近期一些朋友询问我关于如何做特征工程的问题，有没有什么适合初学者的有效操作。特征工程的问题往往需要具体问题具体分析，当然也有一些暴力的策略，可以在竞赛初赛前期可以带来较大提升，而很多竞赛往往依赖这些信息就可以拿到非常好的效果，剩余的则需要结合业务逻辑以及很多其他的技巧，此处我们将平时用得最多的聚合操作罗列在下方。最近刚好看到一篇文章汇总了非常多的聚合函数，就摘录在下方，供许多初入竞赛的朋友参考。聚合特征汇总pandas自带的聚合函数其它重要聚合函数其它重要聚合函数&分类分别如下。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.nan def 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.nan def variance_std_ratio(x): y = np.var(x) if y != 0: return y/np.sqrt(y) else: return np.nan def 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.size def 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)) >= 2 def has_duplicate_min(x): return np.sum(x == np.min(x)) >= 2 def has_duplicate(x): return x.size != np.unique(x).size def 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).size def 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 mine def 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-k def 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-k def 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-j def 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-j def 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.NaN def 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.NaN def 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.NaN def root_mean_square(x): return np.sqrt(np.mean(np.square(x))) if len(x) > 0 else np.NaN def 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 0 def 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 0 def count_above_mean(x): m = np.mean(x) return np.where(x > m)[0].size def count_below_mean(x): m = np.mean(x) return np.where(x < m)[0].size def last_location_of_maximum(x): x = np.asarray(x) return 1.0 - np.argmax(x[::-1]) / len(x) if len(x) > 0 else np.NaN def 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.NaN def last_location_of_minimum(x): x = np.asarray(x) return 1.0 - np.argmin(x[::-1]) / len(x) if len(x) > 0 else np.NaN def 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.size def 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.size def 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].size def absolute_maximum(x): return np.max(np.absolute(x)) if len(x) > 0 else np.NaN def 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].size def range_count(x, min, max): return np.sum((x >= min) & (x < max)) def mean_diff(x): return np.nanmean(np.diff(x.values))base_stats = ['mean','sum','size','count','std','first','last','min','max',median,skewness,kurtosis] higher_order_stats = [abs_energy,root_mean_square,sum_values,realized_volatility,realized_abs_skew,realized_skew,realized_vol_skew,realized_quarticity] additional_quantiles = [quantile_01,quantile_025,quantile_075,quantile_09] other_min_max = [absolute_maximum,max_over_min] min_max_positions = [last_location_of_maximum,first_location_of_maximum,last_location_of_minimum,first_location_of_minimum] peaks = [number_peaks_2, mean_n_absolute_max_2, number_peaks_5, mean_n_absolute_max_5, number_peaks_10, mean_n_absolute_max_10] counts = [count_unique,count,count_above_0,count_below_0,value_count_0,count_near_0] reoccuring_values = [count_above_mean,count_below_mean,percentage_of_reoccurring_values_to_all_values,percentage_of_reoccurring_datapoints_to_all_datapoints,sum_of_reoccurring_values,sum_of_reoccurring_data_points,ratio_value_number_to_time_series_length] count_duplicate = [count_duplicate,count_duplicate_min,count_duplicate_max] variations = [mean_diff,mean_abs_change,mean_change,mean_second_derivative_central,absolute_sum_of_changes,number_crossing_0] ranges = [variance_std_ratio,ratio_beyond_01_sigma,ratio_beyond_02_sigma,ratio_beyond_03_sigma,large_standard_deviation,range_ratio]参考文献：https://www.kaggle.com/code/lucasmorin/amex-feature-engineering-2-aggreg-functions