机器学习特征工程，全面指南！（下）

# pandas自带的聚合函数
mean(): Compute mean of groupssum(): Compute sum of group valuessize(): Compute group sizescount(): Compute count of groupstd(): Standard deviation of groupsvar(): Compute variance of groupssem(): Standard error of the mean of groupsfirst(): Compute first of group valueslast(): Compute last of group valuesnth() : Take nth value, or a subset if n is a listmin(): Compute min of group valuesmax(): Compute max of group values# 自定义函数def median(x):    return np.median(x)def variation_coefficient(x):    mean = np.mean(x)    if mean != 0:        return np.std(x) / mean    else:        return np.nandef variance(x):    return np.var(x)def skewness(x):    if not isinstance(x, pd.Series):        x = pd.Series(x)    return pd.Series.skew(x)def kurtosis(x):    if not isinstance(x, pd.Series):        x = pd.Series(x)    return pd.Series.kurtosis(x)def standard_deviation(x):    return np.std(x)def large_standard_deviation(x):    if (np.max(x)-np.min(x)) == 0:        return np.nan    else:        return np.std(x)/(np.max(x)-np.min(x))def variation_coefficient(x):    mean = np.mean(x)    if mean != 0:        return np.std(x) / mean    else:        return np.nandef variance_std_ratio(x):    y = np.var(x)    if y != 0:        return y/np.sqrt(y)    else:        return np.nandef ratio_beyond_r_sigma(x, r):    if x.size == 0:        return np.nan    else:        return np.sum(np.abs(x - np.mean(x)) > r * np.asarray(np.std(x))) / x.sizedef range_ratio(x):    mean_median_difference = np.abs(np.mean(x) - np.median(x))    max_min_difference = np.max(x) - np.min(x)    if max_min_difference == 0:        return np.nan    else:        return mean_median_difference / max_min_difference
def has_duplicate_max(x):    return np.sum(x == np.max(x)) >= 2def has_duplicate_min(x):    return np.sum(x == np.min(x)) >= 2def has_duplicate(x):    return x.size != np.unique(x).sizedef count_duplicate_max(x):    return np.sum(x == np.max(x))def count_duplicate_min(x):    return np.sum(x == np.min(x))def count_duplicate(x):    return x.size - np.unique(x).sizedef sum_values(x):    if len(x) == 0:        return 0    return np.sum(x)def log_return(list_stock_prices):    return np.log(list_stock_prices).diff() def realized_volatility(series):    return np.sqrt(np.sum(series**2))def realized_abs_skew(series):    return np.power(np.abs(np.sum(series**3)),1/3)def realized_skew(series):    return np.sign(np.sum(series**3))*np.power(np.abs(np.sum(series**3)),1/3)def realized_vol_skew(series):    return np.power(np.abs(np.sum(series**6)),1/6)def realized_quarticity(series):    return np.power(np.sum(series**4),1/4)def count_unique(series):    return len(np.unique(series))def count(series):    return series.size#drawdons functions are minedef maximum_drawdown(series):    series = np.asarray(series)    if len(series)<2:        return 0    k = series[np.argmax(np.maximum.accumulate(series) - series)]    i = np.argmax(np.maximum.accumulate(series) - series)    if len(series[:i])<1:        return np.NaN    else:        j = np.max(series[:i])    return j-kdef maximum_drawup(series):    series = np.asarray(series)    if len(series)<2:        return 0
    series = - series    k = series[np.argmax(np.maximum.accumulate(series) - series)]    i = np.argmax(np.maximum.accumulate(series) - series)    if len(series[:i])<1:        return np.NaN    else:        j = np.max(series[:i])    return j-kdef drawdown_duration(series):    series = np.asarray(series)    if len(series)<2:        return 0    k = np.argmax(np.maximum.accumulate(series) - series)    i = np.argmax(np.maximum.accumulate(series) - series)    if len(series[:i]) == 0:        j=k    else:        j = np.argmax(series[:i])    return k-jdef drawup_duration(series):    series = np.asarray(series)    if len(series)<2:        return 0    series=-series    k = np.argmax(np.maximum.accumulate(series) - series)    i = np.argmax(np.maximum.accumulate(series) - series)    if len(series[:i]) == 0:        j=k    else:        j = np.argmax(series[:i])    return k-jdef max_over_min(series):    if len(series)<2:        return 0    if np.min(series) == 0:        return np.nan    return np.max(series)/np.min(series)def mean_n_absolute_max(x, number_of_maxima = 1):    """ Calculates the arithmetic mean of the n absolute maximum values of the time series."""    