Matplotlib中的平行坐标图

Question

可以使用传统的绘图类型相对直观地查看二维和三维数据.即使使用四维数据,我们也经常可以找到显示数据的方法.但是,高于4的尺寸变得越来越难以显示.幸运的是,平行坐标图提供了一种查看更高维度结果的机制.

几个绘图包提供了平行坐标图,例如Matlab,R,VTK类型1和VTK类型2,但我没有看到如何使用Matplotlib创建一个.

1. Matplotlib中是否有内置的平行坐标图？我当然没有在画廊看到一个.
2. 如果没有内置类型,是否可以使用Matplotlib的标准功能构建平行坐标图？

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编辑:

根据以下振亚提供的答案,我开发了以下支持任意数量轴的概括.按照我在上面原始问题中发布的示例的绘图样式,每个轴都有自己的比例.我通过对每个轴点的数据进行归一化并使轴的范围为0到1来实现这一点.然后返回并为每个刻度线应用标签,在该截距处给出正确的值.

该函数通过接受可迭代的数据集来工作.每个数据集被认为是一组点,其中每个点位于不同的轴上.该示例在__main__两组30行中抓取每个轴的随机数.线条在引起线条聚类的范围内是随机的; 我想验证的行为.

这个解决方案不如内置解决方案好,因为你有奇怪的鼠标行为,而且我通过标签伪造数据范围,但在Matplotlib添加内置解决方案之前,它是可以接受的.

#!/usr/bin/python
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker

def parallel_coordinates(data_sets, style=None):

    dims = len(data_sets[0])
    x    = range(dims)
    fig, axes = plt.subplots(1, dims-1, sharey=False)

    if style is None:
        style = ['r-']*len(data_sets)

    # Calculate the limits on the data
    min_max_range = list()
    for m in zip(*data_sets):
        mn = min(m)
        mx = max(m)
        if mn == mx:
            mn -= 0.5
            mx = mn + 1.
        r  = float(mx - mn)
        min_max_range.append((mn, mx, r))

    # Normalize the data sets
    norm_data_sets = list()
    for ds in data_sets:
        nds = [(value - min_max_range[dimension][0]) / 
                min_max_range[dimension][2] 
                for dimension,value in enumerate(ds)]
        norm_data_sets.append(nds)
    data_sets = norm_data_sets

    # Plot the datasets on all the subplots
    for i, ax in enumerate(axes):
        for dsi, d in enumerate(data_sets):
            ax.plot(x, d, style[dsi])
        ax.set_xlim([x[i], x[i+1]])

    # Set the x axis ticks 
    for dimension, (axx,xx) in enumerate(zip(axes, x[:-1])):
        axx.xaxis.set_major_locator(ticker.FixedLocator([xx]))
        ticks = len(axx.get_yticklabels())
        labels = list()
        step = min_max_range[dimension][2] / (ticks - 1)
        mn   = min_max_range[dimension][0]
        for i in xrange(ticks):
            v = mn + i*step
            labels.append('%4.2f' % v)
        axx.set_yticklabels(labels)


    # Move the final axis' ticks to the right-hand side
    axx = plt.twinx(axes[-1])
    dimension += 1
    axx.xaxis.set_major_locator(ticker.FixedLocator([x[-2], x[-1]]))
    ticks = len(axx.get_yticklabels())
    step = min_max_range[dimension][2] / (ticks - 1)
    mn   = min_max_range[dimension][0]
    labels = ['%4.2f' % (mn + i*step) for i in xrange(ticks)]
    axx.set_yticklabels(labels)

    # Stack the subplots 
    plt.subplots_adjust(wspace=0)

    return plt


if __name__ == '__main__':
    import random
    base  = [0,   0,  5,   5,  0]
    scale = [1.5, 2., 1.0, 2., 2.]
    data = [[base[x] + random.uniform(0., 1.)*scale[x]
            for x in xrange(5)] for y in xrange(30)]
    colors = ['r'] * 30

    base  = [3,   6,  0,   1,  3]
    scale = [1.5, 2., 2.5, 2., 2.]
    data.extend([[base[x] + random.uniform(0., 1.)*scale[x]
                 for x in xrange(5)] for y in xrange(30)])
    colors.extend(['b'] * 30)

    parallel_coordinates(data, style=colors).show()

编辑2:

以下是绘制Fisher's Iris数据时上述代码的示例.它不如维基百科的参考图像那么好,但如果你拥有的只是Matplotlib并且你需要多维图,它是可以通过的.

