BP神經網絡的原理在網上有很詳細的說明，這里就不打算細說，這篇文章主要簡單的方式設計及實現BP神經網絡，并簡單測試下在恒等計算（編碼）作測試。?

BP神經網絡模型圖如下

BP神經網絡基本思想

BP神經網絡學習過程由信息的下向傳遞和誤差的反向傳播兩個過程組成

正向傳遞：由模型圖中的數據x從輸入層到最后輸出層z的過程。

反向傳播：在訓練階段，如果正向傳遞過程中發現輸出的值與期望的傳有誤差，由將誤差從輸出層返傳回輸入層的過程。返回的過程主要是修改每一層每個連接的權值w，達到減少誤的過程。

BP神經網絡設計

設計思路是將神經網絡分為神經元、網絡層及整個網絡三個層次。

首先是定義使用sigmoid函數作為激活函數

[python]?view plaincopy

def?logistic(x):??

????return?1?/?(1?+?np.exp(-x))??

??

def?logistic_derivative(x):??

????return?logistic(x)?*?(1?-?logistic(x))??

神經元的設計

由神經元的設計圖可知，BP神經網絡可拆解成是神經元的集合。

神經元主要功能：

計算數據，輸出結果。

更新各連接權值。

向上一層反饋權值更新值，實現反饋功能。

注意到：

[python]?view plaincopy

weight_add?=?self.input?*?self.deltas_item?*?learning_rate?+?0.9?*?self.last_weight_add#添加沖量??

代碼是添加沖量功能(+ 0.9 * self.last_weight_add )， 這可以加速收斂，如果有興趣可把它去掉看看訓練結果。?

神經元設計代碼如下：

[python]?view plaincopy

class?Neuron:??

????def?__init__(self,?len_input):??

????????#?輸入的初始參數,?隨機取很小的值(<0.1)??

????????self.weights?=?np.random.random(len_input)?*?0.1??

????????#?當前實例的輸入??

????????self.input?=?np.ones(len_input)??

????????#?對下一層的輸出值??

????????self.output?=?1??

????????#?誤差項??

????????self.deltas_item?=?0??

????????#?上一次權重增加的量，記錄起來方便后面擴展時可考慮增加沖量??

????????self.last_weight_add?=?0??

??

????def?calc_output(self,?x):??

????????#?計算輸出值??

????????self.input?=?x??

????????self.output?=?logistic(np.dot(self.weights.T,?self.input))??

????????return?self.output??

??

????def?get_back_weight(self):??

????????#?獲取反饋差值??

????????return?self.weights?*?self.deltas_item??

??

????def?update_weight(self,?target=0,?back_weight=0,?learning_rate=0.1,?layer="OUTPUT"):??

????????#?更新權傳??

????????if?layer?==?"OUTPUT":??

????????????self.deltas_item?=?(target?-?self.output)?*?logistic_derivative(self.output)??

????????elif?layer?==?"HIDDEN":??

????????????self.deltas_item?=?back_weight?*?logistic_derivative(self.output)??

??????????

????????weight_add?=?self.input?*?self.deltas_item?*?learning_rate?+?0.9?*?self.last_weight_add#添加沖量??

????????self.weights?+=?weight_add??

????????self.last_weight_add?=?weight_add??

網絡層設計

管理一個網絡層的代碼，分為隱藏層和輸出層。 （輸入層可直接用輸入數據，不簡單實現。）

網絡層主要管理自己層的神經元，所以封裝的結果與神經元的接口一樣。對向實現自己的功能。

同時為了方便處理，添加了他下一層的引用。

[python]?view plaincopy

class?NetLayer:??

????'''''?

????網絡層封裝?

????管理當前網絡層的神經元列表?

????'''??

????def?__init__(self,?len_node,?in_count):??

????????'''''?

????????:param?len_node:?當前層的神經元數?

????????:param?in_count:?當前層的輸入數?

????????'''??

????????#?當前層的神經元列表??

????????self.neurons?=?[Neuron(in_count)?for?_?in?range(len_node)]??

????????#?記錄下一層的引用，方便遞歸操作??

????????self.next_layer?=?None??

??

????def?calc_output(self,?x):??

