Improve knn classification

2_knn/knn_classification.ipynb

@@ -62,7 +62,7 @@
    "source": [
     "### 1.1 距离计算\n",
     "\n",
-    "要度量空间中点距离的话，有好几种度量方式，比如常见的曼哈顿距离计算、欧式距离计算等等。不过通常 KNN 算法中使用的是欧式距离。这里只是简单说一下，拿二维平面为例，二维空间两个点的欧式距离计算公式如下：\n",
+    "要度量空间中点距离的话，有好几种度量方式，比如常见的曼哈顿距离计算、欧式距离计算等等。不过通常 kNN 算法中使用的是欧式距离。这里只是简单说一下，拿二维平面为例，二维空间两个点的欧式距离计算公式如下：\n",
     "$$\n",
     "d = \\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\n",
     "$$\n",
@@ -72,7 +72,7 @@
     "d(p, q) = \\sqrt{ (p_1-q_1)^2 + (p_1-q_1)^2 + ... + (p_n-q_n)^2 } = \\sqrt{ \\sum_{i=1,n} (p_i-q_i)^2}\n",
     "$$\n",
     "\n",
-    "这样我们就明白了如何计算距离。kNN 算法最简单粗暴的就是将 `预测点` 与 `所有点` 距离进行计算，然后保存并排序，选出前面 k 个值看看哪些类别比较多。"
+    "kNN 算法最简单粗暴的就是将 `预测点` 与 `所有点` 距离进行计算，然后保存并排序，选出前面 k 个值看看哪些类别比较多。"
    ]
   },
   {
@@ -82,7 +82,7 @@
     "\n",
     "## 2. 机器学习的思维模型\n",
     "\n",
-    "针对kNN方法的提出机器学习的思维模型，在给定问题的情况下，是如何思考并解决机器学习问题\n",
+    "针对kNN方法从原理、算法、到实现，可以得出机器学习的思维模型，在给定问题的情况下，是如何思考并解决机器学习问题。\n",
     "\n",
     "![machine learning - methodology](images/ml_methodology.png)\n",
     "\n",
@@ -112,7 +112,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
@@ -146,7 +146,7 @@
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
     "\n",
-    "# data generation\n",
+    "# 生成模拟数据\n",
     "np.random.seed(314)\n",
     "\n",
     "data_size1 = 100\n",
@@ -158,7 +158,7 @@
     "y2 = [1 for _ in range(data_size2)]\n",
     "\n",
     "\n",
-    "# all sample data\n",
+    "# 合并生成全部数据\n",
     "x = np.concatenate((x1, x2), axis=0)\n",
     "y = np.concatenate((y1, y2), axis=0)\n",
     "\n",
@@ -167,7 +167,7 @@
     "x = x[shuffled_index]\n",
     "y = y[shuffled_index]\n",
     "\n",
-    "# split train & test\n",
+    "# 分割训练与测试数据\n",
     "split_index = int(data_size_all*0.7)\n",
     "x_train = x[:split_index]\n",
     "y_train = y[:split_index]\n",
@@ -175,12 +175,14 @@
     "y_test = y[split_index:]\n",
     "\n",
     "\n",
-    "# plot data\n",
+    "# 绘制结果\n",
     "plt.scatter(x_train[:,0], x_train[:,1], c=y_train, marker='.')\n",
     "plt.title(\"train data\")\n",
+    "plt.savefig(\"knn_train_data.pdf\")\n",
     "plt.show()\n",
     "plt.scatter(x_test[:,0], x_test[:,1], c=y_test, marker='.')\n",
     "plt.title(\"test data\")\n",
+    "plt.savefig(\"knn_test_data.pdf\")\n",
     "plt.show()\n"
    ]
   },
@@ -209,38 +211,31 @@
     "import operator\n",
     "\n",
     "def knn_distance(v1, v2):\n",
+    "    \"\"\"计算两个多维向量的距离\"\"\"\n",
     "    return np.sum(np.square(v1-v2))\n",
     "\n",
     "def knn_vote(ys):\n",
-    "    method = 1\n",
-    "    \n",
-    "    # method 1\n",
-    "    if method == 1:\n",
-    "        vote_dict = {}\n",
+    "    \"\"\"根据ys的类别，挑选类别最多一类作为输出\"\"\"\n",
+    "    vote_dict = {}\n",
     "        for y in ys:\n",
     "            if y not in vote_dict.keys():\n",
     "                vote_dict[y] = 1\n",
     "            else:\n",
     "                vote_dict[y] += 1\n",
+    "                \n",
+    "    method = 1\n",
+    "    \n",
+    "    # 方法1 - 使用排序的方法\n",
+    "    if method == 1:\n",
     "        sorted_vote_dict = sorted(vote_dict.items(), \\\n",
     "                                  #key=operator.itemgetter(1), \\\n",
     "                                  key=lambda x:x[1], \\\n",
