From dae9b171ca238ec7cd35ec769d5e5966386f9d5b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn> Date: Sun, 21 Mar 2021 10:41:41 +0800 Subject: [PATCH 01/23] =?UTF-8?q?=E6=96=B0=E5=BB=BA=2017307110367?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-1/submission/17307110367/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-1/submission/17307110367/.keep diff --git a/assignment-1/submission/17307110367/.keep b/assignment-1/submission/17307110367/.keep new file mode 100644 index 0000000..e69de29 -- Gitee From e207e63ac9374f2a1779ff06fd40190ed704bc24 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn> Date: Sun, 21 Mar 2021 10:42:21 +0800 Subject: [PATCH 02/23] =?UTF-8?q?=E5=88=A0=E9=99=A4=E6=96=87=E4=BB=B6=20as?= =?UTF-8?q?signment-1/submission/17307110367?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-1/submission/17307110367/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 assignment-1/submission/17307110367/.keep diff --git a/assignment-1/submission/17307110367/.keep b/assignment-1/submission/17307110367/.keep deleted file mode 100644 index e69de29..0000000 -- Gitee From b4c66f7a5ebd4439b0693ae6fe16b95c1efb0528 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn> Date: Sun, 21 Mar 2021 11:09:05 +0800 Subject: [PATCH 03/23] =?UTF-8?q?=E6=96=B0=E5=BB=BA=2017307110367?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-1/submission/17307110367/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-1/submission/17307110367/.keep diff --git a/assignment-1/submission/17307110367/.keep b/assignment-1/submission/17307110367/.keep new file mode 100644 index 0000000..e69de29 -- Gitee From 676c27b7eec192d96034b1692c5dc0519b95f49d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn> Date: Sun, 21 Mar 2021 11:10:22 +0800 Subject: [PATCH 04/23] =?UTF-8?q?=E6=96=B0=E5=BB=BA=20img?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-1/submission/17307110367/img/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-1/submission/17307110367/img/.keep diff --git a/assignment-1/submission/17307110367/img/.keep b/assignment-1/submission/17307110367/img/.keep new file mode 100644 index 0000000..e69de29 -- Gitee From 49c60403b7c7752bb7c204cfa1ee254f98e7a548 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn> Date: Sun, 21 Mar 2021 11:11:18 +0800 Subject: [PATCH 05/23] =?UTF-8?q?=E5=88=A0=E9=99=A4=E6=96=87=E4=BB=B6=20as?= =?UTF-8?q?signment-1/submission/17307110367/.keep?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-1/submission/17307110367/.keep | 0 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 assignment-1/submission/17307110367/.keep diff --git a/assignment-1/submission/17307110367/.keep b/assignment-1/submission/17307110367/.keep deleted file mode 100644 index e69de29..0000000 -- Gitee From 0fe5d219f3696e4202d87890dc62ed55028506e3 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn> Date: Sun, 21 Mar 2021 11:14:46 +0800 Subject: [PATCH 06/23] source.py --- assignment-1/submission/17307110367/source.py | 152 ++++++++++++++++++ 1 file changed, 152 insertions(+) create mode 100644 assignment-1/submission/17307110367/source.py diff --git a/assignment-1/submission/17307110367/source.py b/assignment-1/submission/17307110367/source.py new file mode 100644 index 0000000..f93d4ce --- /dev/null +++ b/assignment-1/submission/17307110367/source.py @@ -0,0 +1,152 @@ +import sys +import numpy as np +import matplotlib.pyplot as plt + +class KNN: + + def __init__(self): + self.train_data = None + self.train_label = None + self.k = None + + def fit(self, train_data, train_label): + self.train_data = train_data + self.train_label = train_label + # 将训练集打乱 + data_size = self.train_data.shape[0] + shuffled_indices = np.random.permutation(data_size) + shuffled_data = train_data[shuffled_indices] + shuffled_label = train_label[shuffled_indices] + # test_ratio为测试集所占的百分比，划分训练集和验证集 + test_ratio = 0.2 + test_set_size = int(data_size * test_ratio) + valid_data = shuffled_data[:test_set_size] + valid_label = shuffled_label[:test_set_size] + training_data = shuffled_data[test_set_size:] + training_label = shuffled_label[test_set_size:] + # 在验证集上对不同的K值进行测试 + record ={} + for k in range(1,5,2): + data_size = training_data.shape[0] + predict_result = np.array([]) + for i in range(valid_data.shape[0]): + diff = np.tile(valid_data[i], (data_size, 1)) - training_data + sqdiff = diff ** 2 + squareDist = np.sum(sqdiff, axis=1) + dist = squareDist ** 0.5 + # test_data到其它点的距离 + sorteddiffdist = np.argsort(dist) + # 对这些距离从小到大排序 + classCount = {} + for j in range(k): + Label = training_label[sorteddiffdist[j]] + classCount[Label] = classCount.get(Label, 0) + 1 + # 统计距离中前K个值中各个类别的数量 + maxCount = 0 + for key, value in classCount.items(): + if value > maxCount: + maxCount = value + result = key + predict_result = np.append(predict_result, result) + acc = np.mean(np.equal(predict_result, valid_label)) + record[k] = acc + # 取验证准确率最高的K值作为K值 + maxCount = 0 + for key, value in record.items(): + if value > maxCount: + maxCount = value + k_result = key + print("k=",k_result) + self.k = k_result + + def predict(self, test_data): + data_size = self.train_data.shape[0] + predict_result = np.array([]) + for i in range(test_data.shape[0]): + diff = np.tile(test_data[i],(data_size,1)) - self.train_data + sqdiff = diff **2 + squareDist = np.sum(sqdiff, axis =1) + dist = squareDist **0.5 + # test_data到其它点的距离 + sorteddiffdist = np.argsort(dist) + # 对这些距离从小到大排序 + classCount ={} + for j in range(self.k): + Label = self.train_label[sorteddiffdist[j]] + classCount[Label] = classCount.get(Label,0) + 1 + # 统计距离中前K个值中各个类别的数量 + maxCount = 0 + for key, value in classCount.items(): + if value > maxCount: + maxCount = value + result = key + predict_result = np.append(predict_result,result) + # 数量最多的就是预测的结果 + return predict_result + + +def generate(): + mean = (1, 2) + cov = np.array([[73, 0], [0, 22]]) + x = np.random.multivariate_normal(mean, cov, (800,)) + + mean = (16, -5) + cov = np.array([[21.2, 0], [0, 32.1]]) + y = np.random.multivariate_normal(mean, cov, (200,)) + + mean = (10, 22) + cov = np.array([[10, 5], [5, 10]]) + z = np.random.multivariate_normal(mean, cov, (1000,)) + + idx = np.arange(2000) + np.random.shuffle(idx) + data = np.concatenate([x, y, z]) + label = np.concatenate([ + np.zeros((800,), dtype=int), + np.ones((200,), dtype=int), + np.ones((1000,), dtype=int) * 2 + ]) + data = data[idx] + label = label[idx] + + train_data, test_data = data[:1600, ], data[1600:, ] + train_label, test_label = label[:1600, ], label[1600:, ] + np.save("data.npy", ( + (train_data, train_label), (test_data, test_label) + )) + + +def read(): + (train_data, train_label), (test_data, test_label) = np.load("data.npy", allow_pickle=True) + return (train_data, train_label), (test_data, test_label) + + +def display(data, label, name): + datas = [[], [], []] + for i in range(len(data)): + datas[label[i]].append(data[i]) + + for each in datas: + each = np.array(each) + plt.scatter(each[:, 0], each[:, 1]) + plt.savefig(f'./{name}') + plt.show() + + +if __name__ == "__main__": + if len(sys.argv) > 1 and sys.argv[1] == "g": + generate() + if len(sys.argv) > 1 and sys.argv[1] == "d": + (train_data, train_label), (test_data, test_label) = read() + display(train_data, train_label, 'train') + display(test_data, test_label, 'test') + else: + (train_data, train_label), (test_data, test_label) = read() + + model = KNN() + model.fit(train_data, train_label) + res = model.predict(test_data) + print("acc =", np.mean(np.equal(res, test_label))) + + + -- Gitee From f49e6195694de621d4b3a42c3ae3a09dcfa47279 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn> Date: Sun, 21 Mar 2021 17:22:31 +0800 Subject: [PATCH 07/23] !1 [submission] assignment-1 of 17307110367 --- .../submission/17307110367/img/test_1.png | Bin 0 -> 26475 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 assignment-1/submission/17307110367/img/test_1.png diff --git a/assignment-1/submission/17307110367/img/test_1.png b/assignment-1/submission/17307110367/img/test_1.png new file mode 100644 index 0000000000000000000000000000000000000000..eec47aac6c3a4a91fbb79b4e46c19b4dcaf56ad7 GIT binary patch literal 26475 zcmeFYbx<5%6fQWpCP4!PhhV|oEojgnf#B{M+}(q_6Fj)PI|Lb=;O_1YuP49vc5B~O z?Vnqjt_y4(nW=9* zS=ltL^0ZsgZ#GFUA4#ZC+pqeT-$W~8(U79yppi~aPNR%IJ2^9~HXVC=6+8WBiXzEQ!=r&m5=Y{uR-HMamjd%i9DTl zEAE`8{Tm<57B@Pbb^?QeNNgS*CR|YxG$AD=%w32b=OeCkOmV^d)uzVkhCHDs_?^Ms z+4|pBSJp^E-XLa!{#wE*U~1zN6ZM}TuHS0YK(@y7q#ISV)ndIKa4DDD6}24C{>Rqy zetc>gny%S0jhK{_Q0wL9J_4PuUws}P-1;u-YHNSx=jR`gl8H}^4Sz4L$9r^T}!tg6CQ{ptg_pd()7HZ0r@mH z^Gr`q>yD*!hv{S`Bm|b0mKtg?0CVP3obk=YVJi3URBPd}0US46vNi|dw&x$hRu(cN zGknm?!(2yyAC68q&~E}h7c|DUD~#DvHUB?S~a&Ek2Lo@Q=!91XQ*6MbiwXhI!2PP}vOXD4eerMJ2ws3KIGa=g{kB={rJbK=(i3rO< z!SBA~c>XS`VgL{L+E{Dpp2UC=9d~rmudA9-^lvm!GX(MG`%t~%3zB3J(B9lE#J%vB zS*lA-v&P;+ymd|y8ACi1R zL#X$!X2C=ByF1Q*2ISjcF|Wps38(l=saj0MoUL86?7}}0CB$ZoY-vHF0&wv(nC7j9 zz@!fxF}>+ygYxR!2XpLZc-j_w)+aoqF2mx;22vYch>Q3_H3R-uTIBPtJ$bF%^O*qD zx4q<|=(&0fV}sKS&)Z_JG+HAMoCs%m|wbIKtF2eI{~a6 ztcBT(v~YMVvYKQlAPfyq&w!yOGB{Mc>J;bh$wG9&G5pDVrYxCD4|(QJ6Or5Bt=~x$ z`9UHV_osF*IqQ4niWMz41Hg2QlJp7_WNWPOIOg9_i;6QtqT1Y7^Skj96FGTQdV(;8 zzTB@`IuQr_GeWS`w4ZvS{Yc+yS&>cj$40bpR?