Answer 1

pandas有一个平行坐标包装器:

import pandas
import matplotlib.pyplot as plt
from pandas.tools.plotting import parallel_coordinates

data = pandas.read_csv(r'C:\Python27\Lib\site-packages\pandas\tests\data\iris.csv', sep=',')
parallel_coordinates(data, 'Name')
plt.show()

源代码,他们是如何做到的:plotting.py#L494

Answer 2

我确信有更好的方法可以做到这一点,但这是一个快速而肮脏的方法(一个非常脏的方式):

#!/usr/bin/python
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker

#vectors to plot: 4D for this example
y1=[1,2.3,8.0,2.5]
y2=[1.5,1.7,2.2,2.9]

x=[1,2,3,8] # spines

fig,(ax,ax2,ax3) = plt.subplots(1, 3, sharey=False)

# plot the same on all the subplots
ax.plot(x,y1,'r-', x,y2,'b-')
ax2.plot(x,y1,'r-', x,y2,'b-')
ax3.plot(x,y1,'r-', x,y2,'b-')

# now zoom in each of the subplots 
ax.set_xlim([ x[0],x[1]])
ax2.set_xlim([ x[1],x[2]])
ax3.set_xlim([ x[2],x[3]])

# set the x axis ticks 
for axx,xx in zip([ax,ax2,ax3],x[:-1]):
  axx.xaxis.set_major_locator(ticker.FixedLocator([xx]))
ax3.xaxis.set_major_locator(ticker.FixedLocator([x[-2],x[-1]]))  # the last one

# EDIT: add the labels to the rightmost spine
for tick in ax3.yaxis.get_major_ticks():
  tick.label2On=True

# stack the subplots together
plt.subplots_adjust(wspace=0)

plt.show()

这基本上是基于Joe Kingon(Python/Matplotlib)的一个(更好的)- 有没有办法制作一个不连续的轴？.您可能还想查看同一问题的其他答案.

在这个例子中,我甚至没有尝试缩放垂直标度,因为它取决于你想要实现的目标.

编辑:这是结果

Answer 3

在回答相关问题时，我仅使用一个子图（因此它可以很容易地与其他图结合在一起）并可选择使用三次贝塞尔曲线来连接点，得出了一个版本。该图将自身调整为所需的轴数。

import matplotlib.pyplot as plt
from matplotlib.path import Path
import matplotlib.patches as patches
import numpy as np

fig, host = plt.subplots()

# create some dummy data
ynames = ['P1', 'P2', 'P3', 'P4', 'P5']
N1, N2, N3 = 10, 5, 8
N = N1 + N2 + N3
category = np.concatenate([np.full(N1, 1), np.full(N2, 2), np.full(N3, 3)])
y1 = np.random.uniform(0, 10, N) + 7 * category
y2 = np.sin(np.random.uniform(0, np.pi, N)) ** category
y3 = np.random.binomial(300, 1 - category / 10, N)
y4 = np.random.binomial(200, (category / 6) ** 1/3, N)
y5 = np.random.uniform(0, 800, N)

# organize the data
ys = np.dstack([y1, y2, y3, y4, y5])[0]
ymins = ys.min(axis=0)
ymaxs = ys.max(axis=0)
dys = ymaxs - ymins
ymins -= dys * 0.05  # add 5% padding below and above
ymaxs += dys * 0.05
dys = ymaxs - ymins

# transform all data to be compatible with the main axis
zs = np.zeros_like(ys)
zs[:, 0] = ys[:, 0]
zs[:, 1:] = (ys[:, 1:] - ymins[1:]) / dys[1:] * dys[0] + ymins[0]


axes = [host] + [host.twinx() for i in range(ys.shape[1] - 1)]
for i, ax in enumerate(axes):
    ax.set_ylim(ymins[i], ymaxs[i])
    ax.spines['top'].set_visible(False)
    ax.spines['bottom'].set_visible(False)
    if ax != host:
        ax.spines['left'].set_visible(False)
        ax.yaxis.set_ticks_position('right')
        ax.spines["right"].set_position(("axes", i / (ys.shape[1] - 1)))

host.set_xlim(0, ys.shape[1] - 1)
host.set_xticks(range(ys.shape[1]))
host.set_xticklabels(ynames, fontsize=14)
host.tick_params(axis='x', which='major', pad=7)
host.spines['right'].set_visible(False)
host.xaxis.tick_top()
host.set_title('Parallel Coordinates Plot', fontsize=18)

colors = plt.cm.tab10.colors
for j in range(N):
    # to just draw straight lines between the axes:
    # host.plot(range(ys.shape[1]), zs[j,:], c=colors[(category[j] - 1) % len(colors) ])

