python - 如何规范seaborn distplot？

出于可重复性原因，数据集和可重复性原因，我在[此处] [1]共享它。

这就是我正在做的-从第2列开始，我正在读取当前行并将其与上一行的值进行比较。如果更大，我会继续比较。如果当前值小于上一行的值，我想将当前值(较小)除以上一个值(较大)。因此，以下代码:

这给出了以下图表。

sns.distplot(quotient, hist=False, label=protname)

正如我们从情节中看到的那样

如果quotient_times小于3，则数据-V 的商为0.8；如果quotient_times为商，则商保持0.5。
大于3。

我想对这些值进行归一化，以使第二个绘图值的y-axis在0和1之间。我们如何在Python中做到这一点？

最佳答案

前言

据我了解，默认情况下，seaborn distplot会进行kde估计。
如果您想要归一化的distplot图，则可能是因为您假设该图的Ys应该限制在[0; 1]之间。如果是这样，则堆栈溢出问题引发了kde estimators showing values above 1问题。

引用one answer:



引用importanceofbeingernest的第一条评论:



据我所知，CDF (Cumulative Density Function)的值应该在[0; 1]。

注意:所有可能的连续可拟合函数均为on SciPy site and available in the package scipy.stats

也许还看看probability mass functions？

如果您确实希望对同一图进行标准化，则应收集绘制函数(选项1)或函数定义(选项2)的实际数据点，并对其进行归一化并重新绘制。

选项1

import numpy as np
import matplotlib
import matplotlib.pyplot as plt
import seaborn as sns
import sys

print('System versions          : {}'.format(sys.version))
print('System versions          : {}'.format(sys.version_info))
print('Numpy versqion           : {}'.format(np.__version__))
print('matplotlib.pyplot version: {}'.format(matplotlib.__version__))
print('seaborn version          : {}'.format(sns.__version__))

protocols = {}

types = {"data_v": "data_v.csv"}

for protname, fname in types.items():
    col_time,col_window = np.loadtxt(fname,delimiter=',').T
    trailing_window = col_window[:-1] # "past" values at a given index
    leading_window  = col_window[1:]  # "current values at a given index
    decreasing_inds = np.where(leading_window < trailing_window)[0]
    quotient = leading_window[decreasing_inds]/trailing_window[decreasing_inds]
    quotient_times = col_time[decreasing_inds]

    protocols[protname] = {
        "col_time": col_time,
        "col_window": col_window,
        "quotient_times": quotient_times,
        "quotient": quotient,
    }

    fig, (ax1, ax2) = plt.subplots(1,2, sharey=False, sharex=False)
    g = sns.distplot(quotient, hist=True, label=protname, ax=ax1, rug=True)
    ax1.set_title('basic distplot (kde=True)')
    # get distplot line points
    line = g.get_lines()[0]
    xd = line.get_xdata()
    yd = line.get_ydata()
    # https://stackoverflow.com/questions/29661574/normalize-numpy-array-columns-in-python
    def normalize(x):
        return (x - x.min(0)) / x.ptp(0)
    #normalize points
    yd2 = normalize(yd)
    # plot them in another graph
    ax2.plot(xd, yd2)
    ax2.set_title('basic distplot (kde=True)\nwith normalized y plot values')

    plt.show()

选项2

下面，我尝试执行kde并将获得的估计值归一化。我不是统计专家，所以kde用法可能在某些方面是错误的(正如截图中所见，它与seaborn的用法不同，这是因为seaborn的工作方式比我好得多。它只是试图模仿与Scipy拟合的KDE。结果还不错(我猜)

截屏:



代码:

import numpy as np
from scipy import stats
import matplotlib
import matplotlib.pyplot as plt
import seaborn as sns
import sys

print('System versions          : {}'.format(sys.version))
print('System versions          : {}'.format(sys.version_info))
print('Numpy versqion           : {}'.format(np.__version__))
print('matplotlib.pyplot version: {}'.format(matplotlib.__version__))
print('seaborn version          : {}'.format(sns.__version__))

protocols = {}

types = {"data_v": "data_v.csv"}

for protname, fname in types.items():
    col_time,col_window = np.loadtxt(fname,delimiter=',').T
    trailing_window = col_window[:-1] # "past" values at a given index
    leading_window  = col_window[1:]  # "current values at a given index
    decreasing_inds = np.where(leading_window < trailing_window)[0]
    quotient = leading_window[decreasing_inds]/trailing_window[decreasing_inds]
    quotient_times = col_time[decreasing_inds]

    protocols[protname] = {
        "col_time": col_time,
        "col_window": col_window,
        "quotient_times": quotient_times,
        "quotient": quotient,
    }

    fig, (ax1, ax2, ax3, ax4) = plt.subplots(1,4, sharey=False, sharex=False)
    diff=quotient_times
    ax1.plot(diff, quotient, ".", label=protname, color="blue")
    ax1.set_ylim(0, 1.0001)
    ax1.set_title(protname)
    ax1.set_xlabel("quotient_times")
    ax1.set_ylabel("quotient")
    ax1.legend()

    sns.distplot(quotient, hist=True, label=protname, ax=ax2, rug=True)
    ax2.set_title('basic distplot (kde=True)')

    # taken from seaborn's source code (utils.py and distributions.py)
    def seaborn_kde_support(data, bw, gridsize, cut, clip):
        if clip is None:
            clip = (-np.inf, np.inf)
        support_min = max(data.min() - bw * cut, clip[0])
        support_max = min(data.max() + bw * cut, clip[1])
        return np.linspace(support_min, support_max, gridsize)

    kde_estim = stats.gaussian_kde(quotient, bw_method='scott')