????????output?=?np.array([node.calc_output(x)?for?node?in?self.neurons])??

????????if?self.next_layer?is?not?None:??

????????????return?self.next_layer.calc_output(output)??

????????return?output??

??

????def?get_back_weight(self):??

????????return?sum([node.get_back_weight()?for?node?in?self.neurons])??

??

????def?update_weight(self,?learning_rate,?target):??

????????'''''?

????????更新當前網絡層及之后層次的權重?

????????使用了遞歸來操作，所以要求外面調用時必須從網絡層的第一層（輸入層的下一層）來調用?

????????:param?learning_rate:?學習率?

????????:param?target:?輸出值?

????????'''??

????????layer?=?"OUTPUT"??

????????back_weight?=?np.zeros(len(self.neurons))??

????????if?self.next_layer?is?not?None:??

????????????back_weight?=?self.next_layer.update_weight(learning_rate,?target)??

????????????layer?=?"HIDDEN"??

????????for?i,?node?in?enumerate(self.neurons):??

[python]?view plaincopy

<span?style="white-space:pre">????????</span>target_item?=?0?if?len(target)?<=?i?else?target[i]??

????????????????node.update_weight(target=<span?style="font-family:?Arial,?Helvetica,?sans-serif;">target_item</span><span?style="font-family:?Arial,?Helvetica,?sans-serif;">,?back_weight=back_weight[i],?learning_rate=learning_rate,?layer=layer)</span>??

????????return?self.get_back_weight()??

BP神經網絡實現

管理整個網絡，對外提供訓練接口及預測接口。

構建網絡參數為一列表， 第一個元素代碼輸入參數個數， 最后一個代碼輸出神經元個數，中間的為各個隱藏層中的神經元的個數。

由于各層間代碼鏈式存儲， 所以layers[0]操作就代碼了整個網絡。

[python]?view plaincopy

class?NeuralNetWork:??

??

????def?__init__(self,?layers):??

????????self.layers?=?[]??

????????self.construct_network(layers)??

????????pass??

??

????def?construct_network(self,?layers):??

????????last_layer?=?None??

????????for?i,?layer?in?enumerate(layers):??

????????????if?i?==?0:??

????????????????continue??

????????????cur_layer?=?NetLayer(layer,?layers[i-1])??

????????????self.layers.append(cur_layer)??

????????????if?last_layer?is?not?None:??

????????????????last_layer.next_layer?=?cur_layer??

????????????last_layer?=?cur_layer??

??

????def?fit(self,?x_train,?y_train,?learning_rate=0.1,?epochs=100000,?shuffle=False):??

????????'''''?

????????訓練網絡,?默認按順序來訓練?

????????方法?1：按訓練數據順序來訓練?

????????方法?2:?隨機選擇測試?

????????:param?x_train:?輸入數據?

????????:param?y_train:?輸出數據?

????????:param?learning_rate:?學習率?

????????:param?epochs:權重更新次數?

????????:param?shuffle:隨機取數據訓練??

????????'''??

????????indices?=?np.arange(len(x_train))??

????????for?_?in?range(epochs):??

????????????if?shuffle:??

????????????????np.random.shuffle(indices)??

????????????for?i?in?indices:??

????????????????self.layers[0].calc_output(x_train[i])??

????????????????self.layers[0].update_weight(learning_rate,?y_train[i])??

????????pass??

??

????def?predict(self,?x):??

????????return?self.layers[0].calc_output(x)??

測試代碼

測試數據中輸出數據和輸出數據一樣。測試AutoEncoder自動編碼器。（AutoEncoder不了解的可網上找一下。）

[python]?view plaincopy

if?__name__?==?'__main__':??

????print("test?neural?network")??

??

????data?=?np.array([[1,?0,?0,?0,?0,?0,?0,?0],??

?????????????????????[0,?1,?0,?0,?0,?0,?0,?0],??

?????????????????????[0,?0,?1,?0,?0,?0,?0,?0],??

?????????????????????[0,?0,?0,?1,?0,?0,?0,?0],??

?????????????????????[0,?0,?0,?0,?1,?0,?0,?0],??

?????????????????????[0,?0,?0,?0,?0,?1,?0,?0],??

