bushuhui
3 years ago
3 changed files with 41 additions and 29 deletions
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2_knn/knn_classification.ipynb
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| @@ -62,7 +62,7 @@ | |||||
| "source": [ | "source": [ | ||||
| "### 1.1 距离计算\n", | "### 1.1 距离计算\n", | ||||
| "\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", | |||||
| "$$\n", | "$$\n", | ||||
| "d = \\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\n", | "d = \\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\n", | ||||
| "$$\n", | "$$\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", | "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", | ||||
| "\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", | "\n", | ||||
| "## 2. 机器学习的思维模型\n", | "## 2. 机器学习的思维模型\n", | ||||
| "\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", | "\n", | ||||
| "\n", | "\n", | ||||
| "\n", | "\n", | ||||
| @@ -112,7 +112,7 @@ | |||||
| }, | }, | ||||
| { | { | ||||
| "cell_type": "code", | "cell_type": "code", | ||||
| "execution_count": 1, | |||||
| "execution_count": 2, | |||||
| "metadata": {}, | "metadata": {}, | ||||
| "outputs": [ | "outputs": [ | ||||
| { | { | ||||
| @@ -146,7 +146,7 @@ | |||||
| "import numpy as np\n", | "import numpy as np\n", | ||||
| "import matplotlib.pyplot as plt\n", | "import matplotlib.pyplot as plt\n", | ||||
| "\n", | "\n", | ||||
| "# data generation\n", | |||||
| "# 生成模拟数据\n", | |||||
| "np.random.seed(314)\n", | "np.random.seed(314)\n", | ||||
| "\n", | "\n", | ||||
| "data_size1 = 100\n", | "data_size1 = 100\n", | ||||
| @@ -158,7 +158,7 @@ | |||||
| "y2 = [1 for _ in range(data_size2)]\n", | "y2 = [1 for _ in range(data_size2)]\n", | ||||
| "\n", | "\n", | ||||
| "\n", | "\n", | ||||
| "# all sample data\n", | |||||
| "# 合并生成全部数据\n", | |||||
| "x = np.concatenate((x1, x2), axis=0)\n", | "x = np.concatenate((x1, x2), axis=0)\n", | ||||
| "y = np.concatenate((y1, y2), axis=0)\n", | "y = np.concatenate((y1, y2), axis=0)\n", | ||||
| "\n", | "\n", | ||||
| @@ -167,7 +167,7 @@ | |||||
| "x = x[shuffled_index]\n", | "x = x[shuffled_index]\n", | ||||
| "y = y[shuffled_index]\n", | "y = y[shuffled_index]\n", | ||||
| "\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", | "split_index = int(data_size_all*0.7)\n", | ||||
| "x_train = x[:split_index]\n", | "x_train = x[:split_index]\n", | ||||
| "y_train = y[:split_index]\n", | "y_train = y[:split_index]\n", | ||||
| @@ -175,12 +175,14 @@ | |||||
| "y_test = y[split_index:]\n", | "y_test = y[split_index:]\n", | ||||
| "\n", | "\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.scatter(x_train[:,0], x_train[:,1], c=y_train, marker='.')\n", | ||||
| "plt.title(\"train data\")\n", | "plt.title(\"train data\")\n", | ||||
| "plt.savefig(\"knn_train_data.pdf\")\n", | |||||
| "plt.show()\n", | "plt.show()\n", | ||||
| "plt.scatter(x_test[:,0], x_test[:,1], c=y_test, marker='.')\n", | "plt.scatter(x_test[:,0], x_test[:,1], c=y_test, marker='.')\n", | ||||
| "plt.title(\"test data\")\n", | "plt.title(\"test data\")\n", | ||||
| "plt.savefig(\"knn_test_data.pdf\")\n", | |||||
| "plt.show()\n" | "plt.show()\n" | ||||
| ] | ] | ||||
| }, | }, | ||||
| @@ -209,38 +211,31 @@ | |||||
| "import operator\n", | "import operator\n", | ||||
| "\n", | "\n", | ||||
| "def knn_distance(v1, v2):\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", | " return np.sum(np.square(v1-v2))\n", | ||||
| "\n", | "\n", | ||||
| "def knn_vote(ys):\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", | " for y in ys:\n", | ||||
| " if y not in vote_dict.keys():\n", | " if y not in vote_dict.keys():\n", | ||||
| " vote_dict[y] = 1\n", | " vote_dict[y] = 1\n", | ||||
| " else:\n", | " else:\n", | ||||
