From 798b920b033d65c76aa51bf21a74c02c95587831 Mon Sep 17 00:00:00 2001 From: unknown <644255997@qq.com> Date: Thu, 1 Apr 2021 21:33:45 +0800 Subject: [PATCH] [submission] assignment-1 of 18307130341 --- assignment-1/submission/18307130341/README.md | 102 ++++++++++++++++ .../submission/18307130341/img/Fig4.png | Bin 0 -> 43325 bytes .../submission/18307130341/img/Fig5.png | Bin 0 -> 39004 bytes .../submission/18307130341/img/k_acc.png | Bin 0 -> 24577 bytes .../submission/18307130341/img/test_data.png | Bin 0 -> 24650 bytes .../submission/18307130341/img/train_data.png | Bin 0 -> 50015 bytes assignment-1/submission/18307130341/source.py | 112 ++++++++++++++++++ 7 files changed, 214 insertions(+) create mode 100644 assignment-1/submission/18307130341/README.md create mode 100644 assignment-1/submission/18307130341/img/Fig4.png create mode 100644 assignment-1/submission/18307130341/img/Fig5.png create mode 100644 assignment-1/submission/18307130341/img/k_acc.png create mode 100644 assignment-1/submission/18307130341/img/test_data.png create mode 100644 assignment-1/submission/18307130341/img/train_data.png create mode 100644 assignment-1/submission/18307130341/source.py diff --git a/assignment-1/submission/18307130341/README.md b/assignment-1/submission/18307130341/README.md new file mode 100644 index 0000000..e2d7dbd --- /dev/null +++ b/assignment-1/submission/18307130341/README.md @@ -0,0 +1,102 @@ +# 实验报告:ASS1-KNN分类器 + +18307130341 黄韵澄 + +[toc] + +### 1.1 实验概述 + +​ 本实验使用k近邻方法(KNN),实现了对二维带标签点集的分类。 + +​ 在**1.2**中生成了3组符合高斯分布的二维点集,并打上0~2共3种标签。初始数据集被划分为训练数据(train_data,80%)和测试数据(test_data,20%),并将训练数据放进KNN模型中进行训练。 + +​ **1.3**中是对KNN模型的实现部分,包括初始化、模型训练、预测分类三个部分。 + +​ **1.4**中对KNN模型进行测试和实验探究。 + +​ **1.5**中完成实验的自动测试部分。 + +### 1.2 数据集生成 + +​ 数据集的生成在函数`data_generate`中实现。每种标签各生成了`num=200`个点集,通过设置其均值`mean`和协方差`cov`来生成符合高斯分布的二维数据集。生成数据集的参数如下: +$$ +\mu_0 = [6, 4],\ \Sigma_0 = \begin{bmatrix}35&4\\4&11\\\end{bmatrix}\\ +\mu_1 = [11, 14],\ \Sigma_1 = \begin{bmatrix}21&6\\6&24 \\\end{bmatrix}\\ +\mu_2 = [22, 6],\ \Sigma_2 = \begin{bmatrix}25&5\\5&10\\\end{bmatrix}\\ +$$ +​ 生成的数据集组成`data`,使用`shuffle`函数将其打乱,取前80%作为`train_data`,后20%作为`test_data`。 + +​ 使用`matplotlib`绘图,测试集和训练集散点图如下: + +![train_data](img\train_data.png) + +
Fig 1:训练集
+ +![test_data](D:\YC\study\大三下\模式识别与机器学习\pj1\prml-21-spring\assignment-1\submission\18307130341\img\test_data.png) + +
Fig 2: 测试集 + +### 1.3 KNN模型的实现 + +#### 1.3.1 KNN初始化 + +​ `__init__`成员函数中初始化KNN模型。定义`data`、`label`作为k近邻的候选点集,`num`为点集规模,`k`为模型训练后选取的最优k值。 + +#### 1.3.2 模型训练——fit函数 + +​ 将`train_data`再次划分为`train_set_data`和`dev_set_data`。`train_set_data`作为候选点集,`dev_set_data`作为开发集,实现对超参`k`的选取。 + +​ 超参`k`的选取范围设置为`1~15`。 + +​ 对每个候选k,对开发集进行类别预测。具体方式是在训练集中找到最近的k个点中出现中最多的类别作为预测类别。对每个k计算出其类别预测平均准确率acc,绘制成图如下: + +![k_acc](img\k_acc.png) + +
Fig 3:acc-k折线图 + +​ 在1%的波动范围内,选取准确度最高的最小k作为最终选取的超参`k`,此时模型训练完成。在上图的样例中,最终选取的超参`k`为6。 + +#### 1.3.3 类别预测——predict函数 + +​ 对于每个需要预测的数据,找到训练集中距离最近的`k`个点,距离选取为欧几里得距离。 + +​ 最终每个点的预测类别为:`k`个最近邻的点中出现最多的类别。`k`为1.3.2中训练好的超参`k`。 + +### 1.4 模型测试和实验探究 + +#### 1.4.1 模型测试 + +​ 用`test_data`进行模型测试,输出模型的准确率。实验重复10次,结果如下: +$$ +\begin{array}{c|l} {实验次数}&{1}&{2}&{3}&{4}&{5}&{6}&{7}&{8}&{9}&{10}\\ \hline {k}&{5}&{8}&{9}&{3}&{11}&{6}&{8}&{6}&{9}&{7}\\ {acc}&{0.83}&{0.88}&{0.8}&{0.83}&{0.87}&{0.85}&{0.88}&{0.88}&{0.86}&{0.88}\\ \end{array} +$$ + +
Table 1: 模型准确率 + +​ 平均超参`k`为`7~8`之间,平均准确率`acc`为`0.856`。 + +#### 1.4.2 实验探究 + +​ (1) 修改高斯分布距离,使得三种点集更加分散(重合部分更少): + +![Fig4](img\Fig4.png) + +
Fig 4: 修改高斯分布距离后的点集 + +​ 该数据集测试出的模型准确率为92.92%。多次重复实验,增大点集的距离,得出结论:高斯分布距离越大,点集越分散,模型准确率越高。 + +​ (2) 修改高斯分布距离,使得三种点集更加分散(重合部分更少): + +![Fig5](img\Fig5.png) + +
Fig 5: 修改高斯分布方差后的点集 + +​ 该数据集测试出的模型准确率为97.5%。多次重复实验,减小点坐标方差(对角线的值),得出结论:高斯分布方差越小,点集内部更加集中,模型准确率更高。 + +### 1.5 自动化测试 + +​ 程序只导入了`numpy`和`matplotlib`包。 + +​ 配置conda环境进行测试,可以通过测试。 + +​ \ No newline at end of file diff --git a/assignment-1/submission/18307130341/img/Fig4.png b/assignment-1/submission/18307130341/img/Fig4.png new file mode 100644 index 0000000000000000000000000000000000000000..73f0b16e63c730206ad6ef5e0e7ae0357edd87e3 GIT binary patch literal 43325 zcmeFZRa6{N*EZO=Ly+JWJi*;11Pc-*xN8H!-JyX%kl-$%k>Kv`!QC}TaCf&U-uIh- z)_*Z`F;{ajti@`&>QvRPBYW@X+0P+V>5DW5DlsYu1j6_%BcTEU!9qYFm^EZX;0X7` z@+R=X?<}e5{M8QZ>}KR>22wC`wzsx(wzf2;bTxByvb3}1WZ`7tV4}2ecD8pCU}d%W zUkzC79L-r-!?4kSo1oasXgPsESVphEFa@IdmLO0;(PxQ|s_yAWe?8n)x2}**Plls^ znZ|+^@ZLE1hh#FOX(L1+Do>-@%!Fw(KdaUt=)Tb@p00zC%ok~vHn6%B3I<5QNY>#= zeEfr;RYGH=D1JS>yh_3A#xbO~;SnN0xY0 z(*T4G{74eOi2(<)X}UqtAt50Q18g9g*9IKupitm@Ec*X{`u{WC^4Hi0CUp4V%6P6! zuYYtjxO+Y1YU>R)b`0oqtdfC2RBS8`->-obG!qbEuwJukmfOinWg9v$npJCk6n=l! 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train_data + self.label = train_label + + def predict(self, test_data): + predict_label = [] + for x in test_data: + dis = np.array([np.sqrt(sum((x-y)**2)) for y in self.data]) + knn = np.argsort(np.array(dis))[:self.k] + result = np.argmax(np.bincount(self.label[knn])) + predict_label.append(result) + return predict_label + +def data_generate(num): + mean = [(6,4), (11, 14), (22, 6)] + cov = [[35, 4], [4, 11]],[[21, 6], [6, 24]],[[25, 5], [5, 10]] + data0 = np.random.multivariate_normal(mean[0], cov[0], num) + data1 = np.random.multivariate_normal(mean[1], cov[1], num) + data2 = np.random.multivariate_normal(mean[2], cov[2], num) + data = np.concatenate([data0,data1,data2]) + label = np.array([0]*num + [1]*num + [2]*num) + + idx = np.random.permutation(3*num) + + data = data[idx] + label = label[idx] + + return data, label + +def Graph_Plot(acc, name): + plt.plot(acc) + plt.xlabel('k') + plt.ylabel('acc') + plt.savefig(f'img/{name}') + plt.close() + +def Graph_Scatter(data, label, name): + points =[[],[],[]] + for i in range(len(data)): + points[label[i]].append(data[i]) + for points_set in points: + points_set = np.array(points_set) + plt.scatter(points_set[:, 0], points_set[:, 1]) + # plt.show() + plt.savefig(f'img/{name}') + plt.close() + + +if __name__ == "__main__": + num = 400 + data, label = data_generate(num) + train_num = (int)(num* 3 * 0.8) + train_data = data[:train_num] + train_label = label[:train_num] + test_data = data[train_num:] + test_label = label[train_num:] + + # Graph_Scatter(train_data, train_label, "train_data") + # Graph_Scatter(test_data, test_label,"test_data") + + model = KNN() + model.fit(train_data, train_label) + test_predict = model.predict(test_data) + acc = np.mean(np.equal(test_predict, test_label)) + print("k = ", model.k) + print("acc = ", acc) + -- Gitee