吴恩达机器学习-线性回归单变量和多变量题目
import numpy as np
2
import pandas as pd
3
import matplotlib.pyplot as plt
4
A=np.eye(5)
5
print(A)
[[1. 0. 0. 0. 0.] [0. 1. 0. 0. 0.] [0. 0. 1. 0. 0.] [0. 0. 0. 1. 0.] [0. 0. 0. 0. 1.]]
In [2]:
1
data=pd.read_csv(r'C:\Users\Administrator\Desktop\ex1data1.txt',header=None,names=['Population','Profit'])
2
data.insert(0,'Ones',1)#在最前列插入名为Ones,值为一的列，在训练集中添加一列，以便我们可以使用向量化的解决方案来计算代价和梯度。
3
data.head()#默认只读取前五行数据，用于观察数据读取是否准确.
Out[2]:
| Ones | Population | Profit | |
|---|---|---|---|
| 0 | 1 | 6.1101 | 17.5920 |
| 1 | 1 | 5.5277 | 9.1302 |
| 2 | 1 | 8.5186 | 13.6620 |
| 3 | 1 | 7.0032 | 11.8540 |
| 4 | 1 | 5.8598 | 6.8233 |
In [3]:
1
data.plot(kind='scatter',x='Population',y='Profit',figsize=(12,8))#scatter:表示散点图。
2
plt.show()
In [4]:
1
cols=data.shape[1]#shape[o]:行。shape[1]:列
2
print(cols)
3
X = data.iloc[:,:-1]#X是data里的除去最后一列
4
y = data.iloc[:,cols-1:cols]#y是data最后一列
3
In [5]:
1
X.head()
Out[5]:
| Ones | Population | |
|---|---|---|
| 0 | 1 | 6.1101 |
| 1 | 1 | 5.5277 |
| 2 | 1 | 8.5186 |
| 3 | 1 | 7.0032 |
| 4 | 1 | 5.8598 |
In [6]:
1
y.head()
Out[6]:
| Profit | |
|---|---|
| 0 | 17.5920 |
| 1 | 9.1302 |
| 2 | 13.6620 |
| 3 | 11.8540 |
| 4 | 6.8233 |
In [7]:
1
X = np.matrix(X.values)#装入矩阵，后续可以对矩阵进行操作
2
y = np.matrix(y.values)
3
X.shape
Out[7]:
(97, 2)
In [8]:
1
y.shape
Out[8]:
(97, 1)
In [9]:
1
theta=np.matrix(np.array([0,0]))
2
theta.shape
Out[9]:
(1, 2)
In [10]:
1
def computeCost(X,y,theta):
2
inner=np.power(((X*theta.T)-y),2)
3
return np.sum(inner)/(2*len(X))
4
computeCost(X,y,theta)#theta初始值为0时的代价函数。正常来说这应该是代价函数的最大的值，后续会减小直至稳定。
Out[10]:
32.072733877455676
In [11]:
1
#准备的数据已经准备好，开始执行梯度下降算法,目标是找拟合程度最好的theta.
2
def gradientDescent(X,y,theta,alpha,iters):
3
temp=np.matrix(np.zeros(theta.shape))#作为中间变量存储每一次theta的变化
4
parameters=int(theta.ravel().shape[1])#theta的参数个数
5
cost=np.zeros(iters) #默认为1500个浮点类型的0，即生成了array([0.,0.,0.,......1500个])
6
for i in range(iters):
7
error=(X*theta.T)-y
8
#同时改变theta
9
for j in range(parameters):
10
term=np.multiply(error,X[:,j])#multiply是同类型的矩阵里面相对应的每个数点乘，j=0时：乘的数全为一；j=1时：乘的数为Xi.正好对应学习笔记公式。
11
temp[0,j]=theta[0,j]-(alpha/(len(X))*np.sum(term))
12
theta=temp
13
cost[i]=computeCost(X,y,theta)
14
print(theta)#观察theta的变化过程
15
return theta,cost
In [12]:
1
alpha=0.01
2
iters=1500
3
theta_end,cost=gradientDescent(X,y,theta,alpha,iters)
4
for i in range(1500):
5
print(cost[i])#观察cost的变化过程
6
theta_end
[[0.05839135 0.6532885 ]] [[0.06289175 0.77000978]] [[0.05782293 0.79134812]] [[0.05106363 0.79572981]] [[0.04401438 0.79709618]] [[0.03692413 0.79792547]] [[0.02983712 0.79865824]] [[0.02276118 0.79937279]] [[0.0156977 0.80008305]] [[0.0086469 0.8007915]] [[0.00160879 0.80149857]] [[-0.00541662 0.80220436]] [[-0.01242938 0.80290886]] [[-0.01942949 0.8036121 ]] [[-0.02641699 0.80431407]] [[-0.03339189 0.80501478]] [[-0.04035421 0.80571422]] [[-0.04730399 0.8064124 ]] [[-0.05424124 0.80710932]] [[-0.06116598 0.80780498]] [[-0.06807824 0.8084994 ]] [[-0.07497804 0.80919256]] [[-0.08186541 0.80988447]] [[-0.08874035 0.81057513]] [[-0.09560291 0.81126455]] [[-0.10245309 0.81195272]] [[-0.10929093 0.81263966]] [[-0.11611644 0.81332535]] [[-0.12292965 0.81400981]] [[-0.12973057 0.81469304]] [[-0.13651924 0.81537504]] [[-0.14329567 0.8160558 ]] [[-0.15005988 0.81673534]] [[-0.15681191 0.81741365]] [[-0.16355176 0.81809075]] [[-0.17027946 