Notebook

In [1]:

from tsfresh.feature_extraction import extract_features
from tsfresh.feature_extraction.settings import ComprehensiveFCParameters, MinimalFCParameters, EfficientFCParameters
from tsfresh.feature_extraction.settings import from_columns

import numpy as np
import pandas as pd

/Users/mchrist/Documents/Research/tsfresh/venv/lib/python2.7/site-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.
  from pandas.core import datetools

This notebooks illustrates the "fc_parameters" or "kind_to_fc_parameters" dictionaries.

For a detailed explanation, see also http://tsfresh.readthedocs.io/en/latest/text/feature_extraction_settings.html

Construct a time series container¶

We construct the time series container that includes two sensor time series, "temperature" and "pressure", for two devices "a" and "b"

In [2]:

df = pd.DataFrame({"id": ["a", "a", "b", "b"], "temperature": [1,2,3,1], "pressure": [-1, 2, -1, 7]})
df

Out[2]:

	id	pressure	temperature
0	a	-1	1
1	a	2	2
2	b	-1	3
3	b	7	1

The default_fc_parameters¶

Which features are calculated by tsfresh is controlled by a dictionary that contains a mapping from feature calculator names to their parameters. This dictionary is called fc_parameters. It maps feature calculator names (=keys) to parameters (=values). As keys, always the same names as in the tsfresh.feature_extraction.feature_calculators module are used.

In the following we load an exemplary dictionary

In [3]:

settings_minimal = MinimalFCParameters() # only a few basic features
settings_minimal

Out[3]:

{'length': None,
 'maximum': None,
 'mean': None,
 'median': None,
 'minimum': None,
 'standard_deviation': None,
 'sum_values': None,
 'variance': None}

This dictionary can passed to the extract method, resulting in a few basic time series beeing calculated:

In [4]:

X_tsfresh = extract_features(df, column_id="id", default_fc_parameters = settings_minimal)
X_tsfresh.head()

Feature Extraction: 100%|██████████| 4/4 [00:00<00:00, 16336.14it/s]

Out[4]:

variable	pressure__length	pressure__maximum	pressure__mean	pressure__median	pressure__minimum	pressure__standard_deviation	pressure__sum_values	pressure__variance	temperature__length	temperature__maximum	temperature__mean	temperature__median	temperature__minimum	temperature__standard_deviation	temperature__sum_values	temperature__variance
id
a	2.0	2.0	0.5	0.5	-1.0	1.5	1.0	2.25	2.0	2.0	1.5	1.5	1.0	0.5	3.0	0.25
b	2.0	7.0	3.0	3.0	-1.0	4.0	6.0	16.00	2.0	3.0	2.0	2.0	1.0	1.0	4.0	1.00

By using the settings_minimal as value of the default_fc_parameters parameter, those settings are used for all type of time series. In this case, the settings_minimal dictionary is used for both "temperature" and "pressure" time series.

Now, lets say we want to remove the length feature and prevent it from beeing calculated. We just delete it from the dictionary.

In [5]:

del settings_minimal["length"]
settings_minimal

Out[5]:

{'maximum': None,
 'mean': None,
 'median': None,
 'minimum': None,
 'standard_deviation': None,
 'sum_values': None,
 'variance': None}

Now, if we extract features for this reduced dictionary, the length feature will not be calculated

In [6]:

X_tsfresh = extract_features(df, column_id="id", default_fc_parameters = settings_minimal)
X_tsfresh.head()

Feature Extraction: 100%|██████████| 4/4 [00:00<00:00, 1171.27it/s]

Out[6]:

variable	pressure__maximum	pressure__mean	pressure__median	pressure__minimum	pressure__standard_deviation	pressure__sum_values	pressure__variance	temperature__maximum	temperature__mean	temperature__median	temperature__minimum	temperature__standard_deviation	temperature__sum_values	temperature__variance
id
a	2.0	0.5	0.5	-1.0	1.5	1.0	2.25	2.0	1.5	1.5	1.0	0.5	3.0	0.25
b	7.0	3.0	3.0	-1.0	4.0	6.0	16.00	3.0	2.0	2.0	1.0	1.0	4.0	1.00

The kind_to_fc_parameters¶

now, lets say we do not want to calculate the same features for both type of time series. Instead there should be different sets of features for each kind.

To do that, we can use the kind_to_fc_parameters parameter, which lets us finely specifiy which fc_parameters we want to use for which kind of time series:

In [7]:

fc_parameters_pressure = {"length": None, 
                          "sum_values": None}

fc_parameters_temperature = {"maximum": None, 
                             "minimum": None}

kind_to_fc_parameters = {
    "temperature": fc_parameters_temperature,
    "pressure": fc_parameters_pressure
}

print(kind_to_fc_parameters)

{'pressure': {'length': None, 'sum_values': None}, 'temperature': {'minimum': None, 'maximum': None}}

So, in this case, for sensor "pressure" both "max" and "min" are calculated. For the "temperature" signal, the length and sum_values features are extracted instead.

In [8]:

X_tsfresh = extract_features(df, column_id="id", kind_to_fc_parameters = kind_to_fc_parameters)
X_tsfresh.head()

Feature Extraction: 100%|██████████| 4/4 [00:00<00:00, 1473.37it/s]

Out[8]:

variable	pressure__length	pressure__sum_values	temperature__maximum	temperature__minimum
id
a	2.0	1.0	2.0	1.0
b	2.0	6.0	3.0	1.0

So, lets say we lost the kind_to_fc_parameters dictionary. Or we apply a feature selection algorithm to drop irrelevant feature columns, so our extraction settings contain irrelevant features.

In both cases, we can use the provided "from_columns" method to infer the creating dictionary from the dataframe containing the features

In [9]:

recovered_settings = from_columns(X_tsfresh)
recovered_settings

Out[9]:

{'pressure': {'length': None, 'sum_values': None},
 'temperature': {'maximum': None, 'minimum': None}}

Lets drop a column to show that the inferred settings dictionary really changes

In [10]:

X_tsfresh.iloc[:, 1:]

Out[10]:

variable	pressure__sum_values	temperature__maximum	temperature__minimum
id
a	1.0	2.0	1.0
b	6.0	3.0	1.0

In [11]:

recovered_settings = from_columns(X_tsfresh.iloc[:, 1:])
recovered_settings

Out[11]:

{'pressure': {'sum_values': None},
 'temperature': {'maximum': None, 'minimum': None}}

More complex dictionaries¶

We provide custom fc_parameters dictionaries with greater sets of features.

