偏最小二乘回归分析 - 数学建模社区-数学中国

import numpy as np
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from sklearn.cross_decomposition import PLSRegression& W3 m* b \' y+ J. L. t
from sklearn.preprocessing import StandardScaler& B3 e. ]# m o3 s9 e, x
import matplotlib.pyplot as plt4 Y- E' j4 y/ |! o" L& D" P* Y. q
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# 原始数据，自变量X和因变量y* g2 C7 @+ X4 ]: m
X = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])
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y = np.array([1, 2, 3, 4]), v. `: y# O1 P5 w' n. l( V! q
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# 对自变量进行标准化处理
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scaler = StandardScaler()
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X_scaled = scaler.fit_transform(X)
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# 创建PLSRegression对象，并指定主成分个数为29 V+ J/ |: o1 H
pls = PLSRegression(n_components=2). c5 U3 G1 S6 z+ R. A) D4 B
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# 进行偏最小二乘回归分析7 u% W' l4 u k2 ~, M
pls.fit(X_scaled, y)9 `: e5 S" e' B& q7 W
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# 获得预测值6 o# K# |, F; K# o9 f9 [0 _
y_pred = pls.predict(X_scaled) q0 M& H" d, i3 n8 S( F+ R; ]
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# 绘制原始数据和预测值) n* U% x( u W* E4 S7 n8 q
plt.figure(figsize=(8, 6))
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plt.scatter(y, y_pred, c='b', label='Predicted vs. Observed')
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plt.plot([min(y), max(y)], [min(y), max(y)], 'k--', lw=2, label='Perfect Fit')' h! d# O5 g, g; N
plt.xlabel('Observed')
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plt.ylabel('Predicted')
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plt.title('PLS Regression')% _6 Z" y7 l* y5 C8 x
plt.legend()4 Y' E: V0 T# I$ z5 T' c' @) S* r
plt.grid(True)' u1 N; ?5 f- h
plt.show()1 V U! Y# P% W% G& k e9 b
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