?????????????????????[0,?0,?0,?0,?0,?0,?1,?0],??

?????????????????????[0,?0,?0,?0,?0,?0,?0,?1]])??

??

????np.set_printoptions(precision=3,?suppress=True)??

??

????for?item?in?range(10):??

????????network?=?NeuralNetWork([8,?3,?8])??

????????#?讓輸入數據與輸出數據相等??

????????network.fit(data,?data,?learning_rate=0.1,?epochs=10000)??

??

????????print("\n\n",?item,??"result")??

????????for?item?in?data:??

????????????print(item,?network.predict(item))??

結果輸出

效果還不錯，達到了預想的結果。?

問題：可測試結果中有 0.317(已經標紅), 是由于把8個數據編碼成3個數據有點勉強。 如果網絡改成［8，4，8］就能夠不出現這樣的結果。 大家可以試一下。

[html]?view plaincopy

/Library/Frameworks/Python.framework/Versions/3.4/bin/python3.4?/ＸＸＸＸ/機器學習/number/NeuralNetwork.py??

test?neural?network??

??

??

?0?result??

[1?0?0?0?0?0?0?0]?[?0.987??0.?????0.005??0.?????0.?????0.01???0.004??0.???]??

[0?1?0?0?0?0?0?0]?[?0.?????0.985??0.?????0.006??0.?????0.025??0.?????0.008]??

[0?0?1?0?0?0?0?0]?[?0.007??0.?????0.983??0.?????0.007??0.027??0.?????0.???]??

[0?0?0?1?0?0?0?0]?[?0.?????0.005??0.?????0.985??0.007??0.02???0.?????0.???]??

[0?0?0?0?1?0?0?0]?[?0.?????0.?????0.005??0.005??0.983??0.013??0.?????0.???]??

[0?0?0?0?0?1?0?0]?[?0.016??0.017??0.02???0.018??0.018??<span?style="color:#ff0000;">0.317</span>??0.023??0.017]??

[0?0?0?0?0?0?1?0]?[?0.006??0.?????0.?????0.?????0.?????0.026??0.984??0.006]??

[0?0?0?0?0?0?0?1]?[?0.?????0.005??0.?????0.?????0.?????0.01???0.004??0.985]??

??

??

?1?result??

[1?0?0?0?0?0?0?0]?[?0.983??0.?????0.?????0.007??0.007??0.?????0.?????0.027]??

[0?1?0?0?0?0?0?0]?[?0.?????0.986??0.004??0.?????0.?????0.?????0.005??0.01?]??

[0?0?1?0?0?0?0?0]?[?0.?????0.005??0.985??0.?????0.005??0.?????0.?????0.026]??

[0?0?0?1?0?0?0?0]?[?0.005??0.?????0.?????0.983??0.?????0.006??0.?????0.015]??

[0?0?0?0?1?0?0?0]?[?0.005??0.?????0.004??0.?????0.987??0.?????0.?????0.01?]??

[0?0?0?0?0?1?0?0]?[?0.?????0.?????0.?????0.006??0.?????0.984??0.005??0.018]??

[0?0?0?0?0?0?1?0]?[?0.?????0.008??0.?????0.?????0.?????0.006??0.984??0.027]??

[0?0?0?0?0?0?0?1]?[?0.018??0.017??0.025??0.018??0.016??0.018??0.017??<span?style="color:#ff0000;">0.317]</span>??

??

??

?2?result??

[1?0?0?0?0?0?0?0]?[?0.966??0.?????0.016??0.014??0.?????0.?????0.?????0.???]??

[0?1?0?0?0?0?0?0]?[?0.?????0.969??0.?????0.016??0.?????0.?????0.?????0.014]??

[0?0?1?0?0?0?0?0]?[?0.012??0.?????0.969??0.?????0.?????0.013??0.?????0.???]??

[0?0?0?1?0?0?0?0]?[?0.014??0.014??0.?????0.969??0.?????0.?????0.?????0.???]??

[0?0?0?0?1?0?0?0]?[?0.?????0.?????0.?????0.?????0.962??0.016??0.02???0.???]??

