使用Matplotlib进行主成分分析

Question

我有一个大约1500行、包含6个变量的数据集，我用主成分分析（PCA）处理这些数据，然后用以下代码展示出来：

from matplotlib.mlab import PCA
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d import proj3d
import numpy as np

data = np.array(data)

    try:
        results = PCA(data)
    except:
        raise

    #this will return an array of variance percentages for each component
    print results.fracs

    #
    print results.Wt

    #this will return a 2d array of the data projected into PCA space
    print results.Y 

    x = []
    y = []
    z = []
    for item in results.Y:
        x.append(item[0])
        y.append(item[1])
        z.append(item[2])

    fig1 = plt.figure() # Make a plotting figure
    ax = Axes3D(fig1) # use the plotting figure to create a Axis3D object.
    pltData = [x,y,z] 
    ax.scatter(pltData[0], pltData[1], pltData[2], 'bo') # make a scatter plot of blue dots from the data

    # make simple, bare axis lines through space:
    xAxisLine = ((min(pltData[0]), max(pltData[0])), (0, 0), (0,0)) # 2 points make the x-axis line at the data extrema along x-axis 
    ax.plot(xAxisLine[0], xAxisLine[1], xAxisLine[2], 'r') # make a red line for the x-axis.
    yAxisLine = ((0, 0), (min(pltData[1]), max(pltData[1])), (0,0)) # 2 points make the y-axis line at the data extrema along y-axis
    ax.plot(yAxisLine[0], yAxisLine[1], yAxisLine[2], 'r') # make a red line for the y-axis.
    zAxisLine = ((0, 0), (0,0), (min(pltData[2]), max(pltData[2]))) # 2 points make the z-axis line at the data extrema along z-axis
    ax.plot(zAxisLine[0], zAxisLine[1], zAxisLine[2], 'r') # make a red line for the z-axis.

    # label the axes 
    ax.set_xlabel("x-axis label") 
    ax.set_ylabel("y-axis label")
    ax.set_zlabel("y-axis label")
    ax.set_title("The title of the plot")

    plt.show() # show the plot

现在我想要做的是，比如说，如何根据另一个数据变量来给显示的点上色。举个例子，如果我在每一行数据中添加一个叫做颜色的变量，取值范围是 ['蓝色', '红色', '绿色']，那么我能用这个变量来给点上色吗？

Answer 1

我觉得最简单的方法就是，像你说的那样，先准备一个颜色列表，比如 colors=[ 'blue', 'red', 'green',...]，然后把每个数据点单独画出来：

for i,xi in enumerate(x):
    ax.scatter(x[i],y[i],z[i],color=colors[i])

还有一种方法是看看 这个问题。在这里，你可以给每个点分配一个数字，这个数字会在颜色图上显示为一种颜色。这样你就可以展示某个参数的渐变效果。

编辑：为了回应你的评论，颜色可以用一个包含3个值的元组（RGB）来表示，这些值的范围在0到1之间。

from matplotlib.colors import Normalize
xnorm=Normalize(x.min(),x.max())
ynorm=Normalize(y.min(),y.max())
colors=[(xnorm(x[i]),ynorm(y[i]),0) for i in range(x.size)]
ax.scatter(x,y,c=colors)