0.81876662]] [[-0.17699503 0.81944127]] [[-0.1836985 0.8201147]] [[-0.19038988 0.82078693]] [[-0.1970692 0.82145794]] [[-0.20373649 0.82212774]] [[-0.21039175 0.82279633]] [[-0.21703502 0.82346372]] [[-0.22366631 0.8241299 ]] [[-0.23028565 0.82479489]] [[-0.23689305 0.82545867]] [[-0.24348855 0.82612126]] [[-0.25007216 0.82678266]] [[-0.2566439 0.82744286]] [[-0.26320379 0.82810187]] [[-0.26975186 0.8287597 ]] [[-0.27628812 0.82941634]] [[-0.2828126 0.83007179]] [[-0.28932533 0.83072607]] [[-0.29582631 0.83137916]] [[-0.30231557 0.83203108]] [[-0.30879314 0.83268182]] [[-0.31525902 0.83333139]] [[-0.32171326 0.83397978]] [[-0.32815586 0.83462701]] [[-0.33458684 0.83527308]] [[-0.34100624 0.83591797]] [[-0.34741406 0.83656171]] [[-0.35381033 0.83720428]] [[-0.36019507 0.8378457 ]] [[-0.3665683 0.83848596]] [[-0.37293005 0.83912507]] [[-0.37928032 0.83976302]] [[-0.38561915 0.84039982]] [[-0.39194656 0.84103548]] [[-0.39826255 0.84166999]] [[-0.40456717 0.84230336]] [[-0.41086041 0.84293558]] [[-0.41714232 0.84356667]] [[-0.42341289 0.84419662]] [[-0.42967217 0.84482543]] [[-0.43592016 0.84545311]] [[-0.44215689 0.84607965]] [[-0.44838238 0.84670507]] [[-0.45459665 0.84732936]] [[-0.46079971 0.84795253]] [[-0.4669916 0.84857457]] [[-0.47317232 0.84919549]] [[-0.4793419 0.84981529]] [[-0.48550036 0.85043397]] [[-0.49164771 0.85105154]] [[-0.49778399 0.851668 ]] [[-0.5039092 0.85228334]] [[-0.51002338 0.85289758]] [[-0.51612653 0.85351071]] [[-0.52221868 0.85412273]] [[-0.52829985 0.85473365]] [[-0.53437006 0.85534347]] [[-0.54042932 0.85595219]] [[-0.54647767 0.85655981]] [[-0.55251511 0.85716633]] [[-0.55854166 0.85777177]] [[-0.56455736 0.85837611]] [[-0.57056221 0.85897936]] [[-0.57655623 0.85958153]] [[-0.58253945 0.8601826 ]] [[-0.58851189 0.8607826 ]] [[-0.59447356 0.86138151]] [[-0.60042448 0.86197935]] [[-0.60636467 0.86257611]] [[-0.61229416 0.86317179]] [[-0.61821296 0.8637664 ]] [[-0.62412109 0.86435993]] [[-0.63001857 0.8649524 ]] [[-0.63590542 0.8655438 ]] [[-0.64178166 0.86613413]] [[-0.6476473 0.86672339]] [[-0.65350238 0.8673116 ]] [[-0.65934689 0.86789875]] [[-0.66518088 0.86848483]] [[-0.67100434 0.86906986]] [[-0.67681731 0.86965384]] [[-0.6826198 0.87023676]] [[-0.68841183 0.87081863]] [[-0.69419342 0.87139946]] [[-0.69996459 0.87197923]] [[-0.70572536 0.87255796]] [[-0.71147574 0.87313565]] [[-0.71721575 0.8737123 ]] [[-0.72294542 0.87428791]] [[-0.72866476 0.87486248]] [[-0.73437379 0.87543601]] [[-0.74007253 0.87600851]] [[-0.745761 0.87657998]] [[-0.75143921 0.87715042]] [[-0.75710719 0.87771983]] [[-0.76276495 0.87828821]] [[-0.76841251 0.87885557]] [[-0.77404989 0.87942191]] [[-0.77967711 0.87998722]] [[-0.78529418 0.88055152]] [[-0.79090113 0.8811148 ]] [[-0.79649798 0.88167706]] [[-0.80208473 0.88223831]] [[-0.80766141 0.88279855]] [[-0.81322805 0.88335778]] [[-0.81878464 0.883916 ]] [[-0.82433122 0.88447321]] [[-0.82986781 0.88502942]] [[-0.83539441 0.88558463]] [[-0.84091105 0.88613883]] [[-0.84641774 0.88669204]] [[-0.85191451 0.88724425]] [[-0.85740137 0.88779547]] [[-0.86287834 0.88834569]] [[-0.86834544 0.88889492]] [[-0.87380268 0.88944316]] [[-0.87925009 0.88999041]] [[-0.88468767 0.89053667]] [[-0.89011546 0.89108195]] [[-0.89553346 0.89162625]] [[-0.90094169 0.89216956]] [[-0.90634018 0.8927119 ]] [[-0.91172893 