Python:滑动窗口均值，忽略缺失数据

问题描述

我目前正在尝试处理具有缺失值的实验时间序列数据集.我想计算这个数据集的滑动窗口平均值，同时处理 nan 值.我这样做的正确方法是在每个窗口内计算有限元素的总和并将其除以它们的数量.这种非线性迫使我使用非卷积方法来面对这个问题，因此我在这部分过程中遇到了严重的时间瓶颈.作为我正在尝试完成的代码示例，我提出以下内容:

I am currently trying to process an experimental timeseries dataset, which has missing values. I would like to calculate the sliding windowed mean of this dataset along time, while handling nan values. The correct way for me to do it is to compute inside each window the sum of the finite elements and divide it with their number. This nonlinearity forces me to use non convolutional methods to face this problem, thus I have a severe time bottleneck in this part of the process. As a code example of what I am trying to accomplish I present the following:

import numpy as np
#Construct sample data
n = 50
n_miss = 20
win_size = 3
data= np.random.random(50)
data[np.random.randint(0,n-1, n_miss)] = None

#Compute mean
result = np.zeros(data.size)
for count in range(data.size):
    part_data = data[max(count - (win_size - 1) / 2, 0): min(count + (win_size + 1) / 2, data.size)]
    mask = np.isfinite(part_data)
    if np.sum(mask) != 0:
        result[count] = np.sum(part_data[mask]) / np.sum(mask)
    else:
        result[count] = None
print 'Input:	',data
print 'Output:	',result

带输出:

Input:  [ 0.47431791  0.17620835  0.78495647  0.79894688  0.58334064  0.38068788
  0.87829696         nan  0.71589171         nan  0.70359557  0.76113969
  0.13694387  0.32126573  0.22730891         nan  0.35057169         nan
  0.89251851  0.56226354  0.040117           nan  0.37249799  0.77625334
         nan         nan         nan         nan  0.63227417  0.92781944
  0.99416471  0.81850753  0.35004997         nan  0.80743783  0.60828597
         nan  0.01410721         nan         nan  0.6976317          nan
  0.03875394  0.60924066  0.22998065         nan  0.34476729  0.38090961
         nan  0.2021964 ]
Output: [ 0.32526313  0.47849424  0.5867039   0.72241466  0.58765847  0.61410849
  0.62949242  0.79709433  0.71589171  0.70974364  0.73236763  0.53389305
  0.40644977  0.22850617  0.27428732  0.2889403   0.35057169  0.6215451
  0.72739103  0.49829968  0.30119027  0.20630749  0.57437567  0.57437567
  0.77625334         nan         nan  0.63227417  0.7800468   0.85141944
  0.91349722  0.7209074   0.58427875  0.5787439   0.7078619   0.7078619
  0.31119659  0.01410721  0.01410721  0.6976317   0.6976317   0.36819282
  0.3239973   0.29265842  0.41961066  0.28737397  0.36283845  0.36283845
  0.29155301  0.2021964 ]

这个结果可以通过 numpy 操作产生，而不使用 for 循环吗?

Can this result be produced by numpy operations, without using a for loop?

推荐答案

这是一个基于卷积的方法，使用 np.convolve -

Here's a convolution based approach using np.convolve -

mask = np.isnan(data)
K = np.ones(win_size,dtype=int)
out = np.convolve(np.where(mask,0,data), K)/np.convolve(~mask,K)

请注意，这将在两侧有一个额外的元素.

Please note that this would have one extra element on either sides.

如果您使用的是 2D 数据，我们可以使用 Scipy 的二维卷积.

If you are working with 2D data, we can use Scipy's 2D convolution.

方法-

def original_app(data, win_size):
    #Compute mean
    result = np.zeros(data.size)
    for count in range(data.size):
        part_data = data[max(count - (win_size - 1) / 2, 0): 
                 min(count + (win_size + 1) / 2, data.size)]
        mask = np.isfinite(part_data)
        if np.sum(mask) != 0:
            result[count] = np.sum(part_data[mask]) / np.sum(mask)
        else:
            result[count] = None
    return result

def numpy_app(data, win_size):     
    mask = np.isnan(data)
    K = np.ones(win_size,dtype=int)
    out = np.convolve(np.where(mask,0,data), K)/np.convolve(~mask,K)
    return out[1:-1]  # Slice out the one-extra elems on sides

示例运行 -

In [118]: #Construct sample data
     ...: n = 50
     ...: n_miss = 20
     ...: win_size = 3
     ...: data= np.random.random(50)
     ...: data[np.random.randint(0,n-1, n_miss)] = np.nan
     ...: 

In [119]: original_app(data, win_size = 3)
Out[119]: 
array([ 0.88356487,  0.86829731,  0.85249541,  0.83776219,         nan,
               nan,  0.61054015,  0.63111926,  0.63111926,  0.65169837,
        0.1857301 ,  0.58335324,  0.42088104,  0.5384565 ,  0.31027752,
        0.40768907,  0.3478563 ,  0.34089655,  0.55462903,  0.71784816,
        0.93195716,         nan,  0.41635575,  0.52211653,  0.65053379,
        0.76762282,  0.72888574,  0.35250449,  0.35250449,  0.14500637,
        0.06997668,  0.22582318,  0.18621848,  0.36320784,  0.19926647,
        0.24506199,  0.09983572,  0.47595439,  0.79792941,  0.5982114 ,
        0.42389375,  0.28944089,  0.36246113,  0.48088139,  0.71105449,
        0.60234163,  0.40012839,  0.45100475,  0.41768466,  0.41768466])

In [120]: numpy_app(data, win_size = 3)
__main__:36: RuntimeWarning: invalid value encountered in divide
Out[120]: 
array([ 0.88356487,  0.86829731,  0.85249541,  0.83776219,         nan,
               nan,  0.61054015,  0.63111926,  0.63111926,  0.65169837,
        0.1857301 ,  0.58335324,  0.42088104,  0.5384565 ,  0.31027752,
        0.40768907,  0.3478563 ,  0.34089655,  0.55462903,  0.71784816,
        0.93195716,         nan,  0.41635575,  0.52211653,  0.65053379,
        0.76762282,  0.72888574,  0.35250449,  0.35250449,  0.14500637,
        0.06997668,  0.22582318,  0.18621848,  0.36320784,  0.19926647,
        0.24506199,  0.09983572,  0.47595439,  0.79792941,  0.5982114 ,
        0.42389375,  0.28944089,  0.36246113,  0.48088139,  0.71105449,
        0.60234163,  0.40012839,  0.45100475,  0.41768466,  0.41768466])

运行时测试-

In [122]: #Construct sample data
     ...: n = 50000
     ...: n_miss = 20000
     ...: win_size = 3
     ...: data= np.random.random(n)
     ...: data[np.random.randint(0,n-1, n_miss)] = np.nan
     ...: 

In [123]: %timeit original_app(data, win_size = 3)
1 loops, best of 3: 1.51 s per loop

In [124]: %timeit numpy_app(data, win_size = 3)
1000 loops, best of 3: 1.09 ms per loop

In [125]: import pandas as pd

# @jdehesa's pandas solution
In [126]: %timeit pd.Series(data).rolling(window=3, min_periods=1).mean()
100 loops, best of 3: 3.34 ms per loop

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