The EfficientFCParameters contain features and parameters that should be calculated quite fastly:

In [12]:

settings_efficient = EfficientFCParameters()
settings_efficient

Out[12]:

{'abs_energy': None,
 'absolute_sum_of_changes': None,
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  {'coeff': 11, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 11, 'w': 20, 'widths': (2, 5, 10, 20)},
  {'coeff': 12, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 12, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 12, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 12, 'w': 20, 'widths': (2, 5, 10, 20)},
  {'coeff': 13, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 13, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 13, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 13, 'w': 20, 'widths': (2, 5, 10, 20)},
  {'coeff': 14, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 14, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 14, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 14, 'w': 20, 'widths': (2, 5, 10, 20)}],
 'fft_coefficient': [{'attr': 'real', 'coeff': 0},
  {'attr': 'real', 'coeff': 1},
  {'attr': 'real', 'coeff': 2},
  {'attr': 'real', 'coeff': 3},
  {'attr': 'real', 'coeff': 4},
  {'attr': 'real', 'coeff': 5},
  {'attr': 'real', 'coeff': 6},
  {'attr': 'real', 'coeff': 7},
  {'attr': 'real', 'coeff': 8},
  {'attr': 'real', 'coeff': 9},
  {'attr': 'real', 'coeff': 10},
  {'attr': 'real', 'coeff': 11},
  {'attr': 'real', 'coeff': 12},
  {'attr': 'real', 'coeff': 13},
  {'attr': 'real', 'coeff': 14},
  {'attr': 'real', 'coeff': 15},
  {'attr': 'real', 'coeff': 16},
  {'attr': 'real', 'coeff': 17},
  {'attr': 'real', 'coeff': 18},
  {'attr': 'real', 'coeff': 19},
  {'attr': 'real', 'coeff': 20},
  {'attr': 'real', 'coeff': 21},
  {'attr': 'real', 'coeff': 22},
  {'attr': 'real', 'coeff': 23},
  {'attr': 'real', 'coeff': 24},
  {'attr': 'real', 'coeff': 25},
  {'attr': 'real', 'coeff': 26},
  {'attr': 'real', 'coeff': 27},
  {'attr': 'real', 'coeff': 28},
  {'attr': 'real', 'coeff': 29},
  {'attr': 'real', 'coeff': 30},
  {'attr': 'real', 'coeff': 31},
  {'attr': 'real', 'coeff': 32},
  {'attr': 'real', 'coeff': 33},
  {'attr': 'real', 'coeff': 34},
  {'attr': 'real', 'coeff': 35},
  {'attr': 'real', 'coeff': 36},
  {'attr': 'real', 'coeff': 37},
  {'attr': 'real', 'coeff': 38},
  {'attr': 'real', 'coeff': 39},
  {'attr': 'real', 'coeff': 40},
  {'attr': 'real', 'coeff': 41},
  {'attr': 'real', 'coeff': 42},
  {'attr': 'real', 'coeff': 43},
  {'attr': 'real', 'coeff': 44},
  {'attr': 'real', 'coeff': 45},
  {'attr': 'real', 'coeff': 46},
  {'attr': 'real', 'coeff': 47},
  {'attr': 'real', 'coeff': 48},
  {'attr': 'real', 'coeff': 49},
  {'attr': 'real', 'coeff': 50},
  {'attr': 'real', 'coeff': 51},
  {'attr': 'real', 'coeff': 52},
  {'attr': 'real', 'coeff': 53},
  {'attr': 'real', 'coeff': 54},
  {'attr': 'real', 'coeff': 55},
  {'attr': 'real', 'coeff': 56},
  {'attr': 'real', 'coeff': 57},
  {'attr': 'real', 'coeff': 58},
  {'attr': 'real', 'coeff': 59},
  {'attr': 'real', 'coeff': 60},
  {'attr': 'real', 'coeff': 61},
  {'attr': 'real', 'coeff': 62},
  {'attr': 'real', 'coeff': 63},
  {'attr': 'real', 'coeff': 64},
  {'attr': 'real', 'coeff': 65},
  {'attr': 'real', 'coeff': 66},
  {'attr': 'real', 'coeff': 67},
  {'attr': 'real', 'coeff': 68},
  {'attr': 'real', 'coeff': 69},
  {'attr': 'real', 'coeff': 70},
  {'attr': 'real', 'coeff': 71},
  {'attr': 'real', 'coeff': 72},
  {'attr': 'real', 'coeff': 73},
  {'attr': 'real', 'coeff': 74},
  {'attr': 'real', 'coeff': 75},
  {'attr': 'real', 'coeff': 76},
  {'attr': 'real', 'coeff': 77},
  {'attr': 'real', 'coeff': 78},
  {'attr': 'real', 'coeff': 79},
  {'attr': 'real', 'coeff': 80},
  {'attr': 'real', 'coeff': 81},
  {'attr': 'real', 'coeff': 82},
  {'attr': 'real', 'coeff': 83},
  {'attr': 'real', 'coeff': 84},
  {'attr': 'real', 'coeff': 85},
  {'attr': 'real', 'coeff': 86},
  {'attr': 'real', 'coeff': 87},
  {'attr': 'real', 'coeff': 88},
  {'attr': 'real', 'coeff': 89},
  {'attr': 'real', 'coeff': 90},
  {'attr': 'real', 'coeff': 91},
  {'attr': 'real', 'coeff': 92},
  {'attr': 'real', 'coeff': 93},
  {'attr': 'real', 'coeff': 94},
  {'attr': 'real', 'coeff': 95},
  {'attr': 'real', 'coeff': 96},
  {'attr': 'real', 'coeff': 97},
  {'attr': 'real', 'coeff': 98},
  {'attr': 'real', 'coeff': 99},
  {'attr': 'imag', 'coeff': 0},
  {'attr': 'imag', 'coeff': 1},
  {'attr': 'imag', 'coeff': 2},
  {'attr': 'imag', 'coeff': 3},
  {'attr': 'imag', 'coeff': 4},
  {'attr': 'imag', 'coeff': 5},
  {'attr': 'imag', 'coeff': 6},
  {'attr': 'imag', 'coeff': 7},
  {'attr': 'imag', 'coeff': 8},
  {'attr': 'imag', 'coeff': 9},
  {'attr': 'imag', 'coeff': 10},
  {'attr': 'imag', 'coeff': 11},
  {'attr': 'imag', 'coeff': 12},
  {'attr': 'imag', 'coeff': 13},
  {'attr': 'imag', 'coeff': 14},
  {'attr': 'imag', 'coeff': 15},
  {'attr': 'imag', 'coeff': 16},
  {'attr': 'imag', 'coeff': 17},
  {'attr': 'imag', 'coeff': 18},
  {'attr': 'imag', 'coeff': 19},
  {'attr': 'imag', 'coeff': 20},
  {'attr': 'imag', 'coeff': 21},
  {'attr': 'imag', 'coeff': 22},
  {'attr': 'imag', 'coeff': 23},
  {'attr': 'imag', 'coeff': 24},
  {'attr': 'imag', 'coeff': 25},
