神經網絡入門（機器學習、深度學習簡介，神經元-logistic迴歸模型，神經元多輸出，目標函數，梯度下降，神經元實戰，神經網絡基本概念與實戰）

1、機器學習、深度學習簡介

上面這張圖形象的表達了機器學習與深度學習的關係，機器學習是實現人工智能的方法，深度學習是實現機器學習算法的技術。

機器學習是將無序數據轉化爲價值的方法，機器學習的價值是從數據中抽取規律，並用來預測未來。

2、神經元-logistic迴歸模型

神經元是最小的神經網絡，如下圖所示

計算方法舉例：(未考慮偏置b)

偏置b的物理含義（截距）：

3、神經元多輸出

由2的基礎，現在討論神經元的多輸出情況：

計算舉例說明：(未考慮偏置b)

4、目標函數

目標函數就是損失函數，它用來衡量對數據的擬合程度。

常用目標函數有兩種：平方差損失函數與交叉熵損失函數，公式如下：

神經網絡的訓練過程就是：調整參數使模型在訓練集上的損失函數最小的過程。

5、梯度下降

是找到的“下山”的方向

α是沿着方向走的“那一步”的大小

下面介紹學習率α過大或過小對神經網絡訓練的影響：

如果α過小，如圖所示，它可能需要很長時間的迭代纔可能達到最優值

如果α過大，則可能永遠在最優值周圍“徘徊”而無法取到最優值

1、Minni-Batch存在震盪問題：由於隨機採樣不夠多，可能存在震盪問題，這個問題在單個樣本上會反應更明顯，Minni-Batch的size越大，這個問題就越不明顯。

2、局部極值問題：目標函數可能存在多個最優解。如果Learning-rate太小，會導致整個參數停在局部極值點的位置。鞍點，導數爲0，參數變化爲0，無論採用全部數據集，還是mini-batch還是一個樣本都會存在這種問題。

爲了解決剛纔提出的這兩個問題，提出動量梯度下降的算法。

核心：積累值與當前梯度的加法。不僅體現在大小上，還體現在方向上。

6、神經元的Tensorflow1.14.0實現

數據集：cifar10

網址：https://xilesou.hk.gg363.site/search?q=cifar10+download

下載Python版本的數據集

代碼：

import tensorflow as tf
import os
import pickle
import numpy as np

CIFAR_DIR = "./cifar-10-batches-py"
print(os.listdir(CIFAR_DIR))

physical_devices = tf.config.experimental.list_physical_devices('GPU')
assert len(physical_devices) > 0, "Not enough GPU hardware devices available"
tf.config.experimental.set_memory_growth(physical_devices[0], True)

def load_data(filename):
    """read data from data file."""
    with open(filename, 'rb') as f:
        data = pickle.load(f, encoding='bytes')
        return data[b'data'], data[b'labels']

# tensorflow.Dataset.
class CifarData:
    def __init__(self, filenames, need_shuffle):
        all_data = []
        all_labels = []
        for filename in filenames:
            data, labels = load_data(filename)
            for item, label in zip(data, labels):
                if label in [0, 1]:
                    all_data.append(item)
                    all_labels.append(label)
        self._data = np.vstack(all_data) #將numpy向量縱向合併在一起，形成矩陣。
        self._data = self._data / 127.5 - 1  #[-1,1]之間的數，相當於做一個歸一化。
        self._labels = np.hstack(all_labels)#橫向合併,一維向量
        print(self._data.shape)
        print(self._labels.shape)
        
        self._num_examples = self._data.shape[0] #有多少個example
        print(self._num_examples)
       
        self._need_shuffle = need_shuffle
        self._indicator = 0 #記錄數據集遍歷到那個位置上了
        if self._need_shuffle:
            self._shuffle_data()
            
    def _shuffle_data(self):
        # [0,1,2,3,4,5] -> [5,3,2,4,0,1]
        p = np.random.permutation(self._num_examples)
        self._data = self._data[p]
        self._labels = self._labels[p]
    
    def next_batch(self, batch_size):
        """return batch_size examples as a batch."""
        end_indicator = self._indicator + batch_size
        if end_indicator > self._num_examples:
            if self._need_shuffle:
                self._shuffle_data()
                self._indicator = 0
                end_indicator = batch_size
            else:
                raise Exception("have no more examples")
        if end_indicator > self._num_examples:
            raise Exception("batch size is larger than all examples")
        batch_data = self._data[self._indicator: end_indicator]
        batch_labels = self._labels[self._indicator: end_indicator]
        self._indicator = end_indicator
        return batch_data, batch_labels

