数学建模模型代码python

### 数学建模中的Python代码实例

#### 使用线性回归进行预测分析
线性回归是一种常用的数学建模方法，用于建立输入变量和输出变量之间的关系。

import numpy as np
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler

# 创建数据集
X = np.random.rand(100, 1) * 10
y = 2.5 * X.squeeze() + np.random.randn(100)

# 数据标准化处理[^1]
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)

# 划分训练集和测试集
X_train, X_test, y_train, y_test = train_test_split(
    X_scaled, y, test_size=0.2, random_state=42)

# 构建并训练模型
model = LinearRegression()
model.fit(X_train, y_train)

# 输出模型参数
print(f"Coefficients: {model.coef_}")
print(f"Intercept: {model.intercept_}")

# 预测新样本
predictions = model.predict(X_test)

#### 基于隐马尔可夫模型(HMM)的时间序列分类
HMM广泛应用于时间序列数据分析，在自然语言处理等领域有重要应用价值。

from hmmlearn.hmm import GaussianHMM
import numpy as np

# 准备特征向量批次生成器函数[^2]
def batch_generator(features, labels, batch_size):
    n_samples = features.shape[0]
    indices = list(range(n_samples))
    while True:
        np.random.shuffle(indices)
        for i in range(0, n_samples, batch_size):
            excerpt = indices[i:i + batch_size]
            yield features[excerpt], labels[excerpt]

# 初始化HMM模型
n_components = 3  # 状态数量
hmm_model = GaussianHMM(n_components=n_components, covariance_type="diag", n_iter=1000)

# 训练HMM模型
for batch_features, _ in batch_generator(training_data['features'], training_data['labels'], batch_size=64):
    hmm_model.fit(batch_features)

# 序列解码得到最可能的状态路径
logprob, hidden_states = hmm_model.decode(test_sequence, algorithm='viterbi')

#### 文本分类任务下的朴素贝叶斯算法实现
对于大规模文本数据集，可以采用朴素贝叶斯作为基础分类器来进行情感分析等工作。

from sklearn.feature_extraction.text import CountVectorizer
from sklearn.naive_bayes import MultinomialNB
from sklearn.pipeline import Pipeline

# 加载预处理后的语料库信息[^3]
corpus = ["This movie was excellent...", "I did not like this film at all..."]
target = [1, 0]  # 正面评价标记为1；负面评价标记为0

# 定义管道流程
text_clf = Pipeline([
    ('vect', CountVectorizer()),
    ('clf', MultinomialNB())
])

# 模型拟合与评估
text_clf.fit(corpus, target)
predicted = text_clf.predict(["Another great experience watching this picture."])
print(predicted)