`F!^g$w@GDS(+H>-PP<);(;k`8Uc zI5-dUMWuQUgAk5HzPe+Y)~07!j=*Sxzp$T0MZ=1nRP>H43?PQYeEe+I=-M}m`?&C3 z;{)Cmo5x^i#i@M`p2!EA+-aZK(nFHTZpaf1DR_M*d6U4WKidN9PKo4ptVxcYsplsv z;go{q;G!G()0gLj^AP?mo-gKdsoU;FAi16lArJO)O$!yBEL91fh}p_282rGUc>29O zWx`Mikvk9%2-8x(sC=sbtUYxNp2k;r>hc2D8$6k9GS}Lg%8-~FR_L`&v*dw2F9-_W zW`yaW-US}d2^+#f0=!goIH>q}(#+A59kh1zRO6T-LSymU8Ms3G2ewWOrZ<(7Y#YM(qq7G#^9xW^R&_8Osm;XsHWz{$8_gt zc2XlSlKxaF@={)an9=)&rTwi}#Kw}o=H;_R^gQX*H2a>GzRJR7a*CiG^1s28VEo3z z)6o}euz*E>GC!_h%CikIW};HHxO<`kr>*#ksOy)1SArt;U>5#0IcfcrIUp*xfx!ff zk7)sJ=|PM3{TxF-IX-dM#zLRzb26+T*$=-{VjX(g0v8kbe*ZMX33T&~y+w z`p=MX6`#ob;w=_sk?;CG7GmLt%QT$X$e28#wJGHIct0 zn#q!XYVXUo9lWZ;;0^^mk3#DBfd?GK?+(K==13RVc;7p9&*=cxwRYQd=rlRK5MUzc z`d(1*aCdM1i^o;?61dRZ1iQbT<2`3ZBi__XR#2MiQg~HG1UtWY(BPMohX@KXvYso4 z_I`XIXfIbcn+f#4Bt9eQWX+ReawabQe)Wr68$Gt!sP;-iBBZ^&ta48ziBbADS))OgtO*3q?|K?z9n1^F0{y;y=I@hHKELv+HyL1kcB)(H0eh|B>s$h zd{IROuA=Y3Vet>K4%%^=+_>?kCCP`E5kuwBrARGckDGnANQ$^yAC=Onz`8Q^AgG#UdEu zZ`WEZe%_wyAeqVv-R4cCLTwm3PX4)8^~)#%^RY4cSE(Bf~PftI-?LcmE& zs-KyNlF*VkX&RGcPc@x~+#eN~Dj_Mb{2K%*IqP2Dvv~ujRl{-fMfD|9<$%!0cR`VB zu9#=%IIArh^1#T)`4mCv-!rV3t@mppdUDwZcLX_xn}ENJLD^rP5h+(0fBX8}^VlZXvcU%u;SmB#ZZ5pDoVfDE@L0sY@wnmL%_tmzA4V*=ZooExo}57 zM#TgpDZ2I9&FT8x9*+5ra=q4(Mzlni}Z*bofWqMMf6Z#Zv(yR*(S z1Vb2hGw~dU^w_(yGXRQlK?iAuLINfZ#`27TZj>+XYro6z2ePqaM+S3z3j=sYXTT

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z?0QQi3=(EOr(|Rd4J72wp5AiVJgzmHemhxjrE><3fdo)7lnqo8WYg_{RC_%>z|7qV%c$?itGu!@#=I#ESGWDb{Gq4#nz{o614E!N0yaaV&*qBznam)x zU#;4RQ2%GHF3kRYj{GEabcb#AZktQS!^6W9=}7O?)3Qvp^0n(QuuDH`X{8df8hoc^ zV&Ve&mkSB=<UsWn1!6qLK!Z1#{ACNcomU8AsR7K_kP{r3Tl>H8e*XJ; e{r}w~k7RCnEa#zv`%d7cAd;f8B4xt5-~JDYvpd58 literal 0 HcmV?d00001 -- Gitee From b7f28489a9700ae04549e5b7131e38ab8bf0a02d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn> Date: Sun, 21 Mar 2021 23:35:47 +0800 Subject: [PATCH 14/23] =?UTF-8?q?=E5=88=A0=E9=99=A4=E6=96=87=E4=BB=B6=20as?= =?UTF-8?q?signment-1/submission/17307110367/source.py?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-1/submission/17307110367/source.py | 152 ------------------ 1 file changed, 152 deletions(-) delete mode 100644 assignment-1/submission/17307110367/source.py diff --git a/assignment-1/submission/17307110367/source.py b/assignment-1/submission/17307110367/source.py deleted file mode 100644 index f93d4ce..0000000 --- a/assignment-1/submission/17307110367/source.py +++ /dev/null @@ -1,152 +0,0 @@ -import sys -import numpy as np -import matplotlib.pyplot as plt - -class KNN: - - def __init__(self): - self.train_data = None - self.train_label = None - self.k = None - - def fit(self, train_data, train_label): - self.train_data = train_data - self.train_label = train_label - # 将训练集打乱 - data_size = self.train_data.shape[0] - shuffled_indices = np.random.permutation(data_size) - shuffled_data = train_data[shuffled_indices] - shuffled_label = train_label[shuffled_indices] - # test_ratio为测试集所占的百分比，划分训练集和验证集 - test_ratio = 0.2 - test_set_size = int(data_size * test_ratio) - valid_data = shuffled_data[:test_set_size] - valid_label = shuffled_label[:test_set_size] - training_data = shuffled_data[test_set_size:] - training_label = shuffled_label[test_set_size:] - # 在验证集上对不同的K值进行测试 - record ={} - for k in range(1,5,2): - data_size = training_data.shape[0] - predict_result = np.array([]) - for i in range(valid_data.shape[0]): - diff = np.tile(valid_data[i], (data_size, 1)) - training_data - sqdiff = diff ** 2 - squareDist = np.sum(sqdiff, axis=1) - dist = squareDist ** 0.5 - # test_data到其它点的距离 - sorteddiffdist = np.argsort(dist) - # 对这些距离从小到大排序 - classCount = {} - for j in range(k): - Label = training_label[sorteddiffdist[j]] - classCount[Label] = classCount.get(Label, 0) + 1 - # 统计距离中前K个值中各个类别的数量 - maxCount = 0 - for key, value in classCount.items(): - if value > maxCount: - maxCount = value - result = key - predict_result = np.append(predict_result, result) - acc = np.mean(np.equal(predict_result, valid_label)) - record[k] = acc - # 取验证准确率最高的K值作为K值 - maxCount = 0 - for key, value in record.items(): - if value > maxCount: - maxCount = value - k_result = key - print("k=",k_result) - self.k = k_result - - def predict(self, test_data): - data_size = self.train_data.shape[0] - predict_result = np.array([]) - for i in range(test_data.shape[0]): - diff = np.tile(test_data[i],(data_size,1)) - self.train_data - sqdiff = diff **2 - squareDist = np.sum(sqdiff, axis =1) - dist = squareDist **0.5 - # test_data到其它点的距离 - sorteddiffdist = np.argsort(dist) - # 对这些距离从小到大排序 - classCount ={} - for j in range(self.k): - Label = self.train_label[sorteddiffdist[j]] - classCount[Label] = classCount.get(Label,0) + 