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iris數(shù)據(jù)集：

import?numpy?as?np
class?Perceptron(object):
????"""????
????eta:學(xué)習(xí)率????
????n_iter:權(quán)重向量的訓(xùn)練次數(shù)????
????w_:神經(jīng)分叉權(quán)重向量????
????errors:用于記錄神經(jīng)元判斷出錯次數(shù)????
????"""
????def?__init__(self,?eta,?n_iter):????????
????????self.eta=eta????????
????????self.n_iter=n_iter????????
????????pass
????def?net_input(self,X):????????????
????????"""????????????
????????z?=?W0*1?+?W1*X1?+....?Wn*Xn????????????
????????"""????????????
????????return?np.dot(X,self.w_[1:])?+?self.w_[0]????????????
????????pass
????
????def?predict(self,?X):????????
????????return?np.where(self.net_input(X)?>=?0.0?,1,?-1)????????
????????pass
????def?fit(self,X,y):????????
????????"""????????
????????輸入訓(xùn)練數(shù)據(jù)，訓(xùn)練神經(jīng)元，x輸入樣本向量，y對應(yīng)樣本的正確分類????????????????
????????X:shape[n_samples,?n_features]????????
????????eg:X:[[1,?2,?,3],[4,?5,?6]]???????????
???????????n_samples:?2???????????
???????????n_features:?3??????????????????????
???????????y:[1,?-1]????????
????????"""????????
????????"""????????
????????初始化權(quán)重向量為0????????
????????加一是因?yàn)榍懊嫠惴ㄌ岬降膚0,也就是步調(diào)函數(shù)閾值????????
????????"""????????
????????self.w_?=?np.zeros(1+X.shape[1])????????
????????self.errors_?=[]????????????????
????????
????????for?_?in?range(self.n_iter):????????????
????????????errors?=?0????????????
????????????"""????????????
????????????X:[[1,2,3],[4,5,6]]????????????
????????????y:[1,?-1]????????????
????????????zip(X,y)=[[1,2,3,?1],[4,5,6,?-1]]????????????
????????????"""????????????
????????????for?xi,?target?in?zip(X,y):?????????????????
????????????????"""????????????????
????????????????update?=?學(xué)習(xí)率?*?（y-y'）????????????????
????????????????"""????????????????
????????????????update?=?self.eta?*?(target?-?self.predict(xi))????????????????
????????????????"""????????????????
????????????????xi?是一個向量????????????????
????????????????update?*?xi?等價：????????????????
????????????????[更新w(1)?=?X[1]*update,?更新w(2)?=?X[2]*update,更新w(3)?=?X[3]*update,]????????????????
????????????????"""????????????????
????????????????self.w_[1:]+=update?*?xi????????????????
????????????????self.w_[0]?+=?update????????????????????????????????
????????????????errors?+=?int(update?!=?0.0)????????????????
????????????????self.errors_.append(errors)????????????????
????????????????pass????????????????????????
????????????pass???
????pass


file?=?"D:/PyCharm_test_file/Jupyter_test/iris1.xlsx"
import?pandas?as?pd

df?=?pd.read_excel(file,header=None)
#df.head(10)
#print(df)??


import?matplotlib.pyplot?as?plt
import?numpy?as?npy?=?df.loc[0:99,?4].values
y?=?np.where(y?==?'Iris-setosa',?-1,?1)
#print(y)
X?=?df.iloc[0:100,?[0,?2]].values
#print(X)
plt.scatter(X[:50,?0],?X[:50,?1],?color='red',?marker='o',?label='setosa')
plt.scatter(X[50:100,?0],?X[50:100,?1],?color='blue',?marker='x',?label='vericolor')
plt.rcParams['font.sans-serif']=['SimHei']
plt.xlabel('花瓣長度')
plt.ylabel('花莖長度')
plt.legend(loc='upper?left')
plt.show()??