    # create bezier curves
    # for each axis, there will a control vertex at the point itself, one at 1/3rd towards the previous and one
    #   at one third towards the next axis; the first and last axis have one less control vertex
    # x-coordinate of the control vertices: at each integer (for the axes) and two inbetween
    # y-coordinate: repeat every point three times, except the first and last only twice
    verts = list(zip([x for x in np.linspace(0, len(ys) - 1, len(ys) * 3 - 2, endpoint=True)],
                     np.repeat(zs[j, :], 3)[1:-1]))
    # for x,y in verts: host.plot(x, y, 'go') # to show the control points of the beziers
    codes = [Path.MOVETO] + [Path.CURVE4 for _ in range(len(verts) - 1)]
    path = Path(verts, codes)
    patch = patches.PathPatch(path, facecolor='none', lw=1, edgecolor=colors[category[j] - 1])
    host.add_patch(patch)
plt.tight_layout()
plt.show()

这是虹膜数据集的类似代码。反转第二个轴以避免一些交叉线。

import matplotlib.pyplot as plt
from matplotlib.path import Path
import matplotlib.patches as patches
import numpy as np
from sklearn import datasets

iris = datasets.load_iris()
ynames = iris.feature_names
ys = iris.data
ymins = ys.min(axis=0)
ymaxs = ys.max(axis=0)
dys = ymaxs - ymins
ymins -= dys * 0.05  # add 5% padding below and above
ymaxs += dys * 0.05

ymaxs[1], ymins[1] = ymins[1], ymaxs[1]  # reverse axis 1 to have less crossings
dys = ymaxs - ymins

# transform all data to be compatible with the main axis
zs = np.zeros_like(ys)
zs[:, 0] = ys[:, 0]
zs[:, 1:] = (ys[:, 1:] - ymins[1:]) / dys[1:] * dys[0] + ymins[0]

fig, host = plt.subplots(figsize=(10,4))

axes = [host] + [host.twinx() for i in range(ys.shape[1] - 1)]
for i, ax in enumerate(axes):
    ax.set_ylim(ymins[i], ymaxs[i])
    ax.spines['top'].set_visible(False)
    ax.spines['bottom'].set_visible(False)
    if ax != host:
        ax.spines['left'].set_visible(False)
        ax.yaxis.set_ticks_position('right')
        ax.spines["right"].set_position(("axes", i / (ys.shape[1] - 1)))

host.set_xlim(0, ys.shape[1] - 1)
host.set_xticks(range(ys.shape[1]))
host.set_xticklabels(ynames, fontsize=14)
host.tick_params(axis='x', which='major', pad=7)
host.spines['right'].set_visible(False)
host.xaxis.tick_top()
host.set_title('Parallel Coordinates Plot — Iris', fontsize=18, pad=12)

colors = plt.cm.Set2.colors
legend_handles = [None for _ in iris.target_names]
for j in range(ys.shape[0]):
    # create bezier curves
    verts = list(zip([x for x in np.linspace(0, len(ys) - 1, len(ys) * 3 - 2, endpoint=True)],
                     np.repeat(zs[j, :], 3)[1:-1]))
    codes = [Path.MOVETO] + [Path.CURVE4 for _ in range(len(verts) - 1)]
    path = Path(verts, codes)
    patch = patches.PathPatch(path, facecolor='none', lw=2, alpha=0.7, edgecolor=colors[iris.target[j]])
    legend_handles[iris.target[j]] = patch
    host.add_patch(patch)
host.legend(legend_handles, iris.target_names,
            loc='lower center', bbox_to_anchor=(0.5, -0.18),
            ncol=len(iris.target_names), fancybox=True, shadow=True)
plt.tight_layout()
plt.show()

Answer 4

使用pandas时(如theta所示),无法独立缩放轴.

你找不到不同垂直轴的原因是因为没有.我们的平行坐标是通过绘制垂直线和一些标签来"伪造"其他两个轴.

https://github.com/pydata/pandas/issues/7083#issuecomment-74253671

Answer 5

我已将 @JohanC 代码改编为 pandas 数据框，并将其扩展为也可以处理分类变量。该代码需要更多改进，例如能够将数值变量作为数据框中的第一个变量，但我认为目前这很好。

# Paths:
path_data = "data/"

# Packages:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib.colors import LinearSegmentedColormap
from matplotlib.path import Path
import matplotlib.patches as patches
from functools import reduce