1 - # 统计距离中前K个值中各个类别的数量 - maxCount = 0 - for key, value in classCount.items(): - if value > maxCount: - maxCount = value - result = key - predict_result = np.append(predict_result,result) - # 数量最多的就是预测的结果 - return predict_result - - -def generate(): - mean = (1, 2) - cov = np.array([[73, 0], [0, 22]]) - x = np.random.multivariate_normal(mean, cov, (800,)) - - mean = (16, -5) - cov = np.array([[21.2, 0], [0, 32.1]]) - y = np.random.multivariate_normal(mean, cov, (200,)) - - mean = (10, 22) - cov = np.array([[10, 5], [5, 10]]) - z = np.random.multivariate_normal(mean, cov, (1000,)) - - idx = np.arange(2000) - np.random.shuffle(idx) - data = np.concatenate([x, y, z]) - label = np.concatenate([ - np.zeros((800,), dtype=int), - np.ones((200,), dtype=int), - np.ones((1000,), dtype=int) * 2 - ]) - data = data[idx] - label = label[idx] - - train_data, test_data = data[:1600, ], data[1600:, ] - train_label, test_label = label[:1600, ], label[1600:, ] - np.save("data.npy", ( - (train_data, train_label), (test_data, test_label) - )) - - -def read(): - (train_data, train_label), (test_data, test_label) = np.load("data.npy", allow_pickle=True) - return (train_data, train_label), (test_data, test_label) - - -def display(data, label, name): - datas = [[], [], []] - for i in range(len(data)): - datas[label[i]].append(data[i]) - - for each in datas: - each = np.array(each) - plt.scatter(each[:, 0], each[:, 1]) - plt.savefig(f'./{name}') - plt.show() - - -if __name__ == "__main__": - if len(sys.argv) > 1 and sys.argv[1] == "g": - generate() - if len(sys.argv) > 1 and sys.argv[1] == "d": - (train_data, train_label), (test_data, test_label) = read() - display(train_data, train_label, 'train') - display(test_data, test_label, 'test') - else: - (train_data, train_label), (test_data, test_label) = read() - - model = KNN() - model.fit(train_data, train_label) - res = model.predict(test_data) - print("acc =", np.mean(np.equal(res, test_label))) - - - -- Gitee From 8eb0777497545fbceae7106feb0b34f824f09ae5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn> Date: Sun, 21 Mar 2021 23:35:58 +0800 Subject: [PATCH 15/23] !1 [submission] assignment-1 of 17307110367 --- assignment-1/submission/17307110367/source.py | 172 ++++++++++++++++++ 1 file changed, 172 insertions(+) create mode 100644 assignment-1/submission/17307110367/source.py diff --git a/assignment-1/submission/17307110367/source.py b/assignment-1/submission/17307110367/source.py new file mode 100644 index 0000000..bc70f0c --- /dev/null +++ b/assignment-1/submission/17307110367/source.py @@ -0,0 +1,172 @@ +import sys +import numpy as np +import matplotlib.pyplot as plt + +class KNN: + + def __init__(self): + self.train_data = None + self.train_label = None + self.k = None + + def fit(self, train_data, train_label): + self.train_data = train_data + self.train_label = train_label + # 将训练集打乱 + data_size = self.train_data.shape[0] + shuffled_indices = np.random.permutation(data_size) + shuffled_data = train_data[shuffled_indices] + shuffled_label = train_label[shuffled_indices] + # test_ratio为测试集所占的百分比，划分训练集和验证集 + test_ratio = 0.2 + test_set_size = int(data_size * test_ratio) + valid_data = shuffled_data[:test_set_size] + valid_label = shuffled_label[:test_set_size] + training_data = shuffled_data[test_set_size:] + training_label = shuffled_label[test_set_size:] + # 在验证集上对不同的K值进行测试 + record ={} + if training_data.shape[0] < 20: + k_number = training_data.shape[0] + else: + k_number = 20 + for k in range(1,k_number,2): + data_size = training_data.shape[0] + predict_result = np.array([]) + for i in range(valid_data.shape[0]): + diff = np.tile(valid_data[i], (data_size, 1)) - training_data + sqdiff = diff ** 2 + squareDist = np.sum(sqdiff, axis=1) + dist = squareDist ** 0.5 + # test_data到其它点的距离 + sorteddiffdist = np.argsort(dist) + # 对这些距离从小到大排序 + classCount = {} + for j in range(k): + Label = training_label[sorteddiffdist[j]] + classCount[Label] = classCount.get(Label, 0) + 1 + # 统计距离中前K个值中各个类别的数量 + maxCount = 0 + for key, value in classCount.items(): + if value > maxCount: + maxCount = value + result = key + predict_result = np.append(predict_result, result) + acc = np.mean(np.equal(predict_result, valid_label)) + record[k] = acc + # 取验证准确率最高的K值作为K值 + maxCount = 0 + for key, value in record.items(): + if value > maxCount: + maxCount = value + k_result = key + print("k=",k_result) + self.k = k_result + + def predict(self, test_data): + data_size = self.train_data.shape[0] + predict_result = np.array([]) + for i in range(test_data.shape[0]): + diff = np.tile(test_data[i],(data_size,1)) - self.train_data + sqdiff = diff **2 + squareDist = np.sum(sqdiff, axis =1) + dist = squareDist **0.5 + # test_data到其它点的距离 + sorteddiffdist = np.argsort(dist) + # 对这些距离从小到大排序 + classCount ={} + for j in range(self.k): + Label = self.train_label[sorteddiffdist[j]] + classCount[Label] = classCount.get(Label,0) + 1 + # 统计距离中前K个值中各个类别的数量 + maxCount = 0 + for key, value in classCount.items(): + if value > maxCount: + maxCount = value + result = key + predict_result = np.append(predict_result,result) + # 数量最多的就是预测的结果 + return predict_result + + +def generate(): + mean = (1, 2) + cov = np.array([[73, 0], [0, 22]]) + x = np.random.multivariate_normal(mean, cov, (800,)) + #x = np.random.multivariate_normal(mean, cov, (1600,)) + + mean = (16, -5) + #mean = (30, -20) + #mean = (15, 0) + cov = np.array([[21.2, 0], [0, 32.1]]) + #cov = np.array([[73, 0], [0, 22]]) + y = np.random.multivariate_normal(mean, cov, (200,)) + #y = np.random.multivariate_normal(mean, cov, (400,)) + + mean = (10, 22) + #mean = (10,10) + cov = np.array([[10, 5], [5, 10]]) + #cov = np.array([[73, 0], [0, 22]]) + z = np.random.multivariate_normal(mean, cov, (1000,)) + #z = np.random.multivariate_normal(mean, cov, (2000,)) + + idx = np.arange(2000) + #idx = np.arange(2800) + np.random.shuffle(idx) + data = np.concatenate([x, y, z]) + label = np.concatenate([ + np.zeros((800,), dtype=int), + np.ones((200,), dtype=int), + np.ones((1000,), dtype=int) * 2 + ]) + # label = np.concatenate([ + # np.zeros((1600,), dtype=int), + # np.ones((200,), dtype=int), + # np.ones((1000,), dtype=int) * 2 + # ]) + # data = data[idx] + # label = label[idx] + + train_data, test_data = data[:1600, ], data[1600:, ] + train_label, test_label = label[:1600, ], label[1600:, ] + # train_data, test_data = data[:2240, ], data[2240:, ] + # train_label, test_label = label[:2240, ], label[2240:, ] + np.save("data.npy", ( + (train_data, train_label), (test_data, test_label) + )) + + +def read(): + (train_data, train_label), (test_data, test_label) = np.load("data.npy", allow_pickle=True) + return (train_data, train_label), (test_data, test_label) + + +def display(data, label, name): + datas = [[], [], []] + for i in range(len(data)): + datas[label[i]].append(data[i]) + + for each in datas: + each = np.array(each) + plt.scatter(each[:, 0], each[:, 1]) + plt.savefig(f'./{name}') + plt.show() + + +if __name__ == "__main__": + if len(sys.argv) > 1 and sys.argv[1] == "g": + generate() + if len(sys.argv) > 1 and sys.argv[1] == "d": + (train_data, train_label), (test_data, test_label) = read() + display(train_data, train_label, 'train') + display(test_data, test_label, 'test') + else: + (train_data, train_label), (test_data, test_label) = read() + + model = KNN() + model.fit(train_data, train_label) + res = model.predict(test_data) + print("acc =", np.mean(np.equal(res, test_label))) + + + -- Gitee From 0f76b4c94e874d52b15a16e920e3cf22439634b8 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn> Date: Sun, 21 Mar 2021 23:37:22 +0800 Subject: [PATCH 16/23] !1 [submission] assignment-1 of 17307110367 --- .../submission/17307110367/README.md.md | 131 ++++++++++++++++++ 1 file changed, 131 insertions(+) create mode 100644 assignment-1/submission/17307110367/README.md.md diff --git a/assignment-1/submission/17307110367/README.md.md b/assignment-1/submission/17307110367/README.md.md new file mode 100644 index 0000000..76d220c --- /dev/null +++ b/assignment-1/submission/17307110367/README.md.md @@ -0,0 +1,131 @@ +# 课程报告 + 我的KNN模型**只用到了numpy包**，所以我的代码应该可以通过限定依赖包的自动测试。 + ## 一、数据集的生成和划分 + 首先我以如下参数生成了3个符合二维高斯分布的集合的数据集。 + + 第一类数据800个，标注为0： + ```math + \sum = [\begin{matrix}73 & 0\\0 & 22\end{matrix}] + + \mu = [\begin{matrix}1& 2\end{matrix}] + ``` + + 第二类数据200个，标注为1： + ```math + \sum = [\begin{matrix}21.2 & 0\\0 & 32.1\end{matrix}] + + \mu = [\begin{matrix}16& -5\end{matrix}] + ``` + + 第三类数据1000个，标注为2： + ```math + \sum = [\begin{matrix}10 & 5\\5 & 10\end{matrix}] + + \mu = [\begin{matrix}10& 22\end{matrix}] + ``` + 将这些图片和对应的标注混合并打乱次序，就能够得到我们数据集。从其中取出80%(1600对)作为我们的训练集。 + 这是我生成的训练集 + +![train_1](https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-1/submission/17307110367/img/train_1.png) + +取出其中另外的20%(400对)作为我们的测试集。 +这是我生成的测试集 +![test_1](https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-1/submission/17307110367/img/test_1.png) + + ## 二、KNN模型的建立 + 我的KNN模型主要分为两部分。第一部分的fit函数将训练集分为训练集和验证集，根据KNN模型在验证集上的最优结果自动地选择最优的K值。第二部分的predict函数用已选择出的K值代入KNN模型中，预测测试集的标签。 + ### 2.1 fit函数的编写 + fit函数主要包含以下几个步骤： + (1)将已有的训练集的次序打乱，分出其中的20%作为验证集，80%作为测试集。 + + (2)遍历待选的K值，在暂时确定K值的情况下在验证集上测试模型的结果。若训练集数量小于20，则待选K值的范围是range(1,训练集数量,2);若训练集数量大于20，则待选K值的范围是range(1,20,2)。 + + (3)找到验证集预测准确率最高的模型所对应的K值。将该值作为后续在predict函数中运用的K值。 + + ### 2.2 predict函数的编写 + predict函数主要包含以下几个步骤： + (1)遍历测试集中的每一个点。当取出测试集中的某一点时，计算该点与训练集中的每个点的距离。 + + (2)对计算好的距离进行从小到大排序，取出前K个点 + + (3)统计前K个值中各个类别的数量 + + (4)数量最多的类别便是预测结果。 + + + ## 三、实验结果与分析 + 在命令行运行 python source.py g即可生成数据集并查看准确率结果。由于每次随机生成的数据集略有差异，每次的K值和准确率也略有差异。重复实验10次，结果如下表： + + +实验次数 |K值 |准确率 +---|---|--- +1| 11| 0.96 +2 | 9|0.9675 +3| 15| 0.955 +4 | 11|0.9475 +5| 5| 0.94 +6 | 5|0.94 +7| 11| 0.96 +8 | 7|0.945 +9| 7| 0.95 +10 | 19|0.955 +取这10次实验准确率的均值，得到模型的最终准确率为0.952。 +最终的模型准确率较高。准确率不为1的原因是测试集中蓝色与橙色的点有着一定的交集，对于处于交集中的数据我们也很难分清楚数据点到底属于哪一个类别。这部分的失误对于KNN来说似乎是无法避免的。 + + +## 三、修改数据集进行实验探究 +### 3.1 修改高斯分布的距离 +我们的预期是：在其它条件不变的情况下，高斯分布的距离越大，数据分的越开，KNN越容易预测准确。高斯分布的距离越小，数据离得越近，KNN的准确率越低。 +#### (1)设置参数使得三个类别分的更开。 + + 修改第二类数据的均值，使得它与另外两类数据分的更开： + ```math + \mu_2 = [\begin{matrix}30 & -20\end{matrix}] + ``` + + 此时测试集的数据分布如下图： + ![test_2](https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-1/submission/17307110367/img/test_2.png) + 多次实验得到模型的准确率为0.99。符合我们的预期。 + +#### (2)设置参数使得三个类别离得更近。 + + 修改每一类数据的均值，使得它们离得更近： + ```math + \mu_1 = [\begin{matrix}1 & 2\end{matrix}] + + \mu_2 = [\begin{matrix}15 & 0\end{matrix}] + + \mu_3 = [\begin{matrix}10 & 10\end{matrix}] + ``` + + 此时测试集的数据分布如下图： + + ![test_3]( https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-1/submission/17307110367/img/test_3.png) + 此时模型的准确率均值只有0.84。符合我们的预期。 + + ### 3.2 修改高斯分布的方差 + 我们的预期是：在其它条件不变的情况下，高斯分布的方差越大，数据越容易混淆，因此KNN的结果越差。高斯分布的方差越小，数据越集中，KNN的结果越好。 +#### 设置参数使得第二和第三类数据的协方差更大。 + 修改第二，三类数据的方差如下： + + ```math + \sum = [\begin{matrix}73 & 0\\0 & 22\end{matrix}] + ``` + 此时测试集的数据分布如下图： + ![test_4](https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-1/submission/17307110367/img/test_4.png) + + 此时模型的准确率均值只有0.74,符合我们的预期。显然KNN的结果在这种情况下并不理想。 + + ### 3.3 修改数据的数量 + #### (1)使各类数据翻倍。 + 对第一，第二，第三类的训练和测试数据翻倍。 + 此时测试集的数据分布如下图： + ![test_5](https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-1/submission/17307110367/img/test_5.png) + + 对模型运行多次求均值，得到模型的准确率约为0.956。准确率相比于原先提升了一点点。这点提升微乎其微,背后的原因可能是数据翻倍时同样也使得数据间的交叠翻倍，对于这部分的交叠数据，模型很难判别正确。因此准确率没有什么改变。 + + #### (2)使第一类数据翻倍 + 只对第一类的训练和测试数据翻倍。 + 此时测试集的数据分布如下图： + ![test_6](https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-1/submission/17307110367/img/test_6.png) + 对模型运行多次求均值，得到模型的准确率约为0.96。可见准确率提升了一些。这是由于第一类的数据翻倍，导致在数据交叠区域数据点更倾向于被判别为第一类数据，因此准确率必定会有一定的提升 \ No newline at end of file -- Gitee From 0e9a60056fd2917f9df7afaca3926ba527167e96 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn> Date: Sun, 21 Mar 2021 23:37:33 +0800 Subject: [PATCH 17/23] =?UTF-8?q?=E9=87=8D=E5=91=BD=E5=90=8D=20assignment-?= =?UTF-8?q?1/submission/17307110367/README.md.md=20=E4=B8=BA=20assignment-?= =?UTF-8?q?1/submission/17307110367/README.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- assignment-1/submission/17307110367/{README.md.md => README.md} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename assignment-1/submission/17307110367/{README.md.md => README.md} (100%) diff --git a/assignment-1/submission/17307110367/README.md.md b/assignment-1/submission/17307110367/README.md similarity index 100% rename from assignment-1/submission/17307110367/README.md.md rename to assignment-1/submission/17307110367/README.md -- Gitee From d44287b802f83c6f058095cc24dcfb1aa54e52a0 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn> Date: Sun, 21 Mar 2021 23:57:41 +0800 Subject: [PATCH 18/23] update assignment-1/submission/17307110367/README.md. --- assignment-1/submission/17307110367/README.md | 50 +++++++++---------- 1 file changed, 23 insertions(+), 27 deletions(-) diff --git a/assignment-1/submission/17307110367/README.md b/assignment-1/submission/17307110367/README.md index 76d220c..e19f21d 100644 --- a/assignment-1/submission/17307110367/README.md +++ b/assignment-1/submission/17307110367/README.md @@ -4,25 +4,24 @@ 首先我以如下参数生成了3个符合二维高斯分布的集合的数据集。 第一类数据800个，标注为0： - ```math - \sum = [\begin{matrix}73 & 0\\0 & 22\end{matrix}] + +$\sum = [\begin{matrix}73 & 0\\0 & 22\end{matrix}] $ - \mu = [\begin{matrix}1& 2\end{matrix}] - ``` - - 第二类数据200个，标注为1： - ```math - \sum = [\begin{matrix}21.2 & 0\\0 & 32.1\end{matrix}] +$\mu = [\begin{matrix}1& 2\end{matrix}]$ + + 第二类数据200个，标注为1： + +$\sum = [\begin{matrix}21.2 & 0\\0 & 32.1\end{matrix}] $ - \mu = [\begin{matrix}16& -5\end{matrix}] - ``` +$\mu = [\begin{matrix}16& -5\end{matrix}]$ + 第三类数据1000个，标注为2： - ```math - \sum = [\begin{matrix}10 & 5\\5 & 10\end{matrix}] + +$\sum = [\begin{matrix}10 & 5\\5 & 10\end{matrix}]$ - \mu = [\begin{matrix}10& 22\end{matrix}] - ``` +$\mu = [\begin{matrix}10& 22\end{matrix}]$ + 将这些图片和对应的标注混合并打乱次序，就能够得到我们数据集。