0.89325326]] [[-0.91710797 0.89379364]] [[-0.92247731 0.89433305]] [[-0.92783698 0.89487149]] [[-0.93318698 0.89540895]] [[-0.93852734 0.89594545]] [[-0.94385807 0.89648098]] [[-0.9491792 0.89701554]] [[-0.95449073 0.89754914]] [[-0.95979269 0.89808178]] [[-0.96508509 0.89861346]] [[-0.97036795 0.89914418]] [[-0.97564128 0.89967395]] [[-0.98090511 0.90020276]] [[-0.98615946 0.90073061]] [[-0.99140433 0.90125752]] [[-0.99663975 0.90178347]] [[-1.00186573 0.90230848]] [[-1.00708228 0.90283254]] [[-1.01228944 0.90335565]] [[-1.01748721 0.90387782]] [[-1.02267561 0.90439906]] [[-1.02785466 0.90491935]] [[-1.03302437 0.9054387 ]] [[-1.03818476 0.90595712]] [[-1.04333585 0.9064746 ]] [[-1.04847766 0.90699115]] [[-1.0536102 0.90750677]] [[-1.05873348 0.90802146]] [[-1.06384753 0.90853522]] [[-1.06895236 0.90904806]] [[-1.07404799 0.90955997]] [[-1.07913444 0.91007096]] [[-1.08421171 0.91058102]] [[-1.08927983 0.91109017]] [[-1.09433882 0.9115984 ]] [[-1.09938869 0.91210572]] [[-1.10442945 0.91261212]] [[-1.10946113 0.9131176 ]] [[-1.11448374 0.91362218]] [[-1.11949729 0.91412584]] [[-1.12450181 0.9146286 ]] [[-1.12949731 0.91513045]] [[-1.1344838 0.9156314]] [[-1.1394613 0.91613145]] [[-1.14442983 0.91663059]] [[-1.14938941 0.91712883]] [[-1.15434004 0.91762618]] [[-1.15928175 0.91812262]] [[-1.16421455 0.91861818]] [[-1.16913846 0.91911284]] [[-1.17405349 0.91960661]] [[-1.17895967 0.92009948]] [[-1.183857 0.92059147]] [[-1.1887455 0.92108258]] [[-1.19362519 0.9215728 ]] [[-1.19849609 0.92206213]] [[-1.2033582 0.92255058]] [[-1.20821155 0.92303815]] [[-1.21305615 0.92352485]] [[-1.21789202 0.92401066]] [[-1.22271917 0.9244956 ]] [[-1.22753762 0.92497967]] [[-1.23234739 0.92546286]] [[-1.23714848 0.92594518]] [[-1.24194092 0.92642663]] [[-1.24672472 0.92690722]] [[-1.2514999 0.92738694]] [[-1.25626647 0.92786579]] [[-1.26102445 0.92834378]] [[-1.26577385 0.92882091]] [[-1.27051469 0.92929718]] [[-1.27524698 0.92977259]] [[-1.27997074 0.93024714]] [[-1.28468599 0.93072084]] [[-1.28939274 0.93119368]] [[-1.29409101 0.93166568]] [[-1.2987808 0.93213682]] [[-1.30346214 0.93260711]] [[-1.30813505 0.93307655]] [[-1.31279953 0.93354515]] [[-1.3174556 0.9340129]] [[-1.32210327 0.93447981]] [[-1.32674258 0.93494588]] [[-1.33137351 0.93541111]] [[-1.3359961 0.9358755]] [[-1.34061036 0.93633905]] [[-1.3452163 0.93680177]] [[-1.34981394 0.93726365]] [[-1.35440329 0.9377247 ]] [[-1.35898436 0.93818492]] [[-1.36355718 0.93864431]] [[-1.36812176 0.93910287]] [[-1.37267811 0.9395606 ]] [[-1.37722624 0.94001751]] [[-1.38176618 0.9404736 ]] [[-1.38629793 0.94092886]] [[-1.39082151 0.94138331]] [[-1.39533694 0.94183693]] [[-1.39984423 0.94228974]] [[-1.4043434 0.94274172]] [[-1.40883445 0.9431929 ]] [[-1.41331741 0.94364326]] [[-1.41779229 0.94409281]] [[-1.4222591 0.94454155]] [[-1.42671786 0.94498948]] [[-1.43116858 0.94543661]] [[-1.43561128 0.94588292]] [[-1.44004597 0.94632844]] [[-1.44447267 0.94677315]] [[-1.44889139 0.94721705]] [[-1.45330214 0.94766016]] [[-1.45770494 0.94810247]] [[-1.46209981 0.94854398]] [[-1.46648675 0.9489847 ]] [[-1.47086579 0.94942462]] [[-1.47523693 0.94986375]] [[-1.47960019 0.95030209]] [[-1.48395559 0.95073963]] [[-1.48830314 0.95117639]] [[-1.49264285 0.95161236]] [[-1.49697473 0.95204755]] [[-1.50129881 0.95248195]] [[-1.50561509 0.95291557]] [[-1.5099236 