  {'attr': 'imag', 'coeff': 26},
  {'attr': 'imag', 'coeff': 27},
  {'attr': 'imag', 'coeff': 28},
  {'attr': 'imag', 'coeff': 29},
  {'attr': 'imag', 'coeff': 30},
  {'attr': 'imag', 'coeff': 31},
  {'attr': 'imag', 'coeff': 32},
  {'attr': 'imag', 'coeff': 33},
  {'attr': 'imag', 'coeff': 34},
  {'attr': 'imag', 'coeff': 35},
  {'attr': 'imag', 'coeff': 36},
  {'attr': 'imag', 'coeff': 37},
  {'attr': 'imag', 'coeff': 38},
  {'attr': 'imag', 'coeff': 39},
  {'attr': 'imag', 'coeff': 40},
  {'attr': 'imag', 'coeff': 41},
  {'attr': 'imag', 'coeff': 42},
  {'attr': 'imag', 'coeff': 43},
  {'attr': 'imag', 'coeff': 44},
  {'attr': 'imag', 'coeff': 45},
  {'attr': 'imag', 'coeff': 46},
  {'attr': 'imag', 'coeff': 47},
  {'attr': 'imag', 'coeff': 48},
  {'attr': 'imag', 'coeff': 49},
  {'attr': 'imag', 'coeff': 50},
  {'attr': 'imag', 'coeff': 51},
  {'attr': 'imag', 'coeff': 52},
  {'attr': 'imag', 'coeff': 53},
  {'attr': 'imag', 'coeff': 54},
  {'attr': 'imag', 'coeff': 55},
  {'attr': 'imag', 'coeff': 56},
  {'attr': 'imag', 'coeff': 57},
  {'attr': 'imag', 'coeff': 58},
  {'attr': 'imag', 'coeff': 59},
  {'attr': 'imag', 'coeff': 60},
  {'attr': 'imag', 'coeff': 61},
  {'attr': 'imag', 'coeff': 62},
  {'attr': 'imag', 'coeff': 63},
  {'attr': 'imag', 'coeff': 64},
  {'attr': 'imag', 'coeff': 65},
  {'attr': 'imag', 'coeff': 66},
  {'attr': 'imag', 'coeff': 67},
  {'attr': 'imag', 'coeff': 68},
  {'attr': 'imag', 'coeff': 69},
  {'attr': 'imag', 'coeff': 70},
  {'attr': 'imag', 'coeff': 71},
  {'attr': 'imag', 'coeff': 72},
  {'attr': 'imag', 'coeff': 73},
  {'attr': 'imag', 'coeff': 74},
  {'attr': 'imag', 'coeff': 75},
  {'attr': 'imag', 'coeff': 76},
  {'attr': 'imag', 'coeff': 77},
  {'attr': 'imag', 'coeff': 78},
  {'attr': 'imag', 'coeff': 79},
  {'attr': 'imag', 'coeff': 80},
  {'attr': 'imag', 'coeff': 81},
  {'attr': 'imag', 'coeff': 82},
  {'attr': 'imag', 'coeff': 83},
  {'attr': 'imag', 'coeff': 84},
  {'attr': 'imag', 'coeff': 85},
  {'attr': 'imag', 'coeff': 86},
  {'attr': 'imag', 'coeff': 87},
  {'attr': 'imag', 'coeff': 88},
  {'attr': 'imag', 'coeff': 89},
  {'attr': 'imag', 'coeff': 90},
  {'attr': 'imag', 'coeff': 91},
  {'attr': 'imag', 'coeff': 92},
  {'attr': 'imag', 'coeff': 93},
  {'attr': 'imag', 'coeff': 94},
  {'attr': 'imag', 'coeff': 95},
  {'attr': 'imag', 'coeff': 96},
  {'attr': 'imag', 'coeff': 97},
  {'attr': 'imag', 'coeff': 98},
  {'attr': 'imag', 'coeff': 99}],
 'first_location_of_maximum': None,
 'first_location_of_minimum': None,
 'friedrich_coefficients': [{'coeff': 0, 'm': 3, 'r': 30},
  {'coeff': 1, 'm': 3, 'r': 30},
  {'coeff': 2, 'm': 3, 'r': 30},
  {'coeff': 3, 'm': 3, 'r': 30}],
 'has_duplicate': None,
 'has_duplicate_max': None,
 'has_duplicate_min': None,
 'index_mass_quantile': [{'q': 0.1},
  {'q': 0.2},
  {'q': 0.3},
  {'q': 0.4},
  {'q': 0.6},
  {'q': 0.7},
  {'q': 0.8},
  {'q': 0.9}],
 'kurtosis': None,
 'large_standard_deviation': [{'r': 0.05},
  {'r': 0.1},
  {'r': 0.15000000000000002},
  {'r': 0.2},
  {'r': 0.25},
  {'r': 0.30000000000000004},
  {'r': 0.35000000000000003},
  {'r': 0.4},
  {'r': 0.45},
  {'r': 0.5},
  {'r': 0.55},
  {'r': 0.6000000000000001},
  {'r': 0.65},
  {'r': 0.7000000000000001},
  {'r': 0.75},
  {'r': 0.8},
  {'r': 0.8500000000000001},
  {'r': 0.9},
  {'r': 0.9500000000000001}],
 'last_location_of_maximum': None,
 'last_location_of_minimum': None,
 'length': None,
 'linear_trend': [{'attr': 'pvalue'},
  {'attr': 'rvalue'},
  {'attr': 'intercept'},
  {'attr': 'slope'},
  {'attr': 'stderr'}],
 'longest_strike_above_mean': None,
 'longest_strike_below_mean': None,
 'max_langevin_fixed_point': [{'m': 3, 'r': 30}],
 'maximum': None,
 'mean': None,
 'mean_abs_change': None,
 'mean_change': None,
 'mean_second_derivate_central': None,
 'median': None,
 'minimum': None,
 'number_crossing_m': [{'m': 0}, {'m': -1}, {'m': 1}],
 'number_cwt_peaks': [{'n': 1}, {'n': 5}],
 'number_peaks': [{'n': 1}, {'n': 3}, {'n': 5}, {'n': 10}, {'n': 50}],
 'percentage_of_reoccurring_datapoints_to_all_datapoints': None,
 'percentage_of_reoccurring_values_to_all_values': None,
 'quantile': [{'q': 0.1},
  {'q': 0.2},
  {'q': 0.3},
  {'q': 0.4},
  {'q': 0.6},
  {'q': 0.7},
  {'q': 0.8},
  {'q': 0.9}],
 'range_count': [{'max': 1, 'min': -1}],
 'ratio_value_number_to_time_series_length': None,
 'skewness': None,
 'spkt_welch_density': [{'coeff': 2}, {'coeff': 5}, {'coeff': 8}],
 'standard_deviation': None,
 'sum_of_reoccurring_data_points': None,
 'sum_of_reoccurring_values': None,
 'sum_values': None,
 'symmetry_looking': [{'r': 0.0},
  {'r': 0.05},
  {'r': 0.1},
  {'r': 0.15000000000000002},
  {'r': 0.2},
  {'r': 0.25},
  {'r': 0.30000000000000004},
  {'r': 0.35000000000000003},
  {'r': 0.4},
  {'r': 0.45},
  {'r': 0.5},
  {'r': 0.55},
  {'r': 0.6000000000000001},
  {'r': 0.65},
  {'r': 0.7000000000000001},
  {'r': 0.75},
  {'r': 0.8},
  {'r': 0.8500000000000001},
  {'r': 0.9},
  {'r': 0.9500000000000001}],
 'time_reversal_asymmetry_statistic': [{'lag': 1}, {'lag': 2}, {'lag': 3}],
 'value_count': [{'value': 0},
  {'value': 1},
  {'value': nan},
  {'value': inf},
  {'value': -inf}],
 'variance': None,
 'variance_larger_than_standard_deviation': None}