assert (        number_of_maxima > 0    ), f" number_of_maxima={number_of_maxima} which is not greater than 1"    n_absolute_maximum_values = np.sort(np.absolute(x))[-number_of_maxima:]    return np.mean(n_absolute_maximum_values) if len(x) > number_of_maxima else np.NaNdef count_above(x, t):    if len(x)==0:        return np.nan    else:        return np.sum(x >= t) / len(x)def count_below(x, t):    if len(x)==0:        return np.nan    else:        return np.sum(x <= t) / len(x)#number of valleys = number_peaks(-x, n)def number_peaks(x, n):    """    Calculates the number of peaks of at least support n in the time series x. A peak of support n is defined as a    subsequence of x where a value occurs, which is bigger than its n neighbours to the left and to the right.    """    x_reduced = x[n:-n]    res = None    for i in range(1, n + 1):        result_first = x_reduced > _roll(x, i)[n:-n]        if res is None:            res = result_first        else:            res &= result_first        res &= x_reduced > _roll(x, -i)[n:-n]    return np.sum(res)def mean_abs_change(x):    return np.mean(np.abs(np.diff(x)))def mean_change(x):    x = np.asarray(x)    return (x[-1] - x[0]) / (len(x) - 1) if len(x) > 1 else np.NaNdef mean_second_derivative_central(x):    x = np.asarray(x)    return (x[-1] - x[-2] - x[1] + x[0]) / (2 * (len(x) - 2)) if len(x) > 2 else np.NaNdef root_mean_square(x):    return np.sqrt(np.mean(np.square(x))) if len(x) > 0 else np.NaNdef absolute_sum_of_changes(x):    return np.sum(np.abs(np.diff(x)))def longest_strike_below_mean(x):    if not isinstance(x, (np.ndarray, pd.Series)):        x = np.asarray(x)    return np.max(_get_length_sequences_where(x < np.mean(x))) if x.size > 0 else 0def longest_strike_above_mean(x):    if not isinstance(x, (np.ndarray, pd.Series)):        x = np.asarray(x)    return np.max(_get_length_sequences_where(x > np.mean(x))) if x.size > 0 else 0def count_above_mean(x):    m = np.mean(x)    return np.where(x > m)[0].sizedef count_below_mean(x):    m = np.mean(x)    return np.where(x < m)[0].sizedef last_location_of_maximum(x):    x = np.asarray(x)    return 1.0 - np.argmax(x[::-1]) / len(x) if len(x) > 0 else np.NaNdef first_location_of_maximum(x):    if not isinstance(x, (np.ndarray, pd.Series)):        x = np.asarray(x)    return np.argmax(x) / len(x) if len(x) > 0 else np.NaNdef last_location_of_minimum(x):    x = np.asarray(x)    return 1.0 - np.argmin(x[::-1]) / len(x) if len(x) > 0 else np.NaNdef first_location_of_minimum(x):    if not isinstance(x, (np.ndarray, pd.Series)):        x = np.asarray(x)    return np.argmin(x) / len(x) if len(x) > 0 else np.NaN# Test non-consecutive non-reoccuring values ?def percentage_of_reoccurring_values_to_all_values(x):    if len(x) == 0:        return np.nan    unique, counts = np.unique(x, return_counts=True)    if counts.shape[0] == 0:        return 0    return np.sum(counts > 1) / float(counts.shape[0])def percentage_of_reoccurring_datapoints_to_all_datapoints(x):    if len(x) == 0:        return np.nan    if not isinstance(x, pd.Series):        x = pd.Series(x)    value_counts = x.value_counts()    reoccuring_values = value_counts[value_counts > 1].sum()    if np.isnan(reoccuring_values):        return 0    return reoccuring_values / x.sizedef sum_of_reoccurring_values(x):    unique, counts = np.unique(x, return_counts=True)    counts[counts < 2] = 0    counts[counts > 1] = 1    return np.sum(counts * unique)def sum_of_reoccurring_data_points(x):    unique, counts = np.unique(x, return_counts=True)    counts[counts < 2] = 0    return np.sum(counts * unique)def ratio_value_number_to_time_series_length(x):    if not isinstance(x, (np.ndarray, pd.Series)):        x = np.asarray(x)    if x.size == 0:        return np.nan    return np.unique(x).size / x.sizedef abs_energy(x):    if not isinstance(x, (np.ndarray, pd.Series)):        x = np.asarray(x)    return np.dot(x, x)def quantile(x, q):    if len(x) == 0:        return np.NaN    return np.quantile(x, q)# crossing the mean ? other levels ? def number_crossing_m(x, m):    if not isinstance(x, (np.ndarray, pd.Series)):        x = np.asarray(x)    # From https://stackoverflow.com/questions/3843017/efficiently-detect-sign-changes-in-python    positive = x > m    return np.where(np.diff(positive))[0].sizedef absolute_maximum(x):    return np.max(np.absolute(x)) if len(x) > 0 else np.NaNdef value_count(x, value):    if not isinstance(x, (np.ndarray, pd.Series)):        x = np.asarray(x)    if np.isnan(value):        return np.isnan(x).sum()    else:        return x[x == value].sizedef range_count(x, min, max):    return np.sum((x >= min) & (x < max))def mean_diff(x):    return np.nanmean(np.diff(x.values))