0.9533484]] [[-1.51422433 0.95378046]] [[-1.51851732 0.95421173]] [[-1.52280256 0.95464223]] [[-1.52708008 0.95507196]] [[-1.53134989 0.95550091]] [[-1.53561201 0.95592908]] [[-1.53986644 0.95635648]] [[-1.5441132 0.95678312]] [[-1.5483523 0.95720898]] [[-1.55258377 0.95763408]] [[-1.55680761 0.95805841]] [[-1.56102383 0.95848197]] [[-1.56523245 0.95890478]] [[-1.56943349 0.95932682]] [[-1.57362695 0.95974809]] [[-1.57781286 0.96016861]] [[-1.58199122 0.96058838]] [[-1.58616205 0.96100738]] [[-1.59032536 0.96142563]] [[-1.59448116 0.96184313]] [[-1.59862947 0.96225987]] [[-1.60277031 0.96267586]] [[-1.60690368 0.9630911 ]] [[-1.6110296 0.9635056]] [[-1.61514808 0.96391934]] [[-1.61925914 0.96433234]] [[-1.62336279 0.9647446 ]] [[-1.62745904 0.96515611]] [[-1.63154791 0.96556688]] [[-1.63562941 0.96597691]] [[-1.63970355 0.9663862 ]] [[-1.64377034 0.96679476]] [[-1.64782981 0.96720258]] [[-1.65188195 0.96760966]] [[-1.6559268 0.96801601]] [[-1.65996435 0.96842162]] [[-1.66399462 0.96882651]] [[-1.66801763 0.96923066]] [[-1.67203339 0.96963409]] [[-1.67604191 0.97003679]] [[-1.6800432 0.97043876]] [[-1.68403728 0.97084001]] [[-1.68802416 0.97124053]] [[-1.69200385 0.97164034]] [[-1.69597637 0.97203942]] [[-1.69994173 0.97243778]] [[-1.70389994 0.97283543]] [[-1.70785101 0.97323236]] [[-1.71179497 0.97362857]] [[-1.71573181 0.97402407]] [[-1.71966156 0.97441885]] [[-1.72358422 0.97481293]] [[-1.72749981 0.97520629]] [[-1.73140835 0.97559895]] [[-1.73530984 0.97599089]] [[-1.73920429 0.97638213]] [[-1.74309173 0.97677267]] [[-1.74697216 0.9771625 ]] [[-1.75084559 0.97755163]] [[-1.75471204 0.97794006]] [[-1.75857152 0.97832778]] [[-1.76242405 0.97871481]] [[-1.76626963 0.97910114]] [[-1.77010828 0.97948677]] [[-1.77394001 0.97987171]] [[-1.77776483 0.98025596]] [[-1.78158275 0.98063951]] [[-1.7853938 0.98102237]] [[-1.78919797 0.98140454]] [[-1.79299529 0.98178602]] [[-1.79678576 0.98216682]] [[-1.8005694 0.98254693]] [[-1.80434622 0.98292635]] [[-1.80811624 0.98330509]] [[-1.81187945 0.98368314]] [[-1.81563588 0.98406052]] [[-1.81938554 0.98443721]] [[-1.82312844 0.98481323]] [[-1.8268646 0.98518856]] [[-1.83059402 0.98556322]] [[-1.83431672 0.98593721]] [[-1.8380327 0.98631052]] [[-1.84174199 0.98668316]] [[-1.84544459 0.98705512]] [[-1.84914052 0.98742642]] [[-1.85282979 0.98779705]] [[-1.8565124 0.98816701]] [[-1.86018838 0.9885363 ]] [[-1.86385773 0.98890492]] [[-1.86752046 0.98927289]] [[-1.8711766 0.98964018]] [[-1.87482614 0.99000682]] [[-1.87846911 0.9903728 ]] [[-1.8821055 0.99073811]] [[-1.88573535 0.99110277]] [[-1.88935865 0.99146677]] [[-1.89297542 0.99183011]] [[-1.89658566 0.9921928 ]] [[-1.9001894 0.99255483]] [[-1.90378665 0.99291622]] [[-1.90737741 0.99327695]] [[-1.9109617 0.99363703]] [[-1.91453952 0.99399646]] [[-1.9181109 0.99435524]] [[-1.92167584 0.99471338]] [[-1.92523436 0.99507087]] [[-1.92878645 0.99542772]] [[-1.93233215 0.99578392]] [[-1.93587145 0.99613948]] [[-1.93940438 0.9964944 ]] [[-1.94293094 0.99684869]] [[-1.94645113 0.99720233]] [[-1.94996499 0.99755533]] [[-1.95347251 0.9979077 ]] [[-1.9569737 0.99825943]] [[-1.96046859 0.99861053]] [[-1.96395718 0.998961 ]] [[-1.96743947 0.99931083]] [[-1.97091549 0.99966004]] [[-1.97438525 1.00000861]] [[-1.97784875 1.00035656]] [[-1.981306 1.00070388]] [[-1.98475703 