The ComprehensiveFCParameters are the biggest set of features. It will take the longest to calculate

In [13]:

settings_comprehensive = ComprehensiveFCParameters()
settings_comprehensive

Out[13]:

{'abs_energy': None,
 'absolute_sum_of_changes': None,
 'agg_autocorrelation': [{'f_agg': 'mean'},
  {'f_agg': 'median'},
  {'f_agg': 'var'}],
 'agg_linear_trend': [{'attr': 'rvalue', 'chunk_len': 5, 'f_agg': 'max'},
  {'attr': 'rvalue', 'chunk_len': 5, 'f_agg': 'min'},
  {'attr': 'rvalue', 'chunk_len': 5, 'f_agg': 'mean'},
  {'attr': 'rvalue', 'chunk_len': 5, 'f_agg': 'var'},
  {'attr': 'rvalue', 'chunk_len': 10, 'f_agg': 'max'},
  {'attr': 'rvalue', 'chunk_len': 10, 'f_agg': 'min'},
  {'attr': 'rvalue', 'chunk_len': 10, 'f_agg': 'mean'},
  {'attr': 'rvalue', 'chunk_len': 10, 'f_agg': 'var'},
  {'attr': 'rvalue', 'chunk_len': 50, 'f_agg': 'max'},
  {'attr': 'rvalue', 'chunk_len': 50, 'f_agg': 'min'},
  {'attr': 'rvalue', 'chunk_len': 50, 'f_agg': 'mean'},
  {'attr': 'rvalue', 'chunk_len': 50, 'f_agg': 'var'},
  {'attr': 'intercept', 'chunk_len': 5, 'f_agg': 'max'},
  {'attr': 'intercept', 'chunk_len': 5, 'f_agg': 'min'},
  {'attr': 'intercept', 'chunk_len': 5, 'f_agg': 'mean'},
  {'attr': 'intercept', 'chunk_len': 5, 'f_agg': 'var'},
  {'attr': 'intercept', 'chunk_len': 10, 'f_agg': 'max'},
  {'attr': 'intercept', 'chunk_len': 10, 'f_agg': 'min'},
  {'attr': 'intercept', 'chunk_len': 10, 'f_agg': 'mean'},
  {'attr': 'intercept', 'chunk_len': 10, 'f_agg': 'var'},
  {'attr': 'intercept', 'chunk_len': 50, 'f_agg': 'max'},
  {'attr': 'intercept', 'chunk_len': 50, 'f_agg': 'min'},
  {'attr': 'intercept', 'chunk_len': 50, 'f_agg': 'mean'},
  {'attr': 'intercept', 'chunk_len': 50, 'f_agg': 'var'},
  {'attr': 'slope', 'chunk_len': 5, 'f_agg': 'max'},
  {'attr': 'slope', 'chunk_len': 5, 'f_agg': 'min'},
  {'attr': 'slope', 'chunk_len': 5, 'f_agg': 'mean'},
  {'attr': 'slope', 'chunk_len': 5, 'f_agg': 'var'},
  {'attr': 'slope', 'chunk_len': 10, 'f_agg': 'max'},
  {'attr': 'slope', 'chunk_len': 10, 'f_agg': 'min'},
  {'attr': 'slope', 'chunk_len': 10, 'f_agg': 'mean'},
  {'attr': 'slope', 'chunk_len': 10, 'f_agg': 'var'},
  {'attr': 'slope', 'chunk_len': 50, 'f_agg': 'max'},
  {'attr': 'slope', 'chunk_len': 50, 'f_agg': 'min'},
  {'attr': 'slope', 'chunk_len': 50, 'f_agg': 'mean'},
  {'attr': 'slope', 'chunk_len': 50, 'f_agg': 'var'},
  {'attr': 'stderr', 'chunk_len': 5, 'f_agg': 'max'},
  {'attr': 'stderr', 'chunk_len': 5, 'f_agg': 'min'},
  {'attr': 'stderr', 'chunk_len': 5, 'f_agg': 'mean'},
  {'attr': 'stderr', 'chunk_len': 5, 'f_agg': 'var'},
  {'attr': 'stderr', 'chunk_len': 10, 'f_agg': 'max'},
  {'attr': 'stderr', 'chunk_len': 10, 'f_agg': 'min'},
  {'attr': 'stderr', 'chunk_len': 10, 'f_agg': 'mean'},
  {'attr': 'stderr', 'chunk_len': 10, 'f_agg': 'var'},
  {'attr': 'stderr', 'chunk_len': 50, 'f_agg': 'max'},
  {'attr': 'stderr', 'chunk_len': 50, 'f_agg': 'min'},
  {'attr': 'stderr', 'chunk_len': 50, 'f_agg': 'mean'},
  {'attr': 'stderr', 'chunk_len': 50, 'f_agg': 'var'}],
 'approximate_entropy': [{'m': 2, 'r': 0.1},
  {'m': 2, 'r': 0.3},
  {'m': 2, 'r': 0.5},
  {'m': 2, 'r': 0.7},
  {'m': 2, 'r': 0.9}],
 'ar_coefficient': [{'coeff': 0, 'k': 10},
  {'coeff': 1, 'k': 10},
  {'coeff': 2, 'k': 10},
  {'coeff': 3, 'k': 10},
  {'coeff': 4, 'k': 10}],
 'augmented_dickey_fuller': [{'attr': 'teststat'},
  {'attr': 'pvalue'},
  {'attr': 'usedlag'}],
 'autocorrelation': [{'lag': 0},
  {'lag': 1},
  {'lag': 2},
  {'lag': 3},
  {'lag': 4},
  {'lag': 5},
  {'lag': 6},
  {'lag': 7},
  {'lag': 8},
  {'lag': 9}],
 'binned_entropy': [{'max_bins': 10}],
 'c3': [{'lag': 1}, {'lag': 2}, {'lag': 3}],
 'change_quantiles': [{'f_agg': 'mean', 'isabs': False, 'qh': 0.2, 'ql': 0.0},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.2, 'ql': 0.0},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.2, 'ql': 0.0},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.2, 'ql': 0.0},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.4, 'ql': 0.0},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.4, 'ql': 0.0},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.4, 'ql': 0.0},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.4, 'ql': 0.0},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.6, 'ql': 0.0},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.6, 'ql': 0.0},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.6, 'ql': 0.0},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.6, 'ql': 0.0},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.8, 'ql': 0.0},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.8, 'ql': 0.0},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.8, 'ql': 0.0},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.8, 'ql': 0.0},
  {'f_agg': 'mean', 'isabs': False, 'qh': 1.0, 'ql': 0.0},
  {'f_agg': 'var', 'isabs': False, 'qh': 1.0, 'ql': 0.0},
  {'f_agg': 'mean', 'isabs': True, 'qh': 1.0, 'ql': 0.0},
  {'f_agg': 'var', 'isabs': True, 'qh': 1.0, 'ql': 0.0},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.2, 'ql': 0.2},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.2, 'ql': 0.2},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.2, 'ql': 0.2},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.2, 'ql': 0.2},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.4, 'ql': 0.2},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.4, 'ql': 0.2},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.4, 'ql': 0.2},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.4, 'ql': 0.2},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.6, 'ql': 0.2},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.6, 'ql': 0.2},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.6, 'ql': 0.2},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.6, 'ql': 0.2},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.8, 'ql': 0.2},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.8, 'ql': 0.2},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.8, 'ql': 0.2},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.8, 'ql': 0.2},