# Display options:
pd.set_option("display.width", 1200)
pd.set_option("display.max_columns", 300)
pd.set_option("display.max_rows", 300)

# Dataset:
df = pd.read_csv(path_data + "nasa_exoplanets.csv")
df_varnames = pd.read_csv(path_data + "nasa_exoplanets_var_names.csv")

# Variables (the first variable must be categoric):
my_vars = ["discoverymethod", "pl_orbper", "st_teff", "disc_locale", "sy_gaiamag"]
my_vars_names = reduce(pd.DataFrame.append,
                       map(lambda i: df_varnames[df_varnames["var"] == i], my_vars))
my_vars_names = my_vars_names["var_name"].values.tolist()

# Adapt the data:
df = df.loc[df["pl_letter"] == "d"]
df_plot = df[my_vars]
df_plot = df_plot.dropna()
df_plot = df_plot.reset_index(drop = True)

# Convert to numeric matrix:
ym = []
dics_vars = []
for v, var in enumerate(my_vars):
    if df_plot[var].dtype.kind not in ["i", "u", "f"]:
        dic_var = dict([(val, c) for c, val in enumerate(df_plot[var].unique())])
        dics_vars += [dic_var]
        ym += [[dic_var[i] for i in df_plot[var].tolist()]]
    else:
        ym += [df_plot[var].tolist()]
ym = np.array(ym).T

# Padding:
ymins = ym.min(axis = 0)
ymaxs = ym.max(axis = 0)
dys = ymaxs - ymins
ymins -= dys*0.05
ymaxs += dys*0.05

# Reverse some axes for better visual:
axes_to_reverse = [0, 1]
for a in axes_to_reverse:
    ymaxs[a], ymins[a] = ymins[a], ymaxs[a]
dys = ymaxs - ymins

# Adjust to the main axis:
zs = np.zeros_like(ym)
zs[:, 0] = ym[:, 0]
zs[:, 1:] = (ym[:, 1:] - ymins[1:])/dys[1:]*dys[0] + ymins[0]

# Colors:
n_levels = len(dics_vars[0])
my_colors = ["#F41E1E", "#F4951E", "#F4F01E", "#4EF41E", "#1EF4DC", "#1E3CF4", "#F41EF3"]
cmap = LinearSegmentedColormap.from_list("my_palette", my_colors)
my_palette = [cmap(i/n_levels) for i in np.array(range(n_levels))]

# Plot:
fig, host_ax = plt.subplots(
    figsize = (20, 10),
    tight_layout = True
)

# Make the axes:
axes = [host_ax] + [host_ax.twinx() for i in range(ym.shape[1] - 1)]
dic_count = 0
for i, ax in enumerate(axes):
    ax.set_ylim(
        bottom = ymins[i],
        top = ymaxs[i]
    )
    ax.spines.top.set_visible(False)
    ax.spines.bottom.set_visible(False)
    ax.ticklabel_format(style = 'plain')
    if ax != host_ax:
        ax.spines.left.set_visible(False)
        ax.yaxis.set_ticks_position("right")
        ax.spines.right.set_position(
            (
                "axes",
                 i/(ym.shape[1] - 1)
             )
        )
    if df_plot.iloc[:, i].dtype.kind not in ["i", "u", "f"]:
        dic_var_i = dics_vars[dic_count]
        ax.set_yticks(
            range(len(dic_var_i))
        )
        ax.set_yticklabels(
            [key_val for key_val in dics_vars[dic_count].keys()]
        )
        dic_count += 1
host_ax.set_xlim(
    left = 0,
    right = ym.shape[1] - 1
)
host_ax.set_xticks(
    range(ym.shape[1])
)
host_ax.set_xticklabels(
    my_vars_names,
    fontsize = 14
)
host_ax.tick_params(
    axis = "x",
    which = "major",
    pad = 7
)

# Make the curves:
host_ax.spines.right.set_visible(False)
host_ax.xaxis.tick_top()
for j in range(ym.shape[0]):
    verts = list(zip([x for x in np.linspace(0, len(ym) - 1, len(ym)*3 - 2, 
                                             endpoint = True)],
                 np.repeat(zs[j, :], 3)[1: -1]))
    codes = [Path.MOVETO] + [Path.CURVE4 for _ in range(len(verts) - 1)]
    path = Path(verts, codes)
    color_first_cat_var = my_palette[dics_vars[0][df_plot.iloc[j, 0]]]
    patch = patches.PathPatch(
        path,
        facecolor = "none",
        lw = 2,
        alpha = 0.7,
        edgecolor = color_first_cat_var
    )
    host_ax.add_patch(patch)