1.00105057]] [[-1.98820183 1.00139664]] [[-1.99164043 1.00174208]] [[-1.99507282 1.0020869 ]] [[-1.99849903 1.0024311 ]] [[-2.00191906 1.00277468]] [[-2.00533293 1.00311764]] [[-2.00874064 1.00345998]] [[-2.01214221 1.00380171]] [[-2.01553765 1.00414282]] [[-2.01892697 1.00448331]] [[-2.02231018 1.00482319]] [[-2.02568729 1.00516246]] [[-2.02905831 1.00550111]] [[-2.03242326 1.00583916]] [[-2.03578214 1.0061766 ]] [[-2.03913497 1.00651342]] [[-2.04248175 1.00684964]] [[-2.0458225 1.00718526]] [[-2.04915723 1.00752027]] [[-2.05248594 1.00785467]] [[-2.05580866 1.00818848]] [[-2.05912538 1.00852168]] [[-2.06243613 1.00885428]] [[-2.06574091 1.00918628]] [[-2.06903973 1.00951768]] [[-2.07233261 1.00984849]] [[-2.07561955 1.0101787 ]] [[-2.07890056 1.01050831]] [[-2.08217567 1.01083733]] [[-2.08544486 1.01116576]] [[-2.08870817 1.01149359]] [[-2.09196559 1.01182083]] [[-2.09521714 1.01214749]] [[-2.09846283 1.01247355]] [[-2.10170267 1.01279903]] [[-2.10493666 1.01312392]] [[-2.10816483 1.01344822]] [[-2.11138718 1.01377194]] [[-2.11460372 1.01409508]] 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Out[12]:
matrix([[-3.63029144, 1.16636235]])
In [13]:
1
#此时已经找到拟合程度较高的theta的值，可以进行预测。预测35000和70000城市规模的小吃摊利润
2
predict1=[1,3.5]*theta_end.T
3
print("predict 35000 profits:",predict1)
4
predict2=[1,7.0]*theta_end.T
5
print("predict 70000 profits:",predict2)
predict 35000 profits: [[0.45197679]] predict 70000 profits: [[4.53424501]]
In [14]:
1
x=np.linspace(data.Population.min(),data.Population.max(),100)#通过定义均匀间隔创建数值序列。其实，需要指定间隔起始点、终止端，以及指定分隔值总数；最终函数返回间隔类均匀分布的数值序列。示例： #np.linspace(start = 0, stop = 100, num = 5) 结果：array([ 0., 25., 50., 75., 100.])
2
f=theta_end[0,0]+(theta_end[0,1]*x)
3
fig, ax = plt.subplots(figsize=(12,8))#图形宽：12.高：18.fig代表绘图窗口(Figure)；ax代表这个绘图窗口上的坐标系(axis)，一般会继续对ax进行操作。
4
ax.plot(x, f, 'g', label='Prediction')#绘制直线,x:横坐标。f:直线。
5
ax.scatter(data.Population, data.Profit, label='Traning Data')#绘制散点图
6
ax.legend(loc=2)#表示在左上角
7
ax.set_xlabel('Population')
8
ax.set_ylabel('Profit')
9
ax.set_title('Predicted Profit vs. Population Size')
10
plt.show()
In [15]:
1
fig, ax = plt.subplots(figsize=(9,5))
2
ax.plot(np.arange(iters), cost, 'r')
3
ax.set_xlabel('Iterations')
4
ax.set_ylabel('Cost')
5
ax.set_title('Error vs. Trainning data')
6
plt.show()
In [16]:
1
#多变量线性回归
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#第一列是房屋大小，第二列是卧室数量，第三列是房屋售价，据已有数据，建立模型，预测房屋的售价，数据在ex1data2
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import numpy as np
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import pandas as pd
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import matplotlib.pyplot as plt
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data2=pd.read_csv(r'C:\Users\Administrator\Desktop\ex1data2.txt',header=None,names=['hSize','hNum','hPrice'])
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data2.head()
Out[16]:
| hSize | hNum | hPrice | |
|---|---|---|---|
| 0 | 2104 | 3 | 399900 |
| 1 | 1600 | 3 | 329900 |
| 2 | 2400 | 3 | 369000 |
| 3 | 1416 | 2 | 232000 |
| 4 | 3000 | 4 | 539900 |
In [17]:
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#用均值归一化方法处理数据，统一量级会让梯度下降收敛的更快。做法就是，将每类特征减去他的平均值后除以标准差
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data2=(data2-data2.mean())/data2.std()
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data2.head()