  {'f_agg': 'mean', 'isabs': False, 'qh': 1.0, 'ql': 0.2},
  {'f_agg': 'var', 'isabs': False, 'qh': 1.0, 'ql': 0.2},
  {'f_agg': 'mean', 'isabs': True, 'qh': 1.0, 'ql': 0.2},
  {'f_agg': 'var', 'isabs': True, 'qh': 1.0, 'ql': 0.2},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.2, 'ql': 0.4},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.2, 'ql': 0.4},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.2, 'ql': 0.4},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.2, 'ql': 0.4},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.4, 'ql': 0.4},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.4, 'ql': 0.4},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.4, 'ql': 0.4},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.4, 'ql': 0.4},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.6, 'ql': 0.4},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.6, 'ql': 0.4},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.6, 'ql': 0.4},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.6, 'ql': 0.4},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.8, 'ql': 0.4},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.8, 'ql': 0.4},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.8, 'ql': 0.4},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.8, 'ql': 0.4},
  {'f_agg': 'mean', 'isabs': False, 'qh': 1.0, 'ql': 0.4},
  {'f_agg': 'var', 'isabs': False, 'qh': 1.0, 'ql': 0.4},
  {'f_agg': 'mean', 'isabs': True, 'qh': 1.0, 'ql': 0.4},
  {'f_agg': 'var', 'isabs': True, 'qh': 1.0, 'ql': 0.4},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.2, 'ql': 0.6},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.2, 'ql': 0.6},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.2, 'ql': 0.6},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.2, 'ql': 0.6},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.4, 'ql': 0.6},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.4, 'ql': 0.6},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.4, 'ql': 0.6},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.4, 'ql': 0.6},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.6, 'ql': 0.6},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.6, 'ql': 0.6},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.6, 'ql': 0.6},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.6, 'ql': 0.6},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.8, 'ql': 0.6},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.8, 'ql': 0.6},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.8, 'ql': 0.6},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.8, 'ql': 0.6},
  {'f_agg': 'mean', 'isabs': False, 'qh': 1.0, 'ql': 0.6},
  {'f_agg': 'var', 'isabs': False, 'qh': 1.0, 'ql': 0.6},
  {'f_agg': 'mean', 'isabs': True, 'qh': 1.0, 'ql': 0.6},
  {'f_agg': 'var', 'isabs': True, 'qh': 1.0, 'ql': 0.6},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.2, 'ql': 0.8},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.2, 'ql': 0.8},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.2, 'ql': 0.8},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.2, 'ql': 0.8},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.4, 'ql': 0.8},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.4, 'ql': 0.8},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.4, 'ql': 0.8},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.4, 'ql': 0.8},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.6, 'ql': 0.8},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.6, 'ql': 0.8},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.6, 'ql': 0.8},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.6, 'ql': 0.8},
  {'f_agg': 'mean', 'isabs': False, 'qh': 0.8, 'ql': 0.8},
  {'f_agg': 'var', 'isabs': False, 'qh': 0.8, 'ql': 0.8},
  {'f_agg': 'mean', 'isabs': True, 'qh': 0.8, 'ql': 0.8},
  {'f_agg': 'var', 'isabs': True, 'qh': 0.8, 'ql': 0.8},
  {'f_agg': 'mean', 'isabs': False, 'qh': 1.0, 'ql': 0.8},
  {'f_agg': 'var', 'isabs': False, 'qh': 1.0, 'ql': 0.8},
  {'f_agg': 'mean', 'isabs': True, 'qh': 1.0, 'ql': 0.8},
  {'f_agg': 'var', 'isabs': True, 'qh': 1.0, 'ql': 0.8}],
 'count_above_mean': None,
 'count_below_mean': None,
 'cwt_coefficients': [{'coeff': 0, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 0, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 0, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 0, 'w': 20, 'widths': (2, 5, 10, 20)},
  {'coeff': 1, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 1, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 1, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 1, 'w': 20, 'widths': (2, 5, 10, 20)},
  {'coeff': 2, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 2, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 2, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 2, 'w': 20, 'widths': (2, 5, 10, 20)},
  {'coeff': 3, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 3, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 3, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 3, 'w': 20, 'widths': (2, 5, 10, 20)},
  {'coeff': 4, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 4, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 4, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 4, 'w': 20, 'widths': (2, 5, 10, 20)},