from?matplotlib.colors?import?ListedColormap
def?plot_decision_regions(X,?y,?classifier,?resolution=0.02):????
????marker?=?('s',?'x',?'o',?'v')????
????colors?=?('red',?'blue',?'lightgreen',?'gray',?'cyan')????
????cmap?=?ListedColormap(colors[:len(np.unique(y))])????
????x1_min,?x1_max?=?X[:,?0].min()?-?1,?X[:,?0].max()????
????x2_min,?x2_max?=?X[:,?1].min()?-?1,?X[:,?1].max()????
????#將x1、x2最大最小值通過arange函數(shù)得到的向量，擴(kuò)展成兩個二維矩陣????
????xx1,?xx2?=?np.meshgrid(np.arange(x1_min,?x1_max,?resolution),?np.arange(x2_min,?x2_max,?resolution))????
????#預(yù)測????
????Z?=?classifier.predict(np.array([xx1.ravel(),?xx2.ravel()]).T)?#ravel還原成單維向量????
????#繪制????
????Z=?Z.reshape(xx1.shape)?#將Z轉(zhuǎn)換成與xx1一樣的二維數(shù)組????
????plt.contourf(xx1,?xx2,?Z,?alpha=0.4,?cmap=cmap)?#在兩組分類結(jié)果中間畫分割線-->必須線性可分????
????plt.xlim(xx1.min(),?xx1.max())????
????plt.ylim(xx2.min(),?xx2.max())????
????for?idx,?cl?in?enumerate(np.unique(y)):????????
????????plt.scatter(x=X[y==cl,?0],?y=X[y==cl,?1],?alpha=0.8,?c=cmap(idx),?marker=marker[idx],?label=cl)
????????
????????
ppn?=?Perceptron(0.1,?10)
ppn.fit(X,?y)
plot_decision_regions(X,?y,?ppn,?resolution=0.02)

自適應(yīng)線性神經(jīng)元的分類算法

class?AdalineGD(object):
????def?__init__(self,?eta=0.1,?n_iter=50):
????????self.eta?=?eta
????????self.n_iter?=?n_iter
????def?fit(self,?X,?y):?#與感知器最大的不同
????????self.w_?=?np.zeros(1?+?X.shape[1])
????????self.cost_?=?[]?#成本函數(shù)：判斷改進(jìn)效果，使其不斷減小
????????for?i?in?range(self.n_iter):
????????????output?=?self.net_input(X)
????????????errors?=?y?-?output
????????????self.w_[1:]?+=?self.eta?*?X.T.dot(errors)
????????????self.w_[0]?+=?self.eta?*?errors.sum()
????????????cost?=?(errors?**?2).sum()/2.0
????????????self.cost_.append(cost)
????????return?self
????def?net_input(self,?X):
????????return?np.dot(X,?self.w_[1:]?+?self.w_[0])
????def?activation(self,?X):
????????return?self.net_input(self,?X):
????def?predict(self,?X):
????????return?np.where(self.activation(X)?>=?0,?1,?-1)

#運(yùn)行算法???????????????
ada?=?AdalineGD(eta=0.0001,?n_iter=50)?#學(xué)習(xí)率越低，每次權(quán)重的改進(jìn)越精確；迭代次數(shù)越大，優(yōu)化的結(jié)果越準(zhǔn)確。
ada.fit(X,?y)
plot_decision_regions(X,?y,?classifier=ada)?#預(yù)測數(shù)據(jù)輸入到神經(jīng)網(wǎng)絡(luò)后預(yù)測
plt.title('Adaline-Gradient?descent')
plt.xlabel('花莖長度')
plt.ylabel('花瓣長度')
plt.legend(loc='upper?left')
plt.show()

plt.plot(range(1,?len(ada.cost_)+1),?ada.cost_,?marker='o')?#檢測改進(jìn)效果
plt.xlabel('Epochs')?#自我迭代的學(xué)習(xí)次數(shù)
plt.ylabel('sum-squard-error')?#做出錯誤判斷的次數(shù)

感知器的激活函數(shù)是步調(diào)函數(shù)，當(dāng)輸入數(shù)據(jù)大于閾值-->1，小于閾值-->0.

自適應(yīng)線性神經(jīng)元的激活函數(shù)是直接將輸入數(shù)據(jù)與參數(shù)相乘后求和：w0+x1w1+x2w2+……，并且會將計(jì)算結(jié)果與輸入結(jié)果進(jìn)行比較，若不一致，會根據(jù)給定結(jié)果動態(tài)調(diào)整參數(shù)-->漸進(jìn)下降法。

漸進(jìn)下降法：

和方差函數(shù)（U型），當(dāng)函數(shù)對w求偏導(dǎo)后得到的切線斜率小于0（大于0）-->增大（減?。┫鄳?yīng)神經(jīng)元參數(shù)w值

數(shù)據(jù)解析和可視化

import?pandas?as?pd
import?matplotlib.pyplot?as?plt
import?numpy?as?np

df?=?pd.read_csv(file,?header=None)
y?=?df.loc[0:100,?4].values
y?=?np.where(y?==?'Iris-setosa',?-1,?1)
X?=?df.iloc[0:100,?[0,?2]].values
plt.scatter(X[:50,?0],?X[:50,?1],?color='red',?marker='o',?label='setosa')
plt.scatter(X[50:100,?0],?X[50:100,?1],?color='blue',?marker='x',?label='versicolor')
plt.xlabel('花瓣長度')
plt.ylabel('花莖長度')
plt.legend(loc='upper?left')
plt.show()

