pca算法python语言代码
时间: 2023-03-13 19:17:20 浏览: 74
下面是PCA算法的Python代码:from numpy import array
from numpy import mean
from numpy import cov
from numpy.linalg import eig
# define a matrix
A = array([[1, 2], [3, 4], [5, 6]])
print(A)
# calculate the mean of each column
M = mean(A.T, axis=1)
print(M)
# center columns by subtracting column means
C = A - M
print(C)
# calculate covariance matrix of centered matrix
V = cov(C.T)
print(V)
# eigendecomposition of covariance matrix
values, vectors = eig(V)
print(vectors)
print(values)
# project data
P = vectors.T.dot(C.T)
print(P.T)
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DPC-KNN-PCA算法python完整代码
以下是DPC-KNN-PCA算法的Python完整代码,包括数据预处理、DPC-KNN-PCA算法实现和结果可视化:
```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
# 数据预处理
data = pd.read_csv('data.csv')
X = data.values[:, :-1]
y = data.values[:, -1]
# DPC-KNN-PCA算法实现
def DPC_KNN_PCA(X, k, alpha, beta, gamma):
n, m = X.shape
D = np.zeros((n, n))
for i in range(n):
for j in range(n):
D[i, j] = np.linalg.norm(X[i] - X[j])
D_sort = np.sort(D, axis=1)
idx_sort = np.argsort(D, axis=1)
K = np.zeros((n, k))
for i in range(n):
for j in range(k):
K[i, j] = idx_sort[i, j+1]
W = np.zeros((n, n))
for i in range(n):
for j in range(k):
W[int(K[i, j]), i] = 1
W = np.maximum(W, W.T)
D_bar = np.diag(np.sum(W, axis=1))
L = D_bar - W
M = np.dot(X.T, L).dot(X)
[U, S, V] = np.linalg.svd(M)
U_pca = U[:, :2]
Z = np.dot(X, U_pca)
L_pca = np.dot(U_pca.T, M).dot(U_pca)
D_pca = np.diag(np.sum(L_pca, axis=1))
L_norm = np.linalg.inv(np.sqrt(D_pca)).dot(L_pca).dot(np.linalg.inv(np.sqrt(D_pca)))
W_norm = np.exp(-alpha*L_norm) - np.eye(n)
D_norm = np.diag(np.sum(W_norm, axis=1))
L1_norm = D_norm - W_norm
L2_norm = np.linalg.inv(np.sqrt(D_norm)).dot(L_norm).dot(np.linalg.inv(np.sqrt(D_norm)))
W_dpc = np.exp(-beta*L1_norm - gamma*L2_norm) - np.eye(n)
D_dpc = np.diag(np.sum(W_dpc, axis=1))
L_dpc = D_dpc - W_dpc
return Z, L_dpc
# 运行DPC-KNN-PCA算法并可视化结果
Z, L_dpc = DPC_KNN_PCA(X, 10, 0.5, 0.1, 0.1)
plt.scatter(Z[:, 0], Z[:, 1], c=y)
plt.show()
```
pca算法 python
PCA(Principal Component Analysis)是一种常用的降维算法,可以将高维数据映射到低维空间中。下面是使用Python实现PCA的示例代码:
```python
import numpy as np
from sklearn.decomposition import PCA
# 创建示例数据
X = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
# 创建PCA对象,指定要降维的维度
pca = PCA(n_components=2)
# 对数据进行降维
X_new = pca.fit_transform(X)
# 输出降维后的数据
print(X_new)
```
在上述代码中,我们使用NumPy创建了一个3x3的矩阵作为示例数据,然后使用sklearn中的PCA类进行降维操作,指定要将数据降到2维空间中。最后输出降维后的数据。
需要注意的是,PCA算法的本质是对数据进行线性变换,将原始数据映射到一个新的坐标系中,使得新坐标系下的数据方差最大。因此,PCA算法实现的关键是求解数据的协方差矩阵及其特征向量。在实际使用中,我们可以使用现成的库函数来实现PCA算法,如上述示例代码中使用的sklearn库。