"将半高斯滤波器应用于python中的分箱时间序列数据"
[英]Applying a half-gaussian filter to binned time series data in python
问题描述
I am binning some time series data, I need to apply a half-normal filter to the binned data.
我正在对一些时间序列数据进行分箱，我需要对分箱数据应用半正态过滤器。 How can I do this in python?我怎样才能在python中做到这一点？ I've provided a toy example bellow.我在下面提供了一个玩具示例。 I need Xbinned to be smoothed with a half-gaussian filter with std of 0.25 (or what ever).我需要使用标准为 0.25（或其他任何值）的半高斯滤波器对 Xbinned 进行平滑处理。 I'm pretty sure the half gaussian should be facing the forward time direction.我很确定半高斯应该面向正向时间方向。
import numpy as np
X = np.random.randint(2, size=100) #example random process
bin_size = 5
Xbinned = []
for i in range(0, len(X)+1, bin_size):
Xbinned.append(sum(X[i:i+(bin_size-1)])/bin_size)
1 个解决方案
解决方案1
0 2022-02-06 03:03:39
How to implement half-gaussian filtering如何实现半高斯滤波<\/h2>
Scipy has a function called scipy.ndimage.gaussian_filter()<\/a> . Scipy 有一个名为scipy.ndimage.gaussian_filter()<\/a>的函数。 It nearly implements what we want here.它几乎实现了我们在这里想要的。 Unfortunately, there's no option to use a half-gaussian instead of a gaussian.不幸的是，没有选择使用半高斯而不是高斯。 However, scipy is open-source, so we can just take the source code<\/a> and modify it to be a half-gaussian.但是，scipy 是开源的，所以我们可以直接获取源代码<\/a>并将其修改为半高斯。
import scipy.ndimage def halfgaussian_kernel1d(sigma, radius): """ Computes a 1-D Half-Gaussian convolution kernel. """ sigma2 = sigma * sigma x = np.arange(0, radius+1) phi_x = np.exp(-0.5 \/ sigma2 * x ** 2) phi_x = phi_x \/ phi_x.sum() return phi_x def halfgaussian_filter1d(input, sigma, axis=-1, output=None, mode="constant", cval=0.0, truncate=4.0): """ Convolves a 1-D Half-Gaussian convolution kernel. """ sd = float(sigma) # make the radius of the filter equal to truncate standard deviations lw = int(truncate * sd + 0.5) weights = halfgaussian_kernel1d(sigma, lw) origin = -lw \/\/ 2 return scipy.ndimage.convolve1d(input, weights, axis, output, mode, cval, origin)<\/code><\/pre>A short summary of how this works:这是如何工作的简短摘要：
- First, it generates a convolution kernel.首先，它生成一个卷积核。 It uses the formula
e^(-1\/2 * (x\/sigma)^2)<\/code> to generate the gaussian distribution.e^(-1\/2 * (x\/sigma)^2)<\/code>来生成高斯分布。It keeps going until you're 4 standard deviations away from the center.Next, it convolves that kernel against your signal.接下来，它将内核与您的信号进行卷积。 It adjusts the kernel to start at the current timestep instead of being centered on the current timestep.Trying this on your signal, I get a result like this:
array([0.59979879, 0.6 , 0.40006707, 0.59993293, 0.79993293, 0.40013414, 0.20006707, 0.59986586, 0.40006707, 0.4 , 0.99979879, 0.00033535, 0.59979879, 0.40006707, 0.00013414, 0.59979879, 0.20013414, 0.00006707, 0.19993293, 0.59986586])<\/code><\/pre>
If you pick a standard deviation of 0.25, that is going to have almost no effect on your signal.
[0.99966465 0.00033535]<\/code> .[0.99966465 0.00033535]<\/code> 。In other words, this has less than a 0.1% effect on the signal.
I'd recommend using a larger sigma value.我建议使用更大的 sigma 值。
Off by one error因一个错误而关闭<\/h2>Also, I want to point out the off-by-one error here:
for i in range(0, len(X)+1, bin_size): Xbinned.append(sum(X[i:i+(bin_size-1)])\/bin_size)<\/code><\/pre>Numpy ranges are not inclusive, so a range of
i<\/code> toi+(bin_size-1)<\/code> actually captures 4 elements, not 5.Numpy 范围不包含在内，因此i<\/code>到i+(bin_size-1)<\/code>的范围实际上捕获 4 个元素，而不是 5 个。
To fix this, you can change it to this:要解决此问题，您可以将其更改为：for i in range(0, len(X), bin_size): Xbinned.append(X[i:i+bin_size].mean())<\/code><\/pre>(Also, I fixed an off-by-one error in the loop specification and used a numpy shortcut for finding the mean.) （另外，我修复了循环规范中的一个错误，并使用了一个 numpy 快捷方式来查找平均值。）
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