diff --git a/docs/gaussian_mixture.md b/docs/gaussian_mixture.md
index 4f2ea7cbce..5bc0e45fb0 100644
--- a/docs/gaussian_mixture.md
+++ b/docs/gaussian_mixture.md
@@ -44,3 +44,34 @@
 - 异常检测
 - 图像分割
 - 语音识别
+- 
+## 数学公式
+
+GMM 的概率密度函数为：
+
+`p(x) = Σ π_k * N(x | μ_k, Σ_k)`
+
+其中：
+- K 为高斯成分数量
+- π_k 为第 k 个成分的混合权重，满足 Σπ_k = 1
+- N(x | μ_k, Σ_k) 为第 k 个高斯分布
+
+## 代码示例
+
+使用 scikit-learn 拟合高斯混合模型：
+
+```python
+from sklearn.mixture import GaussianMixture
+import numpy as np
+
+# 生成示例数据
+X = np.random.randn(300, 2)
+
+# 创建并训练模型
+gmm = GaussianMixture(n_components=3, random_state=0)
+gmm.fit(X)
+
+# 预测类别
+labels = gmm.predict(X)
+print("各成分权重:", gmm.weights_)
+```
diff --git a/ignore_users.json b/ignore_users.json
index ed695fe839..584595373e 100644
--- a/ignore_users.json
+++ b/ignore_users.json
@@ -1,5 +1,8 @@
 [
-    "Haidong Wang",
-    "donghaiwang",
-    "whd@hutb.edu.cn"
-]
\ No newline at end of file
+    {
+        "name": "Haidong Wang",
+        "github": "donghaiwang",
+        "email": "whd@hutb.edu.cn",
+        "role": "author"
+    }
+]
diff --git a/requirements.txt b/requirements.txt
index b158fd9ffe..be48c60531 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,2 +1,4 @@
-mkdocs
-python-markdown-math
+mkdocs>=1.5.0
+mkdocs-material>=9.0.0
+python-markdown-math>=0.8
+mkdocs-git-revision-date-localized-plugin>=1.2.0