數(shù)據(jù)分類（將預(yù)測的數(shù)據(jù)輸入到神經(jīng)網(wǎng)絡(luò)中，以圖形方式繪制）

from?matplotlib.colors?import?ListedColormap
def?plot_decision_regions(X,?y,?classifier,?resolution=0.02):
????marker?=?('s',?'x',?'o',?'v')
????colors?=?('red',?'blue',?'lightgreen',?'gray',?'cyan')
????cmap?=?ListedColormap(colors[:len(np.unique(y))])
????x1_min,?x1_max?=?X[:,?0].min()?-?1,?X[:,?0].max()
????x2_min,?x2_max?=?X[:,?1].min()?-?1,?X[:,?1].max()
????#將x1、x2最大最小值通過arange函數(shù)得到的向量，擴(kuò)展成兩個二維矩陣
????xx1,?xx2?=?np.meshgrid(np.arange(x1_min,?x1_max,?resolution),?np.arange(x2_min,?x2_max,?resolution))
????#預(yù)測
????Z?=?classifier.predict(np.array([xx1.ravel(),?xx2.ravel()]).T)?#ravel還原成單維向量
????#繪制
????Z=?Z.reshape(xx1.shape)?#將Z轉(zhuǎn)換成與xx1一樣的二維數(shù)組
????plt.contourf(xx1,?xx2,?Z,?alpha=0.4,?cmap=cmap)?#在兩組分類結(jié)果中間畫分割線-->必須線性可分
????plt.xlim(xx1.min(),?xx1.max())
????plt.ylim(xx2.min(),?xx2.max())
????for?idx,?cl?in?enumerate(np.unique(y)):
????????plt.scatter(x=X[y==cl,?0],?y=X[y==cl,?1],?alpha=0.8,?c=cmap(idx),?marker=markers[idx],?label=cl)

感知器的分類算法

import?numpy?as?mp
class?Perception(objet):
????def?__init__(self,?eta=0.01,?n_ier=10):?#eta學(xué)習(xí)率，n_iter訓(xùn)練權(quán)重向量的重復(fù)次數(shù)
????????self.eta?=?eta
????????self.n_iter?=?n_iter
????#根據(jù)輸入樣本培訓(xùn)神經(jīng)元，X：shape[n_sample,?n_feature],?n_feature指神經(jīng)元接收的電信號X數(shù)量
????def?fit(self,?X,?y):?
????????self.w_?=?np.zero(1+X.shape[1])?#初始權(quán)重向量w_為0，括號里加一是包括激勵函數(shù)的閾值w0
????????self.errors_?=?[]?#errors_用于記錄神經(jīng)元判斷出錯次數(shù)，是個隊(duì)列
????????
????????for?_?in?range(self.n_iter):
????????????errors?=?0
????????????for?xi,?target?in?zip(X,?y):
????????????????#權(quán)重更新
????????????????update?=?self.eta?*?(target?-?self.predict(xi))
????????????????self.w_[1:]?+=?update?*?xi
????????????????#閾值更新
????????????????self.w_[0]?+=?update
????????????????
????????????????errors?+=?int(update?!=?0.0)
????????????????self.errors_.append(errors)
?????????
????????def?net_input(self,?X):?#輸入電信號X與權(quán)重w的點(diǎn)積
????????????return?np.dot(X,?self.w_[1:])?+?self.w_[0]
????????????
????????def?predict(self,?X):?#預(yù)測分類
????????????return?np.where(self.net_input(X)?>=?0.0,?1,?-1)

感知器算法：要求數(shù)據(jù)線性可分

????機(jī)器學(xué)習(xí)中用于對數(shù)據(jù)進(jìn)行分類的算法：1.感知器。2.適應(yīng)性的線性神經(jīng)元。

????激活函數(shù)（也叫單元步調(diào)函數(shù)）

????機(jī)器學(xué)習(xí)的本質(zhì)是模擬人的神經(jīng)元對信息的處理方法。根據(jù)神經(jīng)學(xué)的研究，神經(jīng)元可以看做是一個簡單的帶有二進(jìn)制輸出功能的邏輯電路門。

自適應(yīng)線性神經(jīng)元

神經(jīng)元的數(shù)學(xué)表示

激活函數(shù)

向量的轉(zhuǎn)置與乘積的表達(dá)式

課程大綱

算法步驟總結(jié)

感知器數(shù)據(jù)分類算法步驟

更新權(quán)重