diff --git a/2_knn/knn_classification.ipynb b/2_knn/knn_classification.ipynb index 686830d..ae6ea5d 100644 --- a/2_knn/knn_classification.ipynb +++ b/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", diff --git a/2_knn/knn_test_data.pdf b/2_knn/knn_test_data.pdf new file mode 100644 index 0000000..56aad61 Binary files /dev/null and b/2_knn/knn_test_data.pdf differ diff --git a/2_knn/knn_train_data.pdf b/2_knn/knn_train_data.pdf new file mode 100644 index 0000000..fe9887c Binary files /dev/null and b/2_knn/knn_train_data.pdf differ