train_filenames = [os.path.join(CIFAR_DIR, 'data_batch_%d' % i) for i in range(1, 6)]
test_filenames = [os.path.join(CIFAR_DIR, 'test_batch')]

train_data = CifarData(train_filenames, True)
#test_data = CifarData(test_filenames, False)

x = tf.placeholder(tf.float32, [None, 3072])
# [None], 第一維樣本數不確定，爲了應對batch_size的可變性。
y = tf.placeholder(tf.int64, [None])

# (3072, 1)
w = tf.get_variable('w', [x.get_shape()[-1], 1],#單個神經元是二分類器
                   initializer=tf.random_normal_initializer(0, 1))
# (1, )
b = tf.get_variable('b', [1],
                   initializer=tf.constant_initializer(0.0))

# [None, 3072] * [3072, 1] = [None, 1]
y_ = tf.matmul(x, w) + b

#[None, 1]
p_y_1 = tf.nn.sigmoid(y_) #內積值->概率值，輸入到sigmoid中去，得到y=1的概率值。
#  y:[None] -> [None, 1]
y_reshaped = tf.reshape(y, (-1, 1))
y_reshaped_float = tf.cast(y_reshaped, tf.float32)

loss = tf.reduce_mean(tf.square(y_reshaped_float - p_y_1))

# bool
predict = p_y_1 > 0.5
# [1,0,1,1,1,0,0,0]
correct_prediction = tf.equal(tf.cast(predict, tf.int64), y_reshaped)
accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float64))

with tf.name_scope('train_op'):
    train_op = tf.train.AdamOptimizer(1e-3).minimize(loss)

init = tf.global_variables_initializer()
#初始化變量
batch_size = 20
train_steps = 100000
test_steps = 100
#打開一個會話，可以執行計算圖。
with tf.Session() as sess:
    sess.run(init)
    for i in range(train_steps):
        batch_data, batch_labels = train_data.next_batch(batch_size)
        loss_val, acc_val, _ = sess.run(
            [loss, accuracy, train_op],
            feed_dict={
                x: batch_data,
                y: batch_labels})
        if (i+1) % 500 == 0:
            print('[Train] Step: %d, loss: %4.5f, acc: %4.5f' % (i+1, loss_val, acc_val))
        if (i+1) % 5000 == 0:
            test_data = CifarData(test_filenames, False)
            all_test_acc_val = []
            for j in range(test_steps): #正好完整遍歷一次測試集
                test_batch_data, test_batch_labels \
                    = test_data.next_batch(batch_size)
                test_acc_val = sess.run(
                    [accuracy],
                    feed_dict = {
                        x: test_batch_data, 
                        y: test_batch_labels
                    })
                all_test_acc_val.append(test_acc_val)
            test_acc = np.mean(all_test_acc_val)
            print('[Test ] Step: %d, acc: %4.5f' % (i+1, test_acc))

7、神經網絡

多層神經元構成了神經網絡，如下圖是具有一個隱含層的神經網絡。

用梯度下降的方式對神經網絡進行訓練，用損失函數對每一個參數求偏導，再乘以α，用這個結果更新所有的參數，一步一步迭代，得到比較好的神經網絡。

求損失函數對各個參數的偏導數，先看最後一層，假設h採用sigmoid激活函數，則圖中L爲使用了平方差損失函數的損失函數。參數w存在於h21,h22,h23的權重，x是h21,h22,h23的輸出 and +1，可以直接求L對w的導數。

8、神經網絡（多分類logistic迴歸模型）的Tensorflow1.14.0實現

多分類是在第6部分的單個神經元二分類代碼的基礎上修改的。

import tensorflow as tf
import os
import pickle
import numpy as np

CIFAR_DIR = "./cifar-10-batches-py"
print(os.listdir(CIFAR_DIR))
print(tf.__version__)

def load_data(filename):
    """read data from data file."""
    with open(filename, 'rb') as f:
        data = pickle.load(f, encoding='bytes')
        return data[b'data'], data[b'labels']