     "                                  reverse=True)\n",
-    "        \n",
     "        return sorted_vote_dict[0][0]\n",
     "    \n",
-    "    # method 2\n",
+    "    # 方法2 - 使用循环遍历找到类别最多的一类\n",
     "    if method == 2:\n",
-    "        maxv = 0\n",
-    "        maxk = 0\n",
-    "        \n",
-    "        vote_dict = {}\n",
-    "        for y in ys:\n",
-    "            if y not in vote_dict.keys():\n",
-    "                vote_dict[y] = 1\n",
-    "            else:\n",
-    "                vote_dict[y] += 1\n",
-    "                \n",
+    "        maxv = maxk = 0                     \n",
     "        for y in np.unique(ys):\n",
     "            if maxv < vote_dict[y]:\n",
     "                maxv = vote_dict[y]\n",
@@ -248,6 +243,14 @@
     "        return maxk\n",
     "    \n",
     "def knn_predict(x, train_x, train_y, k=3):\n",
+    "    \"\"\"\n",
+    "    针对给定的数据进行分类\n",
+    "    参数\n",
+    "    x - 输入的待分类样本\n",
+    "    train_x - 训练数据的样本\n",
+    "    train_y - 训练数据的标签\n",
+    "    k - 最近邻的样本个数\n",
+    "    \"\"\"\n",
     "    dist_arr = [knn_distance(x, train_x[j]) for j in range(len(train_x))]\n",
     "    sorted_index = np.argsort(dist_arr)\n",
     "    top_k_index = sorted_index[:k]\n",
@@ -255,8 +258,7 @@
     "    return knn_vote(ys)\n",
     "    \n",
     "\n",
-    "#a = knn_predict(x_train[0], x_train, y_train)\n",
-    "\n",
+    "# 对每个样本进行分类\n",
     "y_train_est = [knn_predict(x_train[i], x_train, y_train) for i in range(len(x_train))]\n",
     "print(y_train_est)"
    ]
@@ -275,6 +277,7 @@
     }
    ],
    "source": [
+    "# 计算训练数据的精度\n",
     "n_correct = 0\n",
     "for i in range(len(x_train)):\n",
     "    if y_train_est[i] == y_train[i]:\n",
@@ -298,6 +301,7 @@
     }
    ],
    "source": [
+    "# 计算测试数据的精度\n",
     "y_test_est = [knn_predict(x_test[i], x_train, y_train, 3) for i in range(len(x_test))]\n",
     "n_correct = 0\n",
     "for i in range(len(x_test)):\n",
@@ -317,7 +321,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -325,19 +329,26 @@
     "import operator\n",
     "\n",
     "class KNN(object):\n",
-    "\n",
     "    def __init__(self, k=3):\n",
+    "        \"\"\"对象构造函数，参数为：\n",
+    "        k - 近邻个数\"\"\"\n",
     "        self.k = k\n",
     "\n",
     "    def fit(self, x, y):\n",
+    "        \"\"\"拟合给定的数据，参数为：\n",
+    "        x - 样本的特征；y - 样本的标签\"\"\"\n",
     "        self.x = x\n",
     "        self.y = y\n",
     "        return self\n",
     "\n",
     "    def _square_distance(self, v1, v2):\n",
+    "        \"\"\"计算两个样本点的特征空间距离，参数为：\n",
+    "        v1 - 样本点1；v2 - 样本点2\"\"\"\n",
     "        return np.sum(np.square(v1-v2))\n",
     "\n",
     "    def _vote(self, ys):\n",
+    "        \"\"\"投票算法，参数为：\n",
+    "        ys - k个近邻样本的类别\"\"\"\n",
     "        ys_unique = np.unique(ys)\n",
     "        vote_dict = {}\n",
     "        for y in ys:\n",
@@ -349,6 +360,7 @@
     "        return sorted_vote_dict[0][0]\n",
     "\n",
     "    def predict(self, x):\n",
+    "        \n",
     "        y_pred = []\n",
     "        for i in range(len(x)):\n",
     "            dist_arr = [self._square_distance(x[i], self.x[j]) for j in range(len(self.x))]\n",