  {'coeff': 5, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 5, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 5, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 5, 'w': 20, 'widths': (2, 5, 10, 20)},
  {'coeff': 6, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 6, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 6, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 6, 'w': 20, 'widths': (2, 5, 10, 20)},
  {'coeff': 7, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 7, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 7, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 7, 'w': 20, 'widths': (2, 5, 10, 20)},
  {'coeff': 8, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 8, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 8, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 8, 'w': 20, 'widths': (2, 5, 10, 20)},
  {'coeff': 9, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 9, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 9, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 9, 'w': 20, 'widths': (2, 5, 10, 20)},
  {'coeff': 10, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 10, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 10, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 10, 'w': 20, 'widths': (2, 5, 10, 20)},
  {'coeff': 11, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 11, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 11, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 11, 'w': 20, 'widths': (2, 5, 10, 20)},
  {'coeff': 12, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 12, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 12, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 12, 'w': 20, 'widths': (2, 5, 10, 20)},
  {'coeff': 13, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 13, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 13, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 13, 'w': 20, 'widths': (2, 5, 10, 20)},
  {'coeff': 14, 'w': 2, 'widths': (2, 5, 10, 20)},
  {'coeff': 14, 'w': 5, 'widths': (2, 5, 10, 20)},
  {'coeff': 14, 'w': 10, 'widths': (2, 5, 10, 20)},
  {'coeff': 14, 'w': 20, 'widths': (2, 5, 10, 20)}],
 'fft_coefficient': [{'attr': 'real', 'coeff': 0},
  {'attr': 'real', 'coeff': 1},
  {'attr': 'real', 'coeff': 2},
  {'attr': 'real', 'coeff': 3},
  {'attr': 'real', 'coeff': 4},
  {'attr': 'real', 'coeff': 5},
  {'attr': 'real', 'coeff': 6},
  {'attr': 'real', 'coeff': 7},
  {'attr': 'real', 'coeff': 8},
  {'attr': 'real', 'coeff': 9},
  {'attr': 'real', 'coeff': 10},
  {'attr': 'real', 'coeff': 11},
  {'attr': 'real', 'coeff': 12},
  {'attr': 'real', 'coeff': 13},
  {'attr': 'real', 'coeff': 14},
  {'attr': 'real', 'coeff': 15},
  {'attr': 'real', 'coeff': 16},
  {'attr': 'real', 'coeff': 17},
  {'attr': 'real', 'coeff': 18},
  {'attr': 'real', 'coeff': 19},
  {'attr': 'real', 'coeff': 20},
  {'attr': 'real', 'coeff': 21},
  {'attr': 'real', 'coeff': 22},
  {'attr': 'real', 'coeff': 23},
  {'attr': 'real', 'coeff': 24},
  {'attr': 'real', 'coeff': 25},
  {'attr': 'real', 'coeff': 26},
  {'attr': 'real', 'coeff': 27},
  {'attr': 'real', 'coeff': 28},
  {'attr': 'real', 'coeff': 29},
  {'attr': 'real', 'coeff': 30},
  {'attr': 'real', 'coeff': 31},
  {'attr': 'real', 'coeff': 32},
  {'attr': 'real', 'coeff': 33},
  {'attr': 'real', 'coeff': 34},
  {'attr': 'real', 'coeff': 35},
  {'attr': 'real', 'coeff': 36},
  {'attr': 'real', 'coeff': 37},
  {'attr': 'real', 'coeff': 38},
  {'attr': 'real', 'coeff': 39},
  {'attr': 'real', 'coeff': 40},
  {'attr': 'real', 'coeff': 41},
  {'attr': 'real', 'coeff': 42},
  {'attr': 'real', 'coeff': 43},
  {'attr': 'real', 'coeff': 44},
  {'attr': 'real', 'coeff': 45},
  {'attr': 'real', 'coeff': 46},
  {'attr': 'real', 'coeff': 47},
  {'attr': 'real', 'coeff': 48},
  {'attr': 'real', 'coeff': 49},
  {'attr': 'real', 'coeff': 50},
  {'attr': 'real', 'coeff': 51},
  {'attr': 'real', 'coeff': 52},
  {'attr': 'real', 'coeff': 53},
  {'attr': 'real', 'coeff': 54},
  {'attr': 'real', 'coeff': 55},
  {'attr': 'real', 'coeff': 56},
  {'attr': 'real', 'coeff': 57},
  {'attr': 'real', 'coeff': 58},
  {'attr': 'real', 'coeff': 59},
  {'attr': 'real', 'coeff': 60},
  {'attr': 'real', 'coeff': 61},
  {'attr': 'real', 'coeff': 62},
  {'attr': 'real', 'coeff': 63},
  {'attr': 'real', 'coeff': 64},
  {'attr': 'real', 'coeff': 65},
  {'attr': 'real', 'coeff': 66},
  {'attr': 'real', 'coeff': 67},
  {'attr': 'real', 'coeff': 68},
  {'attr': 'real', 'coeff': 69},
  {'attr': 'real', 'coeff': 70},
  {'attr': 'real', 'coeff': 71},
  {'attr': 'real', 'coeff': 72},
  {'attr': 'real', 'coeff': 73},
  {'attr': 'real', 'coeff': 74},
  {'attr': 'real', 'coeff': 75},
  {'attr': 'real', 'coeff': 76},
  {'attr': 'real', 'coeff': 77},
  {'attr': 'real', 'coeff': 78},
  {'attr': 'real', 'coeff': 79},
  {'attr': 'real', 'coeff': 80},
  {'attr': 'real', 'coeff': 81},
  {'attr': 'real', 'coeff': 82},
  {'attr': 'real', 'coeff': 83},
  {'attr': 'real', 'coeff': 84},
  {'attr': 'real', 'coeff': 85},
  {'attr': 'real', 'coeff': 86},
  {'attr': 'real', 'coeff': 87},
  {'attr': 'real', 'coeff': 88},
  {'attr': 'real', 'coeff': 89},
  {'attr': 'real', 'coeff': 90},
  {'attr': 'real', 'coeff': 91},
  {'attr': 'real', 'coeff': 92},
  {'attr': 'real', 'coeff': 93},
  {'attr': 'real', 'coeff': 94},
  {'attr': 'real', 'coeff': 95},
  {'attr': 'real', 'coeff': 96},
  {'attr': 'real', 'coeff': 97},
  {'attr': 'real', 'coeff': 98},
  {'attr': 'real', 'coeff': 99},
  {'attr': 'imag', 'coeff': 0},
  {'attr': 'imag', 'coeff': 1},
  {'attr': 'imag', 'coeff': 2},
  {'attr': 'imag', 'coeff': 3},
  {'attr': 'imag', 'coeff': 4},
  {'attr': 'imag', 'coeff': 5},
  {'attr': 'imag', 'coeff': 6},
  {'attr': 'imag', 'coeff': 7},
  {'attr': 'imag', 'coeff': 8},
  {'attr': 'imag', 'coeff': 9},