    # manual linearization of data
    #linearized = np.linspace(quotient.min(), quotient.max(), num=500)

    # or better: mimic seaborn's internal stuff
    bw = kde_estim.scotts_factor() * np.std(quotient)
    linearized = seaborn_kde_support(quotient, bw, 100, 3, None)

    # computes values of the estimated function on the estimated linearized inputs
    Z = kde_estim.evaluate(linearized)

    # https://stackoverflow.com/questions/29661574/normalize-numpy-array-columns-in-python
    def normalize(x):
        return (x - x.min(0)) / x.ptp(0)

    # normalize so it is between 0;1
    Z2 = normalize(Z)
    for name, func in {'min': np.min, 'max': np.max}.items():
        print('{}: source={}, normalized={}'.format(name, func(Z), func(Z2)))

    # plot is different from seaborns because not exact same method applied
    ax3.plot(linearized, Z, ".", label=protname, color="orange")
    ax3.set_title('Non linearized gaussian kde values')

    # manual kde result with Y axis avalues normalized (between 0;1)
    ax4.plot(linearized, Z2, ".", label=protname, color="green")
    ax4.set_title('Normalized gaussian kde values')

    plt.show()

输出:

System versions          : 3.7.2 (default, Feb 21 2019, 17:35:59) [MSC v.1915 64 bit (AMD64)]
System versions          : sys.version_info(major=3, minor=7, micro=2, releaselevel='final', serial=0)
Numpy versqion           : 1.16.2
matplotlib.pyplot version: 3.0.2
seaborn version          : 0.9.0
min: source=0.0021601491646143518, normalized=0.0
max: source=9.67319154426489, normalized=1.0

与评论相反，标出:

[(x-min(quotient))/(max(quotient)-min(quotient)) for x in quotient]

不会改变行为!它仅更改用于内核密度估计的源数据。曲线形状将保持不变。

Quoting seaborn's distplot doc:



默认:



默认情况下使用kde。引用seaborn的kde文档:



引用SCiPy gaussian kde method doc:



请注意，我确实相信您的数据是双峰的，就像您自己提到的那样。它们看起来也很离散。据我所知，离散分布函数可能无法以连续的方式进行分析，因此拟合可能会很棘手。

这是各种法律的示例:

import numpy as np
from scipy.stats import uniform, powerlaw, logistic
import matplotlib
import matplotlib.pyplot as plt
import seaborn as sns
import sys

print('System versions          : {}'.format(sys.version))
print('System versions          : {}'.format(sys.version_info))
print('Numpy versqion           : {}'.format(np.__version__))
print('matplotlib.pyplot version: {}'.format(matplotlib.__version__))
print('seaborn version          : {}'.format(sns.__version__))

protocols = {}

types = {"data_v": "data_v.csv"}

for protname, fname in types.items():
    col_time,col_window = np.loadtxt(fname,delimiter=',').T
    trailing_window = col_window[:-1] # "past" values at a given index
    leading_window  = col_window[1:]  # "current values at a given index
    decreasing_inds = np.where(leading_window < trailing_window)[0]
    quotient = leading_window[decreasing_inds]/trailing_window[decreasing_inds]
    quotient_times = col_time[decreasing_inds]

    protocols[protname] = {
        "col_time": col_time,
        "col_window": col_window,
        "quotient_times": quotient_times,
        "quotient": quotient,
    }
    fig, [(ax1, ax2, ax3), (ax4, ax5, ax6)] = plt.subplots(2,3, sharey=False, sharex=False)
    diff=quotient_times
    ax1.plot(diff, quotient, ".", label=protname, color="blue")
    ax1.set_ylim(0, 1.0001)
    ax1.set_title(protname)
    ax1.set_xlabel("quotient_times")
    ax1.set_ylabel("quotient")
    ax1.legend()
    quotient2 = [(x-min(quotient))/(max(quotient)-min(quotient)) for x in quotient]
    print(quotient2)
    sns.distplot(quotient, hist=True, label=protname, ax=ax2, rug=True)
    ax2.set_title('basic distplot (kde=True)')
    sns.distplot(quotient2, hist=True, label=protname, ax=ax3, rug=True)
    ax3.set_title('logistic distplot')

    sns.distplot(quotient, hist=True, label=protname, ax=ax4, rug=True, kde=False, fit=uniform)
    ax4.set_title('uniform distplot')
    sns.distplot(quotient, hist=True, label=protname, ax=ax5, rug=True, kde=False, fit=powerlaw)
    ax5.set_title('powerlaw distplot')
    sns.distplot(quotient, hist=True, label=protname, ax=ax6, rug=True, kde=False, fit=logistic)
    ax6.set_title('logistic distplot')
    plt.show()

输出:

System versions          : 3.7.2 (default, Feb 21 2019, 17:35:59) [MSC v.1915 64 bit (AMD64)]
System versions          : sys.version_info(major=3, minor=7, micro=2, releaselevel='final', serial=0)
Numpy versqion           : 1.16.2
matplotlib.pyplot version: 3.0.2
seaborn version          : 0.9.0
[1.0, 0.05230125523012544, 0.0433775382360589, 0.024590765616971128, 0.05230125523012544, 0.05230125523012544, 0.05230125523012544, 0.02836946874603772, 0.05230125523012544, 0.05230125523012544, 0.05230125523012544, 0.05230125523012544, 0.03393500048652319, 0.05230125523012544, 0.05230125523012544, 0.05230125523012544, 0.0037013196009011043, 0.0, 0.05230125523012544]

截屏: