From a2df14c943b9a9fed21be87f00430fce28ec4a66 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E9=BB=84=E6=B2=B3?= <976836084@qq.com> Date: Sun, 21 Mar 2021 10:33:17 +0800 Subject: [PATCH 01/10] =?UTF-8?q?=E6=96=B0=E5=BB=BA=2016307100065?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-1/16307100065/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-1/16307100065/.keep diff --git a/assignment-1/16307100065/.keep b/assignment-1/16307100065/.keep new file mode 100644 index 0000000..e69de29 -- Gitee From 1fc1498801751a02ede10ba2c49f42fc5f64ff22 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E9=BB=84=E6=B2=B3?= <976836084@qq.com> Date: Mon, 29 Mar 2021 15:36:54 +0800 Subject: [PATCH 02/10] =?UTF-8?q?=E5=88=A0=E9=99=A4=E6=96=87=E4=BB=B6=20as?= =?UTF-8?q?signment-1/16307100065?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-1/16307100065/.keep | 0 1 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Mon, 29 Mar 2021 15:42:02 +0800 Subject: [PATCH 04/10] =?UTF-8?q?=E4=BD=9C=E4=B8=9A=E6=8F=90=E4=BA=A4?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-1/submission/16307100065/README.md | 214 ++++++++++++++++++ assignment-1/submission/16307100065/source.py | 35 +++ .../submission/16307100065/train&test.py | 39 ++++ 3 files changed, 288 insertions(+) create mode 100644 assignment-1/submission/16307100065/README.md create mode 100644 assignment-1/submission/16307100065/source.py create mode 100644 assignment-1/submission/16307100065/train&test.py diff --git a/assignment-1/submission/16307100065/README.md b/assignment-1/submission/16307100065/README.md new file mode 100644 index 0000000..f69bcd7 --- /dev/null +++ b/assignment-1/submission/16307100065/README.md @@ -0,0 +1,214 @@ +# KNN实验探索 + +## 一.KNN算法代码实现 + +首先定义KNN类,KNN类中包括三个方法: + +```python +import numpy as np +from collections import Counter #用于计数 +def __init__(self,k): + #输入超参k,并赋给内部变量self._k;定义另外内部三个重要变量 + #self._train_data,self._train_label,self._test_data + self._k = k + self._train_data=None + self._train_label = None + self._test_data=None +``` + +```python +def fit(self,train_data,train_label): + #输入train_data,train_label并赋给内部变量 + self._train_data=train_data + self._train_label=train_label +``` + +```python +def predict(self,test_data): + #输入test_data并赋给内部变量 + self._test_data=test_data + predicts_ =[] + #遍历测试集 + for i in self._test_data: + #对测试集中的数据求与每一个训练集中数据的欧氏距离 + distances_ = [np.sum((i-x)**2)**0.5 for x in self._train_data] + distances = np.array(distances_) + #用Counter函数求距离前k个中0-1的个数 + sorted_distances = np.argsort(distances) + topK = [self._train_label[j] for j in sorted_distances[0:self._k]] + votes = Counter(topK) + #预测结果为距离前k个中0-1数量多的种类 + predict = votes.most_common(1)[0][0] + predicts_.append(predict) + predicts = np.array(predicts_) + return predicts +``` + + + +## 二.试验探究 + +### 1.二维随机正态分布的简单分类实验 + +(1)两维之间完全不相关 + +```python +import numpy as np +from source import KNN +import matplotlib.pyplot as plt +#每一维均值为0,方差为10,并且两维独立,创建1000个数据 +cov = [[10,0],[0,10]] +data = np.around(np.random.multivariate_normal((0,0),cov,1000),2) +#对应分类随机取0或1 +label = np.random.choice([0,1],size=1000,replace=True) +#按8:2的比例分为训练集和测试集 +n = len(data)//5 +train_data = data[0:4*n] +train_label = label[0:4*n] +test_data = data[4*n:] +test_label = label[4*n:] +#调用KNN类,k赋值5,将训练集输入模型 +model = KNN(5) +model.fit(train_data, train_label) + +#绘制分类图 +#第一维和第二维分别作为x,y轴 +x_show = train_data[:,0] +y_show = train_data[:,1] +x_min,x_max=x_show.min(),x_show.max() +y_min,y_max=y_show.min(),y_show.max() +#将坐标系分为200×200的网格 +xx,yy = np.meshgrid(np.linspace(x_min,x_max,200),np.linspace(y_min,y_max,200)) +#将网格放入模型预测,预测每一个网格的分类 +z1 = np.c_[xx.ravel(),yy.ravel()] +z = np.array(z1) +pred = model.predict(z) +pred = pred.reshape(xx.shape) +#绘制网格分类图和训练集的散点图 +plt.pcolormesh(xx,yy,pred,cmap=plt.cm.Pastel1) +plt.scatter(x_show,y_show,s=80,c=train_label,cmap=plt.cm.spring,edgecolors='k') +plt.xlim(xx.min(),xx.max()) +plt.ylim(yy.min(),yy.max()) +plt.show() +``` + +![完全无关](C:\Users\97683\Desktop\机器学习\KNN\二维结果.png) + +结果如图所示。由于data是根据二元正态分布随机取值的,并且label也是在0-1之间随机选取的,所以data和label之间是完全无关的。所以分类图也是不规则的。 + +(2)二维之间完全正相关 + +```python +#使两个维度相关系数为1 +cov = [[10,10],[10,10]] +``` + +![完全正相关](C:\Users\97683\Desktop\机器学习\KNN\二维相关.png) + +结果如图所示。由于两维相关系数为1,所以所有点都在y=x的直线上。由于label的随机选取,所以0-1分类区域是在这条直线上的随机分布。 + +(3)完全负相关 + +```python +#两个维度相关系数为-1 +cov = [[10,-10],[-10,10]] +``` + +![相关系数为-1](C:\Users\97683\Desktop\机器学习\KNN\负二维.png) + +结果如图所示。 + +(4)一般情况下 + +```python +#使相关系数为0.2 +cov = [[10,2],[2,10]] +``` + +![0.2](C:\Users\97683\Desktop\机器学习\KNN\0.2.png) + +```python +#使相关系数为0.8 +cov = [[10,8],[8,10]] +``` + +![0.8](C:\Users\97683\Desktop\机器学习\KNN\0.8.png) + +分别将相关系数设为0.2与0.8,可以看出0.2时分布还相对散乱,而0.8时已经可以看出明显的线性关系。同样,由于label的随机选取,在直线上0-1的分布仍然是随机的。 + +### 2.二维随机正态分布的多分类实验 + +```python +#相关系数取0.8 +cov = [[10,8],[8,10]] +#五分类任务 +label = np.random.choice([0,1,2,3,4],size=1000,replace=True) +``` + +![5分类0.8](C:\Users\97683\Desktop\机器学习\KNN\五分类0.8.png) + +```python +#相关系数取0.2 +cov = [[10,2],[2,10]] +#五分类任务 +label = np.random.choice([0,1,2,3,4],size=1000,replace=True) +``` + +![五0.2](C:\Users\97683\Desktop\机器学习\KNN\五0.2.png) + +结果如图所示。与简单分类结果类似,这是由于两维的相关系数是一样的,而仅仅是将label从0-1随机取值变为0-1-2-3-4随机取值,并没有本质变化,只是人为定义的分类数变多了。 + +### 3. 实验发现 + +#### (1)简单分类与多分类 + +以相关系数为0.2的二维正态分布,k值取5为例。 + +运行10次0-1的简单二分类实验,结果分别为: + +acc = 0.51,0.545,0.535,0.515 ,0.435, 0.465,0.56,0.53, 0.515,0.53 + +平均acc=0.514 + +运行10次三分类实验,结果如下: + +acc = 0.295,0.32,0.35,0.34,0.31,0.405 ,0.325 ,0.3,0.32,0.32 + +平均acc = 0.329 + +运行10次四分类实验,结果如下: + +acc = 0.25,0.22,0.255,0.19,0.215,0.335,0.3,0.25,0.28,0.225 + +平均acc = 0.252 + +运行10此五分类实验,结果如下: + +acc = 0.265,0.185,0.22,0.235,0.195,0.19,0.22, 0.23,0.2,0.215 + +平均acc = 0.2155 + + + +可以发现,当分类数越多时,预测的准确率越低。这应该是由于data和label本身之间没有相关性,acc近似等于(1/分类数),和瞎猜的准确率是近似的。 + +#### (2)k值的选取 + +以简单二分类为例。 + +k值取5,运行10次的平均acc =0.512 + +k值取4,运行10次的平均acc =0.507 + +k值取6,运行10次的平均acc =0.485 + +k值取3,运行10次的平均acc =0.495 + +k值取7,运行10次的平均acc =0.508 + + + +可知,k取5是恰当的。但同样由于data和label之间没有相关性,所以不同k值之间准确率的差异不大,都在0.5左右,近似于瞎猜。因为分类区域本身就是随机的,距离预测点越近的点并不代表属于该点类别的概率越大。 + +所以,该次尝试的调参是没有意义的。如果选取本身有意义,并且属性与分类有关系的数据组进行测试,取不同的k值的准确率才会有显著差异,此时的调参才有意义。 + diff --git a/assignment-1/submission/16307100065/source.py b/assignment-1/submission/16307100065/source.py new file mode 100644 index 0000000..4ae9785 --- /dev/null +++ b/assignment-1/submission/16307100065/source.py @@ -0,0 +1,35 @@ +#算法代码 +import numpy as np +from collections import Counter +class KNN: + + def __init__(self,k): + self._k = k + self._train_data=None + self._train_label = None + self._test_data=None + + def fit(self,train_data,train_label): + self._train_data=train_data + self._train_label=train_label + + + def predict(self,test_data): + self._test_data=test_data + predicts_ =[] + #遍历测试集 + for i in self._test_data: + #对测试集中的数据求距离每一个训练集中数据的欧氏距离 + distances_ = [np.sum((i-x)**2)**0.5 for x in self._train_data] + distances = np.array(distances_) + #用Counter函数求距离前k个 + sorted_distances = np.argsort(distances) + topK = [self._train_label[j] for j in sorted_distances[0:self._k]] + votes = Counter(topK) + #预测结果 + predict = votes.most_common(1)[0][0] + predicts_.append(predict) + predicts = np.array(predicts_) + return predicts + + diff --git a/assignment-1/submission/16307100065/train&test.py b/assignment-1/submission/16307100065/train&test.py new file mode 100644 index 0000000..31f28e4 --- /dev/null +++ b/assignment-1/submission/16307100065/train&test.py @@ -0,0 +1,39 @@ +#实验代码 +import numpy as np +from lknn import KNN +import matplotlib.pyplot as plt +#每一维均值为0,方差为10,并且两维独立,创建1000个数据 +cov = [[10,0],[0,10]] +data = np.around(np.random.multivariate_normal((0,0),cov,1000),2) +#对应分类随机取0或1 +label = np.random.choice([0,1],size=1000,replace=True) +#按8:2的比例分为训练集和测试集 +n = len(data)//5 +train_data = data[0:4*n] +train_label = label[0:4*n] +test_data = data[4*n:] +test_label = label[4*n:] +#调用KNN类,k赋值5,将训练集输入模型 +model = KNN(5) +model.fit(train_data, train_label) +#绘制分类图 +#第一维和第二维分别作为x,y轴 +x_show = train_data[:,0] +y_show = train_data[:,1] +x_min,x_max=x_show.min(),x_show.max() +y_min,y_max=y_show.min(),y_show.max() +xx,yy = np.meshgrid(np.linspace(x_min,x_max,200),np.linspace(y_min,y_max,200)) +#将网格放入模型预测,预测每一个网格的分类 +z1 = np.c_[xx.ravel(),yy.ravel()] +z = np.array(z1) +pred = model.predict(z) +pred = pred.reshape(xx.shape) +#绘制网格分类图和训练集的散点图 +plt.pcolormesh(xx,yy,pred,cmap=plt.cm.Pastel1) +plt.scatter(x_show,y_show,s=80,c=train_label,cmap=plt.cm.spring,edgecolors='k') +plt.xlim(xx.min(),xx.max()) +plt.ylim(yy.min(),yy.max()) +plt.show() +#计算acc +res = model.predict(test_data) +print("acc =",np.mean(np.equal(res, test_label))) \ No newline at end of file -- Gitee From 861fd928278b56d216fe2ed3a20c7dbace4df05c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E9=BB=84=E6=B2=B3?= <976836084@qq.com> Date: 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zEsp7GiNMTsM#FZ5*tuS32%?z-N~P?8Tm1xJ;173J$6)K9ft)A(w6oD3>dcSOn**g! zxga^7h=}OZ;LPo(aoQ*6qBEdd&?vIeef8=U*>Z4D(Dd&5Oyd!NKoY(f#^t$r$c@HiJdvf`WqHwu^{jtLaSmWj4BkK{pcd zY>^H!WRqc)i8l(Sn(CT=^ZJ9Z&V)?r>1>{^j8sfEA&^KWDAkjalK4A`x{kLix7ngT zE~N!?qkq9FH$T&U6o&_{UBlM@?b{Go$NbHCd`6`X@;L^jc?PiJO5q5^E3mqo28&Li zD_k1k-G}pPWwIAr_p0F_LaEHa3^7OX77n9ESfj=IIk5XUl)^(`T~30<^Sf5&z4yLk z^jDhmOj`a2M;_XHr<=n^__3&hyPY^LQ!7rubi6?Ui}xd CPDOtJ literal 0 HcmV?d00001 -- Gitee From 6b3dd35b93f83a54027bf44ba25f7642ec309751 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E9=BB=84=E6=B2=B3?= <976836084@qq.com> Date: Mon, 29 Mar 2021 15:51:16 +0800 Subject: [PATCH 07/10] update assignment-1/submission/16307100065/README.md. --- assignment-1/submission/16307100065/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-1/submission/16307100065/README.md b/assignment-1/submission/16307100065/README.md index f69bcd7..5784c29 100644 --- a/assignment-1/submission/16307100065/README.md +++ b/assignment-1/submission/16307100065/README.md @@ -92,7 +92,7 @@ plt.ylim(yy.min(),yy.max()) plt.show() ``` -![完全无关](C:\Users\97683\Desktop\机器学习\KNN\二维结果.png) +![无关](assignment-1/submission/16307100065/img/二维结果.png) 结果如图所示。由于data是根据二元正态分布随机取值的,并且label也是在0-1之间随机选取的,所以data和label之间是完全无关的。所以分类图也是不规则的。 -- Gitee From e9c4261b818a6513facff885bc37b8f382763551 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E9=BB=84=E6=B2=B3?= <976836084@qq.com> Date: Mon, 29 Mar 2021 15:57:43 +0800 Subject: [PATCH 08/10] update assignment-1/submission/16307100065/README.md. --- assignment-1/submission/16307100065/README.md | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/assignment-1/submission/16307100065/README.md b/assignment-1/submission/16307100065/README.md index 5784c29..931fdaa 100644 --- a/assignment-1/submission/16307100065/README.md +++ b/assignment-1/submission/16307100065/README.md @@ -103,7 +103,7 @@ plt.show() cov = [[10,10],[10,10]] ``` -![完全正相关](C:\Users\97683\Desktop\机器学习\KNN\二维相关.png) +![完全正相关](assignment-1/submission/16307100065/img/二维相关.png) 结果如图所示。由于两维相关系数为1,所以所有点都在y=x的直线上。由于label的随机选取,所以0-1分类区域是在这条直线上的随机分布。 @@ -114,7 +114,7 @@ cov = [[10,10],[10,10]] cov = [[10,-10],[-10,10]] ``` -![相关系数为-1](C:\Users\97683\Desktop\机器学习\KNN\负二维.png) +![相关系数为-1](assignment-1/submission/16307100065/img/负二维.png) 结果如图所示。 @@ -125,14 +125,14 @@ cov = [[10,-10],[-10,10]] cov = [[10,2],[2,10]] ``` -![0.2](C:\Users\97683\Desktop\机器学习\KNN\0.2.png) +![0.2](assignment-1/submission/16307100065/img/0.2.png) ```python #使相关系数为0.8 cov = [[10,8],[8,10]] ``` -![0.8](C:\Users\97683\Desktop\机器学习\KNN\0.8.png) +![0.8](assignment-1/submission/16307100065/img/0.8.png) 分别将相关系数设为0.2与0.8,可以看出0.2时分布还相对散乱,而0.8时已经可以看出明显的线性关系。同样,由于label的随机选取,在直线上0-1的分布仍然是随机的。 @@ -145,7 +145,7 @@ cov = [[10,8],[8,10]] label = np.random.choice([0,1,2,3,4],size=1000,replace=True) ``` -![5分类0.8](C:\Users\97683\Desktop\机器学习\KNN\五分类0.8.png) +![5分类0.8](assignment-1/submission/16307100065/img/五分类0.8.png) ```python #相关系数取0.2 @@ -154,7 +154,7 @@ cov = [[10,2],[2,10]] label = np.random.choice([0,1,2,3,4],size=1000,replace=True) ``` -![五0.2](C:\Users\97683\Desktop\机器学习\KNN\五0.2.png) +![五0.2](assignment-1/submission/16307100065/img/五0.2.png) 结果如图所示。与简单分类结果类似,这是由于两维的相关系数是一样的,而仅仅是将label从0-1随机取值变为0-1-2-3-4随机取值,并没有本质变化,只是人为定义的分类数变多了。 -- Gitee From 795470c8e3e87996578ab6f3559db9ce339ce50d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E9=BB=84=E6=B2=B3?= <976836084@qq.com> Date: Mon, 29 Mar 2021 19:57:24 +0800 Subject: [PATCH 09/10] update assignment-1/submission/16307100065/README.md. --- assignment-1/submission/16307100065/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-1/submission/16307100065/README.md b/assignment-1/submission/16307100065/README.md index 931fdaa..8b63a17 100644 --- a/assignment-1/submission/16307100065/README.md +++ b/assignment-1/submission/16307100065/README.md @@ -92,7 +92,7 @@ plt.ylim(yy.min(),yy.max()) plt.show() ``` -![无关](assignment-1/submission/16307100065/img/二维结果.png) +(assignment-1/submission/16307100065/img/二维结果.png) 结果如图所示。由于data是根据二元正态分布随机取值的,并且label也是在0-1之间随机选取的,所以data和label之间是完全无关的。所以分类图也是不规则的。 -- Gitee From 7e3a5d1a2f1ffd10c89543a4e6b845395d9e35e2 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E9=BB=84=E6=B2=B3?= <976836084@qq.com> Date: Mon, 29 Mar 2021 20:00:05 +0800 Subject: [PATCH 10/10] update assignment-1/submission/16307100065/README.md. --- assignment-1/submission/16307100065/README.md | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/assignment-1/submission/16307100065/README.md b/assignment-1/submission/16307100065/README.md index 8b63a17..06a0098 100644 --- a/assignment-1/submission/16307100065/README.md +++ b/assignment-1/submission/16307100065/README.md @@ -92,7 +92,7 @@ plt.ylim(yy.min(),yy.max()) plt.show() ``` -(assignment-1/submission/16307100065/img/二维结果.png) +![输入图片说明](https://images.gitee.com/uploads/images/2021/0329/195821_9a6657ad_8843048.png "二维结果.png") 结果如图所示。由于data是根据二元正态分布随机取值的,并且label也是在0-1之间随机选取的,所以data和label之间是完全无关的。所以分类图也是不规则的。 @@ -103,7 +103,7 @@ plt.show() cov = [[10,10],[10,10]] ``` -![完全正相关](assignment-1/submission/16307100065/img/二维相关.png) +![输入图片说明](https://images.gitee.com/uploads/images/2021/0329/195844_3f64dcf7_8843048.png "二维相关.png") 结果如图所示。由于两维相关系数为1,所以所有点都在y=x的直线上。由于label的随机选取,所以0-1分类区域是在这条直线上的随机分布。 @@ -114,7 +114,7 @@ cov = [[10,10],[10,10]] cov = [[10,-10],[-10,10]] ``` -![相关系数为-1](assignment-1/submission/16307100065/img/负二维.png) +![输入图片说明](https://images.gitee.com/uploads/images/2021/0329/195855_21448894_8843048.png "负二维.png") 结果如图所示。 @@ -125,14 +125,14 @@ cov = [[10,-10],[-10,10]] cov = [[10,2],[2,10]] ``` -![0.2](assignment-1/submission/16307100065/img/0.2.png) +![输入图片说明](https://images.gitee.com/uploads/images/2021/0329/195908_c9a5e2fa_8843048.png "0.2.png") ```python #使相关系数为0.8 cov = [[10,8],[8,10]] ``` -![0.8](assignment-1/submission/16307100065/img/0.8.png) +![输入图片说明](https://images.gitee.com/uploads/images/2021/0329/195921_5cf96f45_8843048.png "0.8.png") 分别将相关系数设为0.2与0.8,可以看出0.2时分布还相对散乱,而0.8时已经可以看出明显的线性关系。同样,由于label的随机选取,在直线上0-1的分布仍然是随机的。 @@ -145,7 +145,7 @@ cov = [[10,8],[8,10]] label = np.random.choice([0,1,2,3,4],size=1000,replace=True) ``` -![5分类0.8](assignment-1/submission/16307100065/img/五分类0.8.png) +![输入图片说明](https://images.gitee.com/uploads/images/2021/0329/195937_f438d130_8843048.png "五分类0.8.png") ```python #相关系数取0.2 @@ -154,7 +154,7 @@ cov = [[10,2],[2,10]] label = np.random.choice([0,1,2,3,4],size=1000,replace=True) ``` -![五0.2](assignment-1/submission/16307100065/img/五0.2.png) +![输入图片说明](https://images.gitee.com/uploads/images/2021/0329/195959_868f36e5_8843048.png "五0.2.png") 结果如图所示。与简单分类结果类似,这是由于两维的相关系数是一样的,而仅仅是将label从0-1随机取值变为0-1-2-3-4随机取值,并没有本质变化,只是人为定义的分类数变多了。 -- Gitee

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