  {'attr': 'imag', 'coeff': 10},
  {'attr': 'imag', 'coeff': 11},
  {'attr': 'imag', 'coeff': 12},
  {'attr': 'imag', 'coeff': 13},
  {'attr': 'imag', 'coeff': 14},
  {'attr': 'imag', 'coeff': 15},
  {'attr': 'imag', 'coeff': 16},
  {'attr': 'imag', 'coeff': 17},
  {'attr': 'imag', 'coeff': 18},
  {'attr': 'imag', 'coeff': 19},
  {'attr': 'imag', 'coeff': 20},
  {'attr': 'imag', 'coeff': 21},
  {'attr': 'imag', 'coeff': 22},
  {'attr': 'imag', 'coeff': 23},
  {'attr': 'imag', 'coeff': 24},
  {'attr': 'imag', 'coeff': 25},
  {'attr': 'imag', 'coeff': 26},
  {'attr': 'imag', 'coeff': 27},
  {'attr': 'imag', 'coeff': 28},
  {'attr': 'imag', 'coeff': 29},
  {'attr': 'imag', 'coeff': 30},
  {'attr': 'imag', 'coeff': 31},
  {'attr': 'imag', 'coeff': 32},
  {'attr': 'imag', 'coeff': 33},
  {'attr': 'imag', 'coeff': 34},
  {'attr': 'imag', 'coeff': 35},
  {'attr': 'imag', 'coeff': 36},
  {'attr': 'imag', 'coeff': 37},
  {'attr': 'imag', 'coeff': 38},
  {'attr': 'imag', 'coeff': 39},
  {'attr': 'imag', 'coeff': 40},
  {'attr': 'imag', 'coeff': 41},
  {'attr': 'imag', 'coeff': 42},
  {'attr': 'imag', 'coeff': 43},
  {'attr': 'imag', 'coeff': 44},
  {'attr': 'imag', 'coeff': 45},
  {'attr': 'imag', 'coeff': 46},
  {'attr': 'imag', 'coeff': 47},
  {'attr': 'imag', 'coeff': 48},
  {'attr': 'imag', 'coeff': 49},
  {'attr': 'imag', 'coeff': 50},
  {'attr': 'imag', 'coeff': 51},
  {'attr': 'imag', 'coeff': 52},
  {'attr': 'imag', 'coeff': 53},
  {'attr': 'imag', 'coeff': 54},
  {'attr': 'imag', 'coeff': 55},
  {'attr': 'imag', 'coeff': 56},
  {'attr': 'imag', 'coeff': 57},
  {'attr': 'imag', 'coeff': 58},
  {'attr': 'imag', 'coeff': 59},
  {'attr': 'imag', 'coeff': 60},
  {'attr': 'imag', 'coeff': 61},
  {'attr': 'imag', 'coeff': 62},
  {'attr': 'imag', 'coeff': 63},
  {'attr': 'imag', 'coeff': 64},
  {'attr': 'imag', 'coeff': 65},
  {'attr': 'imag', 'coeff': 66},
  {'attr': 'imag', 'coeff': 67},
  {'attr': 'imag', 'coeff': 68},
  {'attr': 'imag', 'coeff': 69},
  {'attr': 'imag', 'coeff': 70},
  {'attr': 'imag', 'coeff': 71},
  {'attr': 'imag', 'coeff': 72},
  {'attr': 'imag', 'coeff': 73},
  {'attr': 'imag', 'coeff': 74},
  {'attr': 'imag', 'coeff': 75},
  {'attr': 'imag', 'coeff': 76},
  {'attr': 'imag', 'coeff': 77},
  {'attr': 'imag', 'coeff': 78},
  {'attr': 'imag', 'coeff': 79},
  {'attr': 'imag', 'coeff': 80},
  {'attr': 'imag', 'coeff': 81},
  {'attr': 'imag', 'coeff': 82},
  {'attr': 'imag', 'coeff': 83},
  {'attr': 'imag', 'coeff': 84},
  {'attr': 'imag', 'coeff': 85},
  {'attr': 'imag', 'coeff': 86},
  {'attr': 'imag', 'coeff': 87},
  {'attr': 'imag', 'coeff': 88},
  {'attr': 'imag', 'coeff': 89},
  {'attr': 'imag', 'coeff': 90},
  {'attr': 'imag', 'coeff': 91},
  {'attr': 'imag', 'coeff': 92},
  {'attr': 'imag', 'coeff': 93},
  {'attr': 'imag', 'coeff': 94},
  {'attr': 'imag', 'coeff': 95},
  {'attr': 'imag', 'coeff': 96},
  {'attr': 'imag', 'coeff': 97},
  {'attr': 'imag', 'coeff': 98},
  {'attr': 'imag', 'coeff': 99}],
 'first_location_of_maximum': None,
 'first_location_of_minimum': None,
 'friedrich_coefficients': [{'coeff': 0, 'm': 3, 'r': 30},
  {'coeff': 1, 'm': 3, 'r': 30},
  {'coeff': 2, 'm': 3, 'r': 30},
  {'coeff': 3, 'm': 3, 'r': 30}],
 'has_duplicate': None,
 'has_duplicate_max': None,
 'has_duplicate_min': None,
 'index_mass_quantile': [{'q': 0.1},
  {'q': 0.2},
  {'q': 0.3},
  {'q': 0.4},
  {'q': 0.6},
  {'q': 0.7},
  {'q': 0.8},
  {'q': 0.9}],
 'kurtosis': None,
 'large_standard_deviation': [{'r': 0.05},
  {'r': 0.1},
  {'r': 0.15000000000000002},
  {'r': 0.2},
  {'r': 0.25},
  {'r': 0.30000000000000004},
  {'r': 0.35000000000000003},
  {'r': 0.4},
  {'r': 0.45},
  {'r': 0.5},
  {'r': 0.55},
  {'r': 0.6000000000000001},
  {'r': 0.65},
  {'r': 0.7000000000000001},
  {'r': 0.75},
  {'r': 0.8},
  {'r': 0.8500000000000001},
  {'r': 0.9},
  {'r': 0.9500000000000001}],
 'last_location_of_maximum': None,
 'last_location_of_minimum': None,
 'length': None,
 'linear_trend': [{'attr': 'pvalue'},
  {'attr': 'rvalue'},
  {'attr': 'intercept'},
  {'attr': 'slope'},
  {'attr': 'stderr'}],
 'longest_strike_above_mean': None,
 'longest_strike_below_mean': None,
 'max_langevin_fixed_point': [{'m': 3, 'r': 30}],
 'maximum': None,
 'mean': None,
 'mean_abs_change': None,
 'mean_change': None,
 'mean_second_derivate_central': None,
 'median': None,
 'minimum': None,
 'number_crossing_m': [{'m': 0}, {'m': -1}, {'m': 1}],
 'number_cwt_peaks': [{'n': 1}, {'n': 5}],
 'number_peaks': [{'n': 1}, {'n': 3}, {'n': 5}, {'n': 10}, {'n': 50}],
 'percentage_of_reoccurring_datapoints_to_all_datapoints': None,
 'percentage_of_reoccurring_values_to_all_values': None,
 'quantile': [{'q': 0.1},
  {'q': 0.2},
  {'q': 0.3},
  {'q': 0.4},
  {'q': 0.6},
  {'q': 0.7},
  {'q': 0.8},
  {'q': 0.9}],
 'range_count': [{'max': 1, 'min': -1}],
 'ratio_value_number_to_time_series_length': None,
 'sample_entropy': None,
 'skewness': None,
 'spkt_welch_density': [{'coeff': 2}, {'coeff': 5}, {'coeff': 8}],
 'standard_deviation': None,
 'sum_of_reoccurring_data_points': None,
 'sum_of_reoccurring_values': None,
 'sum_values': None,
 'symmetry_looking': [{'r': 0.0},
  {'r': 0.05},
  {'r': 0.1},
  {'r': 0.15000000000000002},
  {'r': 0.2},
  {'r': 0.25},
  {'r': 0.30000000000000004},
  {'r': 0.35000000000000003},
  {'r': 0.4},
  {'r': 0.45},
  {'r': 0.5},
  {'r': 0.55},
  {'r': 0.6000000000000001},
  {'r': 0.65},
  {'r': 0.7000000000000001},
  {'r': 0.75},
  {'r': 0.8},
  {'r': 0.8500000000000001},
  {'r': 0.9},
  {'r': 0.9500000000000001}],
 'time_reversal_asymmetry_statistic': [{'lag': 1}, {'lag': 2}, {'lag': 3}],
 'value_count': [{'value': 0},
  {'value': 1},
  {'value': nan},
  {'value': inf},
  {'value': -inf}],
 'variance': None,
 'variance_larger_than_standard_deviation': None}

