60 个“特征工程”计算函数（Python 代码）

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



推荐阅读

（点击标题可跳转阅读）

《机器学习 100 天》视频讲解

公众号历史文章精选

我的深度学习入门路线


重磅！

1700多页的《人工智能学习路线、干货分享全集》PDF文档



扫描下方二维码，添加我的微信，领取1700多页的《人工智能学习路线、干货分享全集》PDF文档（一定要备注：入群 + 地点 + 学校/公司。例如：入群+上海+复旦。 



长按扫码，申请入群



感谢你的分享，点赞，在看三连  


   

  

 



    
相关推荐

    
  • 解约！211 新校区，不建了！
    • 
    
  • AI浪潮，Spring也赶上了！？
    • 
    
  • 2024年上半年大模型发展回顾暨7月份半月度KG/RAG/LLM技术总结
    • 
    
  • 如果网站的 Cookie 超过 4K，会发生什么情况？
    • 
    
  • 上手 Day.js 日期处理库
    • 
    
  • 飞书一键复制网页内容为图片原理
    • 
    
  • 大脑一片空白：难倒 90% 前端的 Vue 面试题！
    • 
    
  • 万万没想到，用浏览器打开终端竟这么容易实现
    • 
    
  • 萝卜快写、萝卜快画来了？自动写小说、自动画漫画，两个最新的开源项目
    • 
    
  • 高手必知的Linux三剑客 (grep、sed、awk)
    • 
    
  • 列表是怎么实现的？解密列表的数据结构
    • 
    
  • 一文读懂数据血缘分析原理与建设方法
    • 
    
  • 橙单，一个免费的代码生成神器
    • 
    
  • Git版本管理工具，每个工程师都应该知道的基础操作!
    • 
    
  • Obsidian插件：Make.md为你量身打造一个完美的个人系统。
    • 
    
  • 从零预训练LLAMA3的完整指南：一个文件，探索Scaling Law
    • 
    
  • 开源仅 1 天就斩获近万星！超越 RAG、让大模型拥有超强记忆力的 Mem0 火了！
    • 
    
  • 拿下NeurIPS 2024金牌。
    • 
    
  • 博士申请 | 香港理工大学石杰明老师招收大数据/机器学习方向全奖博士/博后
    • 
    
  • 文末送书 | 连续25年美国统计类教材排名第一，这本统计学神书中文版来啦！
    •