| " vote_dict[y] += 1\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", | " sorted_vote_dict = sorted(vote_dict.items(), \\\n", | ||||
| " #key=operator.itemgetter(1), \\\n", | " #key=operator.itemgetter(1), \\\n", | ||||
| " key=lambda x:x[1], \\\n", | " key=lambda x:x[1], \\\n", | ||||
| " reverse=True)\n", | " reverse=True)\n", | ||||
| " \n", | |||||
| " return sorted_vote_dict[0][0]\n", | " return sorted_vote_dict[0][0]\n", | ||||
| " \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", | " 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", | " for y in np.unique(ys):\n", | ||||
| " if maxv < vote_dict[y]:\n", | " if maxv < vote_dict[y]:\n", | ||||
| " maxv = vote_dict[y]\n", | " maxv = vote_dict[y]\n", | ||||
| @@ -248,6 +243,14 @@ | |||||
| " return maxk\n", | " return maxk\n", | ||||
| " \n", | " \n", | ||||
| "def knn_predict(x, train_x, train_y, k=3):\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", | " dist_arr = [knn_distance(x, train_x[j]) for j in range(len(train_x))]\n", | ||||
| " sorted_index = np.argsort(dist_arr)\n", | " sorted_index = np.argsort(dist_arr)\n", | ||||
| " top_k_index = sorted_index[:k]\n", | " top_k_index = sorted_index[:k]\n", | ||||
| @@ -255,8 +258,7 @@ | |||||
| " return knn_vote(ys)\n", | " return knn_vote(ys)\n", | ||||
| " \n", | " \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", | "y_train_est = [knn_predict(x_train[i], x_train, y_train) for i in range(len(x_train))]\n", | ||||
| "print(y_train_est)" | "print(y_train_est)" | ||||
| ] | ] | ||||
| @@ -275,6 +277,7 @@ | |||||
| } | } | ||||
| ], | ], | ||||
| "source": [ | "source": [ | ||||
| "# 计算训练数据的精度\n", | |||||
| "n_correct = 0\n", | "n_correct = 0\n", | ||||
| "for i in range(len(x_train)):\n", | "for i in range(len(x_train)):\n", | ||||
| " if y_train_est[i] == y_train[i]:\n", | " if y_train_est[i] == y_train[i]:\n", | ||||
| @@ -298,6 +301,7 @@ | |||||
| } | } | ||||
| ], | ], | ||||
| "source": [ | "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", | "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", | "n_correct = 0\n", | ||||
| "for i in range(len(x_test)):\n", | "for i in range(len(x_test)):\n", | ||||
| @@ -317,7 +321,7 @@ | |||||
| }, | }, | ||||
| { | { | ||||
| "cell_type": "code", | "cell_type": "code", | ||||
| "execution_count": 5, | |||||
| "execution_count": 3, | |||||
| "metadata": {}, | "metadata": {}, | ||||
| "outputs": [], | "outputs": [], | ||||
| "source": [ | "source": [ | ||||
| @@ -325,19 +329,26 @@ | |||||
| "import operator\n", | "import operator\n", | ||||
| "\n", | "\n", | ||||
| "class KNN(object):\n", | "class KNN(object):\n", | ||||
| "\n", | |||||
| " def __init__(self, k=3):\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", | " self.k = k\n", | ||||
| "\n", | "\n", | ||||
| " def fit(self, x, y):\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.x = x\n", | ||||
| " self.y = y\n", | " self.y = y\n", | ||||
| " return self\n", | " return self\n", | ||||
| "\n", | "\n", | ||||
| " def _square_distance(self, v1, v2):\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", | " return np.sum(np.square(v1-v2))\n", | ||||
| "\n", | "\n", | ||||
| " def _vote(self, ys):\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", | " ys_unique = np.unique(ys)\n", | ||||
| " vote_dict = {}\n", | " vote_dict = {}\n", | ||||
| " for y in ys:\n", | " for y in ys:\n", | ||||
| @@ -349,6 +360,7 @@ | |||||
| " return sorted_vote_dict[0][0]\n", | " return sorted_vote_dict[0][0]\n", | ||||
| "\n", | "\n", | ||||
| " def predict(self, x):\n", | " def predict(self, x):\n", | ||||
| " \n", | |||||
| " y_pred = []\n", | " y_pred = []\n", | ||||
| " for i in range(len(x)):\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", | " dist_arr = [self._square_distance(x[i], self.x[j]) for j in range(len(self.x))]\n", | ||||