NN：神经网络算法进阶优化法，进一步提高手写数字识别的准确率—Jason niu

上一篇文章，比较了三种算法实现对手写数字识别，其中，SVM和神经网络算法表现非常好准确率都在90%以上，本文章进一步探讨对神经网络算法优化，进一步提高准确率，通过测试发现，准确率提高了很多。

首先，改变之一：

先在初始化权重的部分，采取一种更为好的随机初始化方法，我们依旧保持正态分布的均值不变，只对标准差进行改动，

初始化权重改变前，

 def large_weight_initializer(self):
        self.biases = [np.random.randn(y, 1) for y in self.sizes[1:]]
        self.weights = [np.random.randn(y, x)  for x, y in zip(self.sizes[:-1], self.sizes[1:])]

初始化权重改变后，

    def default_weight_initializer(self):
        self.biases = [np.random.randn(y, 1) for y in self.sizes[1:]]
        self.weights = [np.random.randn(y, x)/np.sqrt(x)  for x, y in zip(self.sizes[:-1], self.sizes[1:])]

改变之二：

为了减少Overfitting，降低数据局部噪音影响，将原先的目标函数由 quadratic cost 改为 cross-enrtopy cost

class CrossEntropyCost(object):
    def fn(a, y):
        return np.sum(np.nan_to_num(-y*np.log(a)-(1-y)*np.log(1-a)))
    def delta(z, a, y):
        return (a-y)

改变之三：

将S函数改为Softmax函数

class SoftmaxLayer(object):
    def __init__(self, n_in, n_out, p_dropout=0.0):
        self.n_in = n_in
        self.n_out = n_out
        self.p_dropout = p_dropout
        self.w = theano.shared(
            np.zeros((n_in, n_out), dtype=theano.config.floatX),
            name='w', borrow=True)
        self.b = theano.shared(
            np.zeros((n_out,), dtype=theano.config.floatX),
            name='b', borrow=True)
        self.params = [self.w, self.b]

    def set_inpt(self, inpt, inpt_dropout, mini_batch_size):
        self.inpt = inpt.reshape((mini_batch_size, self.n_in))
        self.output = softmax((1-self.p_dropout)*T.dot(self.inpt, self.w) + self.b)
        self.y_out = T.argmax(self.output, axis=1)
        self.inpt_dropout = dropout_layer(
            inpt_dropout.reshape((mini_batch_size, self.n_in)), self.p_dropout)
        self.output_dropout = softmax(T.dot(self.inpt_dropout, self.w) + self.b)

    def cost(self, net):
        "Return the log-likelihood cost."
        return -T.mean(T.log(self.output_dropout)[T.arange(net.y.shape[0]), net.y])

    def accuracy(self, y):
        "Return the accuracy for the mini-batch."
        return T.mean(T.eq(y, self.y_out))