You see those parameters as values in the fc_paramter dictionary? Those are the parameters of the feature extraction methods.

In detail, the value in a fc_parameters dicitonary can contain a list of dictionaries. Every dictionary in that list is one feature.

So, for example

In [14]:

settings_comprehensive['large_standard_deviation']

Out[14]:

[{'r': 0.05},
 {'r': 0.1},
 {'r': 0.15000000000000002},
 {'r': 0.2},
 {'r': 0.25},
 {'r': 0.30000000000000004},
 {'r': 0.35000000000000003},
 {'r': 0.4},
 {'r': 0.45},
 {'r': 0.5},
 {'r': 0.55},
 {'r': 0.6000000000000001},
 {'r': 0.65},
 {'r': 0.7000000000000001},
 {'r': 0.75},
 {'r': 0.8},
 {'r': 0.8500000000000001},
 {'r': 0.9},
 {'r': 0.9500000000000001}]

would trigger the calculation of 20 different 'large_standard_deviation' features, one for r=0.05, for n=0.10 up to r=0.95. Lets just take them and extract some features

In [15]:

settings_value_count = {'large_standard_deviation': settings_comprehensive['large_standard_deviation']}
settings_value_count

Out[15]:

{'large_standard_deviation': [{'r': 0.05},
  {'r': 0.1},
  {'r': 0.15000000000000002},
  {'r': 0.2},
  {'r': 0.25},
  {'r': 0.30000000000000004},
  {'r': 0.35000000000000003},
  {'r': 0.4},
  {'r': 0.45},
  {'r': 0.5},
  {'r': 0.55},
  {'r': 0.6000000000000001},
  {'r': 0.65},
  {'r': 0.7000000000000001},
  {'r': 0.75},
  {'r': 0.8},
  {'r': 0.8500000000000001},
  {'r': 0.9},
  {'r': 0.9500000000000001}]}

In [16]:

X_tsfresh = extract_features(df, column_id="id", default_fc_parameters=settings_value_count)
X_tsfresh.head()

Feature Extraction: 100%|██████████| 4/4 [00:00<00:00, 772.36it/s]

Out[16]:

variable	pressure__large_standard_deviation__r_0.05	pressure__large_standard_deviation__r_0.1	pressure__large_standard_deviation__r_0.15	pressure__large_standard_deviation__r_0.2	pressure__large_standard_deviation__r_0.25	pressure__large_standard_deviation__r_0.3	pressure__large_standard_deviation__r_0.35	pressure__large_standard_deviation__r_0.4	pressure__large_standard_deviation__r_0.45	pressure__large_standard_deviation__r_0.5	...	temperature__large_standard_deviation__r_0.5	temperature__large_standard_deviation__r_0.55	temperature__large_standard_deviation__r_0.6	temperature__large_standard_deviation__r_0.65	temperature__large_standard_deviation__r_0.7	temperature__large_standard_deviation__r_0.75	temperature__large_standard_deviation__r_0.8	temperature__large_standard_deviation__r_0.85	temperature__large_standard_deviation__r_0.9	temperature__large_standard_deviation__r_0.95
id
a	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
b	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0

2 rows × 38 columns

The nice thing is, we actually contain the parameters in the feature name, so it is possible to reconstruct how the feature was calculated.

In [17]:

from_columns(X_tsfresh)

Out[17]:

{'pressure': {'large_standard_deviation': [{'r': 0.05},
   {'r': 0.1},
   {'r': 0.15},
   {'r': 0.2},
   {'r': 0.25},
   {'r': 0.3},
   {'r': 0.35},
   {'r': 0.4},
   {'r': 0.45},
   {'r': 0.5},
   {'r': 0.55},
   {'r': 0.6},
   {'r': 0.65},
   {'r': 0.7},
   {'r': 0.75},
   {'r': 0.8},
   {'r': 0.85},
   {'r': 0.9},
   {'r': 0.95}]},
 'temperature': {'large_standard_deviation': [{'r': 0.05},
   {'r': 0.1},
   {'r': 0.15},
   {'r': 0.2},
   {'r': 0.25},
   {'r': 0.3},
   {'r': 0.35},
   {'r': 0.4},
   {'r': 0.45},
   {'r': 0.5},
   {'r': 0.55},
   {'r': 0.6},
   {'r': 0.65},
   {'r': 0.7},
   {'r': 0.75},
   {'r': 0.8},
   {'r': 0.85},
   {'r': 0.9},
   {'r': 0.95}]}}

This means that you should never change a column name. Otherwise the information how it was calculated can get lost.

variable	pressure__large_standard_deviation__r_0.05	pressure__large_standard_deviation__r_0.1	pressure__large_standard_deviation__r_0.15	pressure__large_standard_deviation__r_0.2	pressure__large_standard_deviation__r_0.25	pressure__large_standard_deviation__r_0.3	pressure__large_standard_deviation__r_0.35	pressure__large_standard_deviation__r_0.4	pressure__large_standard_deviation__r_0.45	pressure__large_standard_deviation__r_0.5	...	temperature__large_standard_deviation__r_0.5	temperature__large_standard_deviation__r_0.55	temperature__large_standard_deviation__r_0.6	temperature__large_standard_deviation__r_0.65	temperature__large_standard_deviation__r_0.7	temperature__large_standard_deviation__r_0.75	temperature__large_standard_deviation__r_0.8	temperature__large_standard_deviation__r_0.85	temperature__large_standard_deviation__r_0.9	temperature__large_standard_deviation__r_0.95
id
a	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
b	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0

variable	pressure__large_standard_deviation__r_0.05	pressure__large_standard_deviation__r_0.1	pressure__large_standard_deviation__r_0.15	pressure__large_standard_deviation__r_0.2	pressure__large_standard_deviation__r_0.25	pressure__large_standard_deviation__r_0.3	pressure__large_standard_deviation__r_0.35	pressure__large_standard_deviation__r_0.4	pressure__large_standard_deviation__r_0.45	pressure__large_standard_deviation__r_0.5	...	temperature__large_standard_deviation__r_0.5	temperature__large_standard_deviation__r_0.55	temperature__large_standard_deviation__r_0.6	temperature__large_standard_deviation__r_0.65	temperature__large_standard_deviation__r_0.7	temperature__large_standard_deviation__r_0.75	temperature__large_standard_deviation__r_0.8	temperature__large_standard_deviation__r_0.85	temperature__large_standard_deviation__r_0.9	temperature__large_standard_deviation__r_0.95
id
a	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
b	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0

variable	pressure__large_standard_deviation__r_0.05	pressure__large_standard_deviation__r_0.1	pressure__large_standard_deviation__r_0.15	pressure__large_standard_deviation__r_0.2	pressure__large_standard_deviation__r_0.25	pressure__large_standard_deviation__r_0.3	pressure__large_standard_deviation__r_0.35	pressure__large_standard_deviation__r_0.4	pressure__large_standard_deviation__r_0.45	pressure__large_standard_deviation__r_0.5	...	temperature__large_standard_deviation__r_0.5	temperature__large_standard_deviation__r_0.55	temperature__large_standard_deviation__r_0.6	temperature__large_standard_deviation__r_0.65	temperature__large_standard_deviation__r_0.7	temperature__large_standard_deviation__r_0.75	temperature__large_standard_deviation__r_0.8	temperature__large_standard_deviation__r_0.85	temperature__large_standard_deviation__r_0.9	temperature__large_standard_deviation__r_0.95
id
a	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
b	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0.0	...	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0