[0?0?0?0?0?1?0?0]?[?0.?????0.?????0.02???0.?????0.016??0.963??0.?????0.???]??

[0?0?0?0?0?0?1?0]?[?0.?????0.?????0.?????0.?????0.012??0.?????0.969??0.011]??

[0?0?0?0?0?0?0?1]?[?0.?????0.014??0.?????0.?????0.?????0.?????0.016??0.966]??

??

??

?3?result??

[1?0?0?0?0?0?0?0]?[?0.983??0.?????0.?????0.007??0.027??0.?????0.?????0.007]??

[0?1?0?0?0?0?0?0]?[?0.?????0.986??0.004??0.?????0.01???0.005??0.?????0.???]??

[0?0?1?0?0?0?0?0]?[?0.?????0.006??0.984??0.006??0.026??0.?????0.?????0.???]??

[0?0?0?1?0?0?0?0]?[?0.005??0.?????0.004??0.987??0.01???0.?????0.?????0.???]??

[0?0?0?0?1?0?0?0]?[?0.019??0.017??0.024??0.016??<span?style="color:#ff0000;">0.317</span>??0.017??0.018??0.018]??

[0?0?0?0?0?1?0?0]?[?0.?????0.008??0.?????0.?????0.026??0.984??0.006??0.???]??

[0?0?0?0?0?0?1?0]?[?0.?????0.?????0.?????0.?????0.019??0.005??0.984??0.007]??

[0?0?0?0?0?0?0?1]?[?0.005??0.?????0.?????0.?????0.014??0.?????0.005??0.983]??

??

??

?4?result??

[1?0?0?0?0?0?0?0]?[?0.969??0.014??0.?????0.?????0.?????0.?????0.014??0.???]??

[0?1?0?0?0?0?0?0]?[?0.014??0.966??0.016??0.?????0.?????0.?????0.?????0.???]??

[0?0?1?0?0?0?0?0]?[?0.?????0.011??0.969??0.?????0.?????0.012??0.?????0.???]??

[0?0?0?1?0?0?0?0]?[?0.?????0.?????0.?????0.966??0.?????0.?????0.013??0.016]??

[0?0?0?0?1?0?0?0]?[?0.?????0.?????0.?????0.?????0.963??0.016??0.?????0.02?]??

[0?0?0?0?0?1?0?0]?[?0.?????0.?????0.02???0.?????0.016??0.963??0.?????0.???]??

[0?0?0?0?0?0?1?0]?[?0.016??0.?????0.?????0.014??0.?????0.?????0.969??0.???]??

[0?0?0?0?0?0?0?1]?[?0.?????0.?????0.?????0.011??0.012??0.?????0.?????0.969]??

??

??

?5?result??

[1?0?0?0?0?0?0?0]?[?0.966??0.?????0.016??0.?????0.?????0.018??0.?????0.???]??

[0?1?0?0?0?0?0?0]?[?0.?????0.969??0.012??0.?????0.?????0.?????0.011??0.???]??

[0?0?1?0?0?0?0?0]?[?0.015??0.018??0.964??0.?????0.?????0.?????0.?????0.???]??

[0?0?0?1?0?0?0?0]?[?0.?????0.?????0.?????0.968??0.013??0.?????0.?????0.013]??

[0?0?0?0?1?0?0?0]?[?0.?????0.?????0.?????0.015??0.965??0.015??0.?????0.???]??

[0?0?0?0?0?1?0?0]?[?0.013??0.?????0.?????0.?????0.013??0.968??0.?????0.???]??

[0?0?0?0?0?0?1?0]?[?0.?????0.018??0.?????0.?????0.?????0.?????0.965??0.014]??

[0?0?0?0?0?0?0?1]?[?0.?????0.?????0.?????0.018??0.?????0.?????0.015??0.967]??

??

??

?6?result??

[1?0?0?0?0?0?0?0]?[?0.983??0.006??0.?????0.005??0.?????0.?????0.?????0.016]??

[0?1?0?0?0?0?0?0]?[?0.006??0.983??0.?????0.?????0.?????0.005??0.?????0.017]??

[0?0?1?0?0?0?0?0]?[?0.?????0.?????0.987??0.005??0.?????0.?????0.004??0.01?]??

