer form of the PeriodIndex | ||
| int_index = time_index.astype("int64") - self.min_t_ | ||
|
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| for sp_k in self.sp_k_pairs_list_: | ||
| sp = sp_k[0] | ||
| k = sp_k[1] | ||
|
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| X_transformed[f"sin_{sp}_{k}"] = np.sin(int_index * 2 * k * np.pi / sp) | ||
| X_transformed[f"cos_{sp}_{k}"] = np.cos(int_index * 2 * k * np.pi / sp) | ||
|
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| if self.keep_original_columns: | ||
| X_transformed = pd.concat([X, X_transformed], axis=1, copy=True) | ||
|
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| return X_transformed | ||
|
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||
| @classmethod | ||
| def get_test_params(cls, parameter_set="default"): | ||
| """Return testing parameter settings for the estimator. | ||
| Parameters | ||
| ---------- | ||
| parameter_set : str, default="default" | ||
| Name of the set of test parameters to return, for use in tests. If no | ||
| special parameters are defined for a value, will return `"default"` set. | ||
| There are currently no reserved values for transformers. | ||
| Returns | ||
| ------- | ||
| params : dict or list of dict, default = {} | ||
| Parameters to create testing instances of the class | ||
| Each dict are parameters to construct an "interesting" test instance, i.e., | ||
| `MyClass(**params)` or `MyClass(**params[i])` creates a valid test instance. | ||
| `create_test_instance` uses the first (or only) dictionary in `params`. | ||
| """ | ||
| params = [ | ||
| {"sp_list": [12], "fourier_terms_list": [4]}, | ||
| {"sp_list": [12, 6.2], "fourier_terms_list": [3, 4]}, | ||
| ] | ||
| return params |
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