从其中取出80%(1600对)作为我们的训练集。 这是我生成的训练集 @@ -79,9 +78,7 @@ #### (1)设置参数使得三个类别分的更开。 修改第二类数据的均值，使得它与另外两类数据分的更开： - ```math - \mu_2 = [\begin{matrix}30 & -20\end{matrix}] - ``` +$\mu_2 = [\begin{matrix}30 & -20\end{matrix}]$ 此时测试集的数据分布如下图： ![test_2](https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-1/submission/17307110367/img/test_2.png) @@ -89,14 +86,14 @@ #### (2)设置参数使得三个类别离得更近。 - 修改每一类数据的均值，使得它们离得更近： - ```math - \mu_1 = [\begin{matrix}1 & 2\end{matrix}] + 修改每一类数据的均值，使得它们离得更近： + +$\mu_1 = [\begin{matrix}1 & 2\end{matrix}] $ - \mu_2 = [\begin{matrix}15 & 0\end{matrix}] +$\mu_2 = [\begin{matrix}15 & 0\end{matrix}] $ - \mu_3 = [\begin{matrix}10 & 10\end{matrix}] - ``` +$\mu_3 = [\begin{matrix}10 & 10\end{matrix}] $ + 此时测试集的数据分布如下图： @@ -107,10 +104,9 @@ 我们的预期是：在其它条件不变的情况下，高斯分布的方差越大，数据越容易混淆，因此KNN的结果越差。高斯分布的方差越小，数据越集中，KNN的结果越好。 #### 设置参数使得第二和第三类数据的协方差更大。 修改第二，三类数据的方差如下： - - ```math - \sum = [\begin{matrix}73 & 0\\0 & 22\end{matrix}] - ``` + +$\sum = [\begin{matrix}73 & 0\\0 & 22\end{matrix}]$ + 此时测试集的数据分布如下图： ![test_4](https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-1/submission/17307110367/img/test_4.png) -- Gitee From c3f3b717762844aaea9eeeb8481d064878a3cb15 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn> Date: Sun, 21 Mar 2021 23:58:44 +0800 Subject: [PATCH 19/23] update assignment-1/submission/17307110367/README.md. --- assignment-1/submission/17307110367/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/17307110367/README.md b/assignment-1/submission/17307110367/README.md index e19f21d..64d08b6 100644 --- a/assignment-1/submission/17307110367/README.md +++ b/assignment-1/submission/17307110367/README.md @@ -5,13 +5,13 @@ 第一类数据800个，标注为0： -$\sum = [\begin{matrix}73 & 0\\0 & 22\end{matrix}] $ +$\sum = [\begin{matrix}73 & 0\\\\0 & 22\end{matrix}] $ $\mu = [\begin{matrix}1& 2\end{matrix}]$ 第二类数据200个，标注为1： -$\sum = [\begin{matrix}21.2 & 0\\0 & 32.1\end{matrix}] $ +$\sum = [\begin{matrix}21.2 & 0\\\\0 & 32.1\end{matrix}] $ $\mu = [\begin{matrix}16& -5\end{matrix}]$ -- Gitee From 86ccfdc980d5bf6ec31882a0333254414e76c4d5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn> Date: Sun, 21 Mar 2021 23:59:20 +0800 Subject: [PATCH 20/23] update assignment-1/submission/17307110367/README.md. --- assignment-1/submission/17307110367/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/17307110367/README.md b/assignment-1/submission/17307110367/README.md index 64d08b6..3977002 100644 --- a/assignment-1/submission/17307110367/README.md +++ b/assignment-1/submission/17307110367/README.md @@ -18,7 +18,7 @@ $\mu = [\begin{matrix}16& -5\end{matrix}]$ 第三类数据1000个，标注为2： -$\sum = [\begin{matrix}10 & 5\\5 & 10\end{matrix}]$ +$\sum = [\begin{matrix}10 & 5\\\\5 & 10\end{matrix}]$ $\mu = [\begin{matrix}10& 22\end{matrix}]$ @@ -105,7 +105,7 @@ $\mu_3 = [\begin{matrix}10 & 10\end{matrix}] $ #### 设置参数使得第二和第三类数据的协方差更大。 修改第二，三类数据的方差如下： -$\sum = [\begin{matrix}73 & 0\\0 & 22\end{matrix}]$ +$\sum = [\begin{matrix}73 & 0\\\\0 & 22\end{matrix}]$ 此时测试集的数据分布如下图： ![test_4](https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-1/submission/17307110367/img/test_4.png) -- Gitee From 44e3f20547987822c3ec12521b7674a9f344cc66 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn> Date: Mon, 22 Mar 2021 00:04:34 +0800 Subject: [PATCH 21/23] update assignment-1/submission/17307110367/README.md. --- assignment-1/submission/17307110367/README.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/17307110367/README.md b/assignment-1/submission/17307110367/README.md index 3977002..74f4673 100644 --- a/assignment-1/submission/17307110367/README.md +++ b/assignment-1/submission/17307110367/README.md @@ -25,7 +25,7 @@ $\mu = [\begin{matrix}10& 22\end{matrix}]$ 将这些图片和对应的标注混合并打乱次序，就能够得到我们数据集。从其中取出80%(1600对)作为我们的训练集。 这是我生成的训练集 -![train_1](https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-1/submission/17307110367/img/train_1.png) +![train_1](./img/train_1.png) 取出其中另外的20%(400对)作为我们的测试集。 这是我生成的测试集 @@ -67,7 +67,8 @@ $\mu = [\begin{matrix}10& 22\end{matrix}]$ 7| 11| 0.96 8 | 7|0.945 9| 7| 0.95 -10 | 19|0.955 +10 | 19|0.955 + 取这10次实验准确率的均值，得到模型的最终准确率为0.952。 最终的模型准确率较高。准确率不为1的原因是测试集中蓝色与橙色的点有着一定的交集，对于处于交集中的数据我们也很难分清楚数据点到底属于哪一个类别。这部分的失误对于KNN来说似乎是无法避免的。 -- Gitee From 4f53e676a46360e8784e96a021316b6e33a4e7c2 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn> Date: Mon, 22 Mar 2021 00:13:52 +0800 Subject: [PATCH 22/23] update assignment-1/submission/17307110367/README.md. --- assignment-1/submission/17307110367/README.md | 94 +++++++++++++------ 1 file changed, 64 insertions(+), 30 deletions(-) diff --git a/assignment-1/submission/17307110367/README.md b/assignment-1/submission/17307110367/README.md index 74f4673..8f6c591 100644 --- a/assignment-1/submission/17307110367/README.md +++ b/assignment-1/submission/17307110367/README.md @@ -3,24 +3,46 @@ ## 一、数据集的生成和划分 首先我以如下参数生成了3个符合二维高斯分布的集合的数据集。 - 第一类数据800个，标注为0： + 第一类数据800个，标注为0： +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +73 & 0 \\\\ +0 & 22 +\end{array}\right] \\\\ +\mu=\left[\begin{array}{ll} +1 & 2 +\end{array}\right] +\end{array} +$$ -$\sum = [\begin{matrix}73 & 0\\\\0 & 22\end{matrix}] $ - -$\mu = [\begin{matrix}1& 2\end{matrix}]$ 第二类数据200个，标注为1： - -$\sum = [\begin{matrix}21.2 & 0\\\\0 & 32.1\end{matrix}] $ - -$\mu = [\begin{matrix}16& -5\end{matrix}]$ - +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +21.2 & 0 \\\\ +0 & 32.1 +\end{array}\right] \\\\ +\mu=\left[\begin{array}{ll} +16 & -5 +\end{array}\right] +\end{array} +$$ - 第三类数据1000个，标注为2： - -$\sum = [\begin{matrix}10 & 5\\\\5 & 10\end{matrix}]$ - -$\mu = [\begin{matrix}10& 22\end{matrix}]$ + 第三类数据1000个，标注为2： + +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +10 & 5 \\\\ +5 & 10 +\end{array}\right] \\\\ +\mu=\left[\begin{array}{ll} +10 & 22 +\end{array}\right] +\end{array} +$$ 将这些图片和对应的标注混合并打乱次序，就能够得到我们数据集。从其中取出80%(1600对)作为我们的训练集。 这是我生成的训练集 @@ -29,7 +51,7 @@ $\mu = [\begin{matrix}10& 22\end{matrix}]$ 取出其中另外的20%(400对)作为我们的测试集。 这是我生成的测试集 -![test_1](https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-1/submission/17307110367/img/test_1.png) +![test_1](./img/test_1.png) ## 二、KNN模型的建立 我的KNN模型主要分为两部分。第一部分的fit函数将训练集分为训练集和验证集，根据KNN模型在验证集上的最优结果自动地选择最优的K值。第二部分的predict函数用已选择出的K值代入KNN模型中，预测测试集的标签。 @@ -79,37 +101,49 @@ $\mu = [\begin{matrix}10& 22\end{matrix}]$ #### (1)设置参数使得三个类别分的更开。 修改第二类数据的均值，使得它与另外两类数据分的更开： -$\mu_2 = [\begin{matrix}30 & -20\end{matrix}]$ +$$ +\mu_2 = [\begin{matrix}30 & -20\end{matrix}] +$$ 此时测试集的数据分布如下图： - ![test_2](https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-1/submission/17307110367/img/test_2.png) + ![test_2](./img/test_2.png) 多次实验得到模型的准确率为0.99。符合我们的预期。 #### (2)设置参数使得三个类别离得更近。 修改每一类数据的均值，使得它们离得更近： -$\mu_1 = [\begin{matrix}1 & 2\end{matrix}] $ - -$\mu_2 = [\begin{matrix}15 & 0\end{matrix}] $ - -$\mu_3 = [\begin{matrix}10 & 10\end{matrix}] $ - +$$ +\mu_1 = [\begin{matrix}1 & 2\end{matrix}] +$$ + +$$ +\mu_2 = [\begin{matrix}15 & 0\end{matrix}] +$$ +$$ +\mu_3 = [\begin{matrix}10 & 10\end{matrix}] +$$ 此时测试集的数据分布如下图： - ![test_3]( https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-1/submission/17307110367/img/test_3.png) + ![test_3](./img/test_3.png) 此时模型的准确率均值只有0.84。符合我们的预期。 ### 3.2 修改高斯分布的方差 我们的预期是：在其它条件不变的情况下，高斯分布的方差越大，数据越容易混淆，因此KNN的结果越差。高斯分布的方差越小，数据越集中，KNN的结果越好。 #### 设置参数使得第二和第三类数据的协方差更大。 - 修改第二，三类数据的方差如下： - -$\sum = [\begin{matrix}73 & 0\\\\0 & 22\end{matrix}]$ + 修改第二，三类数据的方差如下： +$$ +\begin{array}{l} +\Sigma=\left[\begin{array}{cc} +73 & 0 \\\\ +0 & 22 +\end{array}\right] +\end{array} +$$ 此时测试集的数据分布如下图： - ![test_4](https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-1/submission/17307110367/img/test_4.png) + ![test_4](./img/test_4.png) 此时模型的准确率均值只有0.74,符合我们的预期。显然KNN的结果在这种情况下并不理想。 @@ -117,12 +151,12 @@ $\sum = [\begin{matrix}73 & 0\\\\0 & 22\end{matrix}]$ #### (1)使各类数据翻倍。 对第一，第二，第三类的训练和测试数据翻倍。 此时测试集的数据分布如下图： - ![test_5](https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-1/submission/17307110367/img/test_5.png) + ![test_5](./img/test_5.png) 对模型运行多次求均值，得到模型的准确率约为0.956。准确率相比于原先提升了一点点。这点提升微乎其微,背后的原因可能是数据翻倍时同样也使得数据间的交叠翻倍，对于这部分的交叠数据，模型很难判别正确。因此准确率没有什么改变。 #### (2)使第一类数据翻倍 只对第一类的训练和测试数据翻倍。 此时测试集的数据分布如下图： - ![test_6](https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-1/submission/17307110367/img/test_6.png) + ![test_6](./img/test_6.png) 对模型运行多次求均值，得到模型的准确率约为0.96。可见准确率提升了一些。这是由于第一类的数据翻倍，导致在数据交叠区域数据点更倾向于被判别为第一类数据，因此准确率必定会有一定的提升 \ No newline at end of file -- Gitee From 8291779aa33462b344bb2067cf9894984dd67bd2 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn> Date: Mon, 22 Mar 2021 00:16:30 +0800 Subject: [PATCH 23/23] update assignment-1/submission/17307110367/README.md. --- assignment-1/submission/17307110367/README.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/assignment-1/submission/17307110367/README.md b/assignment-1/submission/17307110367/README.md index 8f6c591..f34b168 100644 --- a/assignment-1/submission/17307110367/README.md +++ b/assignment-1/submission/17307110367/README.md @@ -142,7 +142,8 @@ $$ \end{array} $$ - 此时测试集的数据分布如下图： + 此时测试集的数据分布如下图： + ![test_4](./img/test_4.png) 此时模型的准确率均值只有0.74,符合我们的预期。显然KNN的结果在这种情况下并不理想。 -- Gitee