Out[17]:
| hSize | hNum | hPrice | |
|---|---|---|---|
| 0 | 0.130010 | -0.223675 | 0.475747 |
| 1 | -0.504190 | -0.223675 | -0.084074 |
| 2 | 0.502476 | -0.223675 | 0.228626 |
| 3 | -0.735723 | -1.537767 | -0.867025 |
| 4 | 1.257476 | 1.090417 | 1.595389 |
In [18]:
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data2.insert(0,'ones',1)
In [19]:
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data2.head()
Out[19]:
| ones | hSize | hNum | hPrice | |
|---|---|---|---|---|
| 0 | 1 | 0.130010 | -0.223675 | 0.475747 |
| 1 | 1 | -0.504190 | -0.223675 | -0.084074 |
| 2 | 1 | 0.502476 | -0.223675 | 0.228626 |
| 3 | 1 | -0.735723 | -1.537767 | -0.867025 |
| 4 | 1 | 1.257476 | 1.090417 | 1.595389 |
In [20]:
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cols=data2.shape[1]
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cols
Out[20]:
4
In [21]:
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X2=data2.iloc[:,0:cols-1]
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Y2=data2.iloc[:,cols-1:cols]
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X2=np.matrix(X2.values)
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Y2=np.matrix(Y2.values)
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theta2=np.matrix(np.array([0,0,0]))
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def computeCost2(X,y,theta):
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inner=np.power(((X*theta.T)-y),2)
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return np.sum(inner)/(2*len(X))
In [22]:
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def gradientDescent(X,y,theta,alpha,iters):
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temp=np.matrix(np.zeros(theta.shape))#作为中间变量存储每一次theta的变化
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parameters=int(theta.ravel().shape[1])#theta的参数个数
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cost=np.zeros(iters) #默认为1500个浮点类型的0，即生成了array([0.,0.,0.,......1500个])
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for i in range(iters):
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error=(X*theta.T)-y
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#同时改变theta
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for j in range(parameters):
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term=np.multiply(error,X[:,j])#multiply是同类型的矩阵里面相对应的每个数点乘，j=0时：乘的数全为一；j=1时：乘的数为Xi.正好对应学习笔记公式。
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temp[0,j]=theta[0,j]-(alpha/(len(X))*np.sum(term))
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theta=temp
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cost[i]=computeCost(X,y,theta)
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#print(theta)#观察theta的变化过程
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return theta,cost
In [23]:
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g2, cost2 = gradientDescent(X2, Y2, theta2, alpha, iters)
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g2
Out[23]:
matrix([[-1.10856950e-16, 8.84042349e-01, -5.24551809e-02]])
In [24]:
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def normalEqu(X,y):
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theta=np.linalg.inv(X.T*X)*X.T*y
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return theta
