我如何使用神經網絡來識別手寫數字

Question

其次要想使用signoidal功能「Using neural nets to recognize handwritten digits」一個簡單的神經網絡教程，教程很簡單，用理論和代碼示例。

的問題是，它並沒有使用network.py給數字識別的任何實例。

例如，我有以下號碼，我想從下面的圖像中將其識別爲0 接下來應該如何處理號碼識別？

爲了識別號碼需要使用其他技術，如theano或tensorflow的？ 美好的一天！

Answer 1

在下面的例子中樓，你可以在NeuralNetwork類增加一個功能進行預測：

def predict(self, image): 
    return np.argmax(self.__feedforward(image.astype(bool).astype(int))) 

一旦你已經訓練您的神經網絡成功，你可以預測一個未知的數字與高達97％的準確率搭配：

prediction = NN.predict(image) 

---

從Neural Networks - Getting Started: A Simple ANN with Python摘錄。原作者爲cᴏʟᴅsᴘᴇᴇᴅ和dontloo。您可以在contributor page上找到署名詳情。信息來源根據CC BY-SA 3.0獲得許可，可在Documentation archive中找到。參考主題ID：2709和示例ID：9069.

下面的代碼嘗試對來自MNIST數據集的手寫數字進行分類。數字是這樣的：

代碼將預處理這些數字中，每個圖像轉換成0和1的2D陣列，然後使用該數據來訓練神經網絡以高達97％的準確度（ 50個時代）。

""" 
Deep Neural Net 

(Name: Classic Feedforward) 

""" 

import numpy as np 
import pickle, json 
import sklearn.datasets 
import random 
import time 
import os 

# cataloguing the various activation functions and their derivatives 

def sigmoid(z): 
    return 1.0/(1.0 + np.exp(-z)) 

def sigmoid_prime(z): 
    return sigmoid(z) * (1 - sigmoid(z)) 

def relU(z): 
    return np.maximum(z, 0, z) 

def relU_prime(z): 
    return z * (z <= 0) 

def tanh(z): 
    return np.tanh(z) 

def tanh_prime(z): 
    return 1 - (tanh(z) ** 2) 

def transform_target(y): 
    t = np.zeros((10, 1)) 
    t[int(y)] = 1.0 
    return t 


class NeuralNet: 

    def __init__(self, layers, learning_rate=0.05, reg_lambda=0.01): 
     self.num_layers = len(layers) 

     # initialising network parameters 
     self.layers = layers   
     self.biases = [np.zeros((y, 1)) for y in layers[1:]]  
     self.weights = [np.random.normal(loc=0.0, scale=0.1, size=(y, x)) 
             for x, y in zip(layers[:-1], layers[1:])] 
     self.learning_rate = learning_rate 
     self.reg_lambda = reg_lambda 

     # initialising network activation function 
     self.nonlinearity = relU 
     self.nonlinearity_prime = relU_prime 

    def __feedforward(self, x): 
     ''' Returns softmax probabilities for the output layer ''' 

     for w, b in zip(self.weights, self.biases): 
      x = self.nonlinearity(np.dot(w, np.reshape(x, (len(x), 1))) + b) 

     return np.exp(x)/np.sum(np.exp(x)) 

    def __backpropagation(self, x, y): 
     ''' 
     Perform the forward pass followed by backprop 
     :param x: input 
     :param y: target 

     ''' 

     weight_gradients = [np.zeros(w.shape) for w in self.weights] 
     bias_gradients = [np.zeros(b.shape) for b in self.biases] 

     # forward pass - transform input to output softmax probabilities 
     activation = x 
     hidden_activations = [np.reshape(x, (len(x), 1))] 
     z_list = [] 

     for w, b in zip(self.weights, self.biases):  
      z = np.dot(w, np.reshape(activation, (len(activation), 1))) + b 
      z_list.append(z) 
      activation = self.nonlinearity(z) 
      hidden_activations.append(activation) 

     t = hidden_activations[-1] 
     hidden_activations[-1] = np.exp(t)/np.sum(np.exp(t)) # softmax layer 

     # backward pass 
     delta = (hidden_activations[-1] - y) * (z_list[-1] > 0) 
     weight_gradients[-1] = np.dot(delta, hidden_activations[-2].T) 
     bias_gradients[-1] = delta 

     for l in range(2, self.num_layers): 
      z = z_list[-l] 
      delta = np.dot(self.weights[-l + 1].T, delta) * (z > 0) 
      weight_gradients[-l] = np.dot(delta, hidden_activations[-l - 1].T) 
      bias_gradients[-l] = delta 

     return (weight_gradients, bias_gradients) 

    def __update_params(self, weight_gradients, bias_gradients): 
     ''' Update network parameters after backprop step ''' 
     for i in xrange(len(self.weights)): 
      self.weights[i] += -self.learning_rate * weight_gradients[i] 
      self.biases[i] += -self.learning_rate * bias_gradients[i] 

    def train(self, training_data, validation_data=None, epochs=10): 
     ''' Train the network for `epoch` iterations ''' 

     bias_gradients = None 
     for i in xrange(epochs): 
      random.shuffle(training_data) 
      inputs = [data[0] for data in training_data] 
      targets = [data[1] for data in training_data] 

      for j in xrange(len(inputs)): 
       (weight_gradients, bias_gradients) = self.__backpropagation(inputs[j], targets[j]) 
       self.__update_params(weight_gradients, bias_gradients) 

      if validation_data: 
       random.shuffle(validation_data) 
       inputs = [data[0] for data in validation_data] 
       targets = [data[1] for data in validation_data] 

       for j in xrange(len(inputs)): 
        (weight_gradients, bias_gradients) = self.__backpropagation(inputs[j], targets[j]) 
        self.__update_params(weight_gradients, bias_gradients) 

      print("{} epoch(s) done".format(i + 1)) 

     print("Training done.") 

    def test(self, test_data): 
     test_results = [(np.argmax(self.__feedforward(x[0])), np.argmax(x[1])) for x in test_data] 
     return float(sum([int(x == y) for (x, y) in test_results]))/len(test_data) * 100 

    def dump(self, file): 
     pickle.dump(self, open(file, "wb")) 



if __name__ == "__main__": 
    total = 5000 
    training = int(total * 0.7) 
    val = int(total * 0.15) 
    test = int(total * 0.15) 

    mnist = sklearn.datasets.fetch_mldata('MNIST original', data_home='./data') 

    data = zip(mnist.data, mnist.target) 
    random.shuffle(data) 
    data = data[:total] 
    data = [(x[0].astype(bool).astype(int), transform_target(x[1])) for x in data] 

    train_data = data[:training] 
    val_data = data[training:training+val] 
    test_data = data[training+val:] 

    print "Data fetched" 

    NN = NeuralNet([784, 32, 10]) # defining an ANN with 1 input layer (size 784 = size of the image flattened), 1 hidden layer (size 32), and 1 output layer (size 10, unit at index i will predict the probability of the image being digit i, where 0 <= i <= 9) 

    NN.train(train_data, val_data, epochs=5) 

    print "Network trained" 

    print "Accuracy:", str(NN.test(test_data)) + "%" 

這是一個自包含的代碼示例，可以在沒有任何進一步修改的情況下運行。確保你已經爲你的python版本安裝了numpy和scikit。