# tensorflow.Dataset.
class CifarData:
    def __init__(self, filenames, need_shuffle):
        all_data = []
        all_labels = []
        for filename in filenames:
            data, labels = load_data(filename)
            all_data.append(data)
            all_labels.append(labels)
        self._data = np.vstack(all_data)
        self._data = self._data / 127.5 - 1
        self._labels = np.hstack(all_labels)
        print(self._data.shape)
        print(self._labels.shape)
        
        self._num_examples = self._data.shape[0]
        self._need_shuffle = need_shuffle
        self._indicator = 0
        if self._need_shuffle:
            self._shuffle_data()
            
    def _shuffle_data(self):
        # [0,1,2,3,4,5] -> [5,3,2,4,0,1]
        p = np.random.permutation(self._num_examples)
        self._data = self._data[p]
        self._labels = self._labels[p]
    
    def next_batch(self, batch_size):
        """return batch_size examples as a batch."""
        end_indicator = self._indicator + batch_size
        if end_indicator > self._num_examples:
            if self._need_shuffle:
                self._shuffle_data()
                self._indicator = 0
                end_indicator = batch_size
            else:
                raise Exception("have no more examples")
        if end_indicator > self._num_examples:
            raise Exception("batch size is larger than all examples")
        batch_data = self._data[self._indicator: end_indicator]
        batch_labels = self._labels[self._indicator: end_indicator]
        self._indicator = end_indicator
        return batch_data, batch_labels

train_filenames = [os.path.join(CIFAR_DIR, 'data_batch_%d' % i) for i in range(1, 6)]
test_filenames = [os.path.join(CIFAR_DIR, 'test_batch')]

train_data = CifarData(train_filenames, True)
test_data = CifarData(test_filenames, False)

x = tf.placeholder(tf.float32, [None, 3072])
# [None], eg: [0,5,6,3]
y = tf.placeholder(tf.int64, [None])

# (3072, 10)
w = tf.get_variable('w', [x.get_shape()[-1], 10], #10個神經元，沒有隱含層的神經網絡
                   initializer=tf.random_normal_initializer(0, 1))
# (10, )
b = tf.get_variable('b', [10],
                   initializer=tf.constant_initializer(0.0))

# [None, 3072] * [3072, 10] = [None, 10]
y_ = tf.matmul(x, w) + b

# mean square loss
"""
# course: 1 + e^x
# api: e^x / sum(e^x)
# [[0.01, 0.9, ..., 0.03], []]
p_y = tf.nn.softmax(y_)
# 5 -> [0,0,0,0,0,1,0,0,0,0]
y_one_hot = tf.one_hot(y, 10, dtype=tf.float32)
loss = tf.reduce_mean(tf.square(y_one_hot - p_y))

"""

loss = tf.losses.sparse_softmax_cross_entropy(labels=y, logits=y_)
# y_ -> sofmax
# y -> one_hot
# loss = ylogy_

# indices
predict = tf.argmax(y_, 1)#對每個樣本求最大值
# [1,0,1,1,1,0,0,0]
correct_prediction = tf.equal(predict, y)
accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float64))

with tf.name_scope('train_op'):
    train_op = tf.train.AdamOptimizer(1e-3).minimize(loss)

init = tf.global_variables_initializer()
batch_size = 20
train_steps = 100000
test_steps = 100

# run 100k: 30.95%
with tf.Session() as sess:
    sess.run(init)
    for i in range(train_steps):
        batch_data, batch_labels = train_data.next_batch(batch_size)
        loss_val, acc_val, _ = sess.run(
            [loss, accuracy, train_op],
            feed_dict={
                x: batch_data,
                y: batch_labels})
        if (i+1) % 500 == 0:
            print('[Train] Step: %d, loss: %4.5f, acc: %4.5f' 
                  % (i+1, loss_val, acc_val))
        if (i+1) % 5000 == 0:
            test_data = CifarData(test_filenames, False)
            all_test_acc_val = []
            for j in range(test_steps):
                test_batch_data, test_batch_labels \
                    = test_data.next_batch(batch_size)
                test_acc_val = sess.run(
                    [accuracy],
                    feed_dict = {
                        x: test_batch_data, 
                        y: test_batch_labels
                    })
                all_test_acc_val.append(test_acc_val)
            test_acc = np.mean(all_test_acc_val)
            print('[Test ] Step: %d, acc: %4.5f' % (i+1, test_acc))