绘制 PCA 双标图和碎石图

1、双标图

import numpy as np
import matplotlib.pyplot as plt
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
from sklearn import datasets


# data = np.random.random((1000,10))
# y = np.random.randint(0,6,1000)

iris = datasets.load_iris()
data = iris.data
y = iris.target

# In general, it's a good idea to scale the data prior to PCA.
# scaler = StandardScaler()
# scaler.fit(data)
# data = scaler.transform(data)
pca = PCA()
x_new = pca.fit_transform(data)

def myplot(score,coeff,labels=None):
    xs = score[:,0]
    ys = score[:,1]
    n = coeff.shape[0]
    scalex = 1.0/(xs.max() - xs.min())
    scaley = 1.0/(ys.max() - ys.min())
    plt.scatter(xs * scalex,ys * scaley, c=y)
    for i in range(n):
        plt.arrow(0, 0, coeff[i,0], coeff[i,1],color='r',alpha = 1,
                  head_width=0.04,head_length=0.03,overhang=1)
        if labels is None:
            plt.text(coeff[i,0]* 1.15, coeff[i,1] * 1.15, "Var"+str(i+1), color = 'g', ha = 'center', va = 'center')
        else:
            plt.text(coeff[i,0]* 1.15, coeff[i,1] * 1.15, labels[i], color = 'g', ha = 'center', va = 'center')
    plt.xlim(-1,1)
    plt.ylim(-1,1)
    plt.xlabel("PC{}".format(1))
    plt.ylabel("PC{}".format(2))
    plt.grid()

#Call the function. Use only the 2 PCs.
myplot(x_new[:,0:2],np.transpose(pca.components_[0:2, :]),
       ["a1","a2","a3","a4","a5","a6","a7","a8","a9","a10"])
plt.show()

2、碎石图

import numpy as np
import matplotlib.pyplot as plt
from sklearn.decomposition import PCA
from sklearn import datasets


# data = np.random.random((1000,10))
# y = np.random.randint(0,6,1000)

iris = datasets.load_iris()
data = iris.data
y = iris.target

# 使用自助法随机抽样
np.random.seed(0)
sample = data[np.random.randint(0,100,100)]
var = []
for i in range(500):
    sample_n = sample[np.random.randint(0,100,100)]
    pca = PCA()
    pca.fit(sample_n)
    var.append(pca.explained_variance_ratio_)
var = np.array(var)
plt.errorbar(np.linspace(1,data.shape[1],data.shape[1]),np.mean(var,axis=0),yerr=np.std(var,axis=0),
             lw=2,elinewidth=1.5,ms=5,capsize=3,fmt='b-o') # 'r-x': k控制折线颜色，o控制点的类型

# print(pca.components_)
# print(pca.explained_variance_ratio_)
# print(np.mean(pca.components_,axis=1).sum())
# plt.plot(pca.explained_variance_ratio_,marker='o')
# plt.legend()
plt.show()

3、附录

绘图效果来自nature communications的一篇论文。

参考：Leaf-level coordination principles propagate to the ecosystem scale (https://doi.org/10.1038/s41467-023-39572-5)

此图相关R代码、数据：PCA双标图、碎石图R代码、数据