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theta2=normalEqu(X,y)
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theta2
Out[24]:
matrix([[-3.89578088],
[ 1.19303364]])
In [25]:
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fig, ax = plt.subplots(figsize=(9,5))
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ax.plot(np.arange(iters), cost2, 'r')
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ax.set_xlabel('Iterations')
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ax.set_ylabel('Cost')
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ax.set_title('Error vs. Training Epoch')
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plt.show()
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In [26]:
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fig = plt.figure()
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ax = fig.gca(projection='3d') # 创建三维坐标
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ax.scatter(X2.A[:, 1], X2.A[:, 2], Y2.A, c = 'b',s = 5)
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ax.set(xlabel='ares', ylabel='num', zlabel='price') # 坐标轴
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plt.show()#可视化三维数据
In [33]:
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fig = plt.figure()
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ax = fig.gca(projection='3d')
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x1, x2 = np.meshgrid(np.linspace(-2, 3.5, 11), np.linspace(-3, 2.5, 11))
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h_x = g2[0,0] + g2[0,1] * x1 + g2[0,2] * x2
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ax.scatter(X2.A[:, 1], X2.A[:, 2], Y2.A, c='b', s=5)
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ax.plot_wireframe(x1, x2, h_x, color='g', alpha=0.4) # 绘制线框 alpha表示透明度
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ax.plot_surface(x1, x2, h_x, color='g', alpha=0.6) # 绘制平面
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ax.set(xlabel='ares', ylabel='num', zlabel='price') # 坐标轴
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plt.show()
In [28]:
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alpha_list = [0.03, 0.0001, 0.001, 0.01]
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iters = 1000
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fig, ax = plt.subplots()
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for alpha in alpha_list:
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non, costs = gradientDescent(X,y,theta,alpha,iters)
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ax.plot(np.arange(iters), costs, label=alpha)
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ax.legend()
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ax.set(xlabel='iters', ylabel='cost1', title='cost vs iters')
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plt.show()
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C:\ProgramData\Anaconda3\lib\site-packages\numpy\core\_methods.py:47: RuntimeWarning: overflow encountered in reduce return umr_sum(a, axis, dtype, out, keepdims, initial, where) <ipython-input-10-0289d65cc058>:2: RuntimeWarning: overflow encountered in power inner=np.power(((X*theta.T)-y),2)
不同学习率的代价函数变化曲线没有显示成功，显示超时的错误，随着深入理解，后续进行debug.
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