[0?0?0?1?0?0?0?0]?[?0.007??0.?????0.007??0.983??0.?????0.?????0.?????0.027]??

[0?0?0?0?1?0?0?0]?[?0.?????0.?????0.?????0.?????0.987??0.005??0.004??0.01?]??

[0?0?0?0?0?1?0?0]?[?0.?????0.007??0.?????0.?????0.008??0.983??0.?????0.027]??

[0?0?0?0?0?0?1?0]?[?0.?????0.?????0.005??0.?????0.005??0.?????0.985??0.026]??

[0?0?0?0?0?0?0?1]?[?0.018??0.018??0.017??0.017??0.017??0.017??0.025??<span?style="color:#ff0000;">0.317</span>]??

??

??

?7?result??

[1?0?0?0?0?0?0?0]?[?0.969??0.?????0.?????0.?????0.014??0.?????0.?????0.015]??

[0?1?0?0?0?0?0?0]?[?0.?????0.963??0.02???0.?????0.?????0.017??0.?????0.???]??

[0?0?1?0?0?0?0?0]?[?0.?????0.012??0.969??0.?????0.?????0.?????0.011??0.???]??

[0?0?0?1?0?0?0?0]?[?0.?????0.?????0.?????0.969??0.011??0.013??0.?????0.???]??

[0?0?0?0?1?0?0?0]?[?0.014??0.?????0.?????0.016??0.966??0.?????0.?????0.???]??

[0?0?0?0?0?1?0?0]?[?0.?????0.016??0.?????0.02???0.?????0.962??0.?????0.???]??

[0?0?0?0?0?0?1?0]?[?0.?????0.?????0.016??0.?????0.?????0.?????0.966??0.014]??

[0?0?0?0?0?0?0?1]?[?0.015??0.?????0.?????0.?????0.?????0.?????0.014??0.969]??

??

??

?8?result??

[1?0?0?0?0?0?0?0]?[?0.966??0.016??0.013??0.?????0.?????0.?????0.?????0.???]??

[0?1?0?0?0?0?0?0]?[?0.011??0.969??0.?????0.?????0.?????0.?????0.012??0.???]??

[0?0?1?0?0?0?0?0]?[?0.014??0.?????0.969??0.015??0.?????0.?????0.?????0.???]??

[0?0?0?1?0?0?0?0]?[?0.?????0.?????0.015??0.969??0.?????0.014??0.?????0.???]??

[0?0?0?0?1?0?0?0]?[?0.?????0.?????0.?????0.?????0.963??0.?????0.016??0.02?]??

[0?0?0?0?0?1?0?0]?[?0.?????0.?????0.?????0.013??0.?????0.966??0.?????0.016]??

[0?0?0?0?0?0?1?0]?[?0.?????0.02???0.?????0.?????0.016??0.?????0.963??0.???]??

[0?0?0?0?0?0?0?1]?[?0.?????0.?????0.?????0.?????0.012??0.011??0.?????0.969]??

??

??

?9?result??

[1?0?0?0?0?0?0?0]?[?0.969??0.?????0.?????0.?????0.?????0.011??0.?????0.011]??

[0?1?0?0?0?0?0?0]?[?0.?????0.968??0.?????0.?????0.?????0.?????0.018??0.015]??

[0?0?1?0?0?0?0?0]?[?0.?????0.?????0.965??0.?????0.015??0.?????0.015??0.???]??

[0?0?0?1?0?0?0?0]?[?0.?????0.?????0.?????0.966??0.018??0.016??0.?????0.???]??

[0?0?0?0?1?0?0?0]?[?0.?????0.?????0.013??0.013??0.968??0.?????0.?????0.???]??

[0?0?0?0?0?1?0?0]?[?0.018??0.?????0.?????0.014??0.?????0.964??0.?????0.???]??

[0?0?0?0?0?0?1?0]?[?0.?????0.013??0.013??0.?????0.?????0.?????0.968??0.???]??

[0?0?0?0?0?0?0?1]?[?0.018??0.014??0.?????0.?????0.?????0.?????0.?????0.965]??

??

Process?finished?with?exit?code?0??

總結

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