自动编码器

将自动编码器应用于图像处理，主要是利用其无监督学习能力对图像进行降维、特征提取和数据压缩等操作。以下是将自动编码器应用于图像的具体步骤：1. 准备数据：首先，需要收集大量的图像数据，这些数据可以来自于不同的来源，例如公开的数据集或专业的图像库。2. 构建编码器：根据图像数据的特点，选择适当的神经网络结构作为编码器。常见的编码器结构包括卷积神经网络（CNN）和循环神经网络（RNN）。CNN 编码器适合处理静态图像，而 RNN 编码器适合处理动态图像（如视频）。3. 构建解码器：根据原始图像数据的维度和编码器的输出尺寸，选择适当的神经网络结构作为解码器。解码器的任务是将编码器生成的隐向量还原回原始图像空间。4. 训练自动编码器：将编码器和解码器连接在一起，形成一个端到端的神经网络。使用无监督学习方法（如随机梯度下降法或变分自编码器）训练该网络，使其在重建输入图像时达到最小损失。5. 应用自动编码器：训练好的自动编码器可以用于多种任务，如图像降维、特征提取、图像数据压缩和生成新的图像样本等。例如，可以使用自动编码器将原始图像压缩成低维度的隐向量，从而实现图像压缩；也可以使用自动编码器生成与原始图像相似的新图像样本，从而实现图像生成。总之，将自动编码器应用于图像处理，可以利用其无监督学习能力对图像进行降维、特征提取和数据压缩等操作。通过训练编码器和解码器，自动编码器可以学习到图像数据的主要特征，并将这些特征用于其他任务。

Viterbi parse of a Hidden Markov model
Import TensorFlow and Numpy

import numpy as np
import tensorflow as tf
Create the same HMM model as before. This time, we'll include a couple additional functions.

# initial parameters can be learned on training data
# theory reference https://web.stanford.edu/~jurafsky/slp3/8.pdf
# code reference https://phvu.net/2013/12/06/sweet-implementation-of-viterbi-in-python/
class HMM(object):
    def __init__(self, initial_prob, trans_prob, obs_prob):
        self.N = np.size(initial_prob)
        self.initial_prob = initial_prob
        self.trans_prob = trans_prob
        self.obs_prob = obs_prob
        self.emission = tf.constant(obs_prob)
        assert self.initial_prob.shape == (self.N, 1)
        assert self.trans_prob.shape == (self.N, self.N)
        assert self.obs_prob.shape[0] == self.N
        self.obs = tf.placeholder(tf.int32)
        self.fwd = tf.placeholder(tf.float64)
        self.viterbi = tf.placeholder(tf.float64)

    def get_emission(self, obs_idx):
        slice_location = [0, obs_idx]
        num_rows = tf.shape(self.emission)[0]
        slice_shape = [num_rows, 1]
        return tf.slice(self.emission, slice_location, slice_shape)

    def forward_init_op(self):
        obs_prob = self.get_emission(self.obs)
        fwd = tf.multiply(self.initial_prob, obs_prob)
        return fwd

    def forward_op(self):
        transitions = tf.matmul(self.fwd, tf.transpose(self.get_emission(self.obs)))
        weighted_transitions = transitions * self.trans_prob
        fwd = tf.reduce_sum(weighted_transitions, 0)
        return tf.reshape(fwd, tf.shape(self.fwd))

    def decode_op(self):
        transitions = tf.matmul(self.viterbi, tf.transpose(self.get_emission(self.obs)))
        weighted_transitions = transitions * self.trans_prob
        viterbi = tf.reduce_max(weighted_transitions, 0)
        return tf.reshape(viterbi, tf.shape(self.viterbi))

    def backpt_op(self):
        back_transitions = tf.matmul(self.viterbi, np.ones((1, self.N)))
        weighted_back_transitions = back_transitions * self.trans_prob
        return tf.argmax(weighted_back_transitions, 0)
Define the forward algorithm from Concept01.

def forward_algorithm(sess, hmm, observations):
    fwd = sess.run(hmm.forward_init_op(), feed_dict={hmm.obs: observations[0]})
    for t in range(1, len(observations)):
        fwd = sess.run(hmm.forward_op(), feed_dict={hmm.obs: observations[t], hmm.fwd: fwd})
    prob = sess.run(tf.reduce_sum(fwd))
    return prob
Now, let's compute the Viterbi likelihood of the observed sequence:

def viterbi_decode(sess, hmm, observations):
    viterbi = sess.run(hmm.forward_init_op(), feed_dict={hmm.obs: observations[0]})
    backpts = np.ones((hmm.N, len(observations)), 'int32') * -1
    for t in range(1, len(observations)):
        viterbi, backpt = sess.run([hmm.decode_op(), hmm.backpt_op()],
                                    feed_dict={hmm.obs: observations[t],
                                               hmm.viterbi: viterbi})
        backpts[:, t] = backpt
    tokens = [viterbi[:, -1].argmax()]
    for i in range(len(observations) - 1, 0, -1):
        tokens.append(backpts[tokens[-1], i])
    return tokens[::-1]
Let's try it out on some example data:

if __name__ == '__main__':
    states = ('Healthy', 'Fever')
#     observations = ('normal', 'cold', 'dizzy')
#     start_probability = {'Healthy': 0.6, 'Fever': 0.4}
#     transition_probability = {
#         'Healthy': {'Healthy': 0.7, 'Fever': 0.3},
#         'Fever': {'Healthy': 0.4, 'Fever': 0.6}
#     }
#     emission_probability = {
#         'Healthy': {'normal': 0.5, 'cold': 0.4, 'dizzy': 0.1},
#         'Fever': {'normal': 0.1, 'cold': 0.3, 'dizzy': 0.6}
#     }
    initial_prob = np.array([[0.6], [0.4]])
    trans_prob = np.array([[0.7, 0.3], [0.4, 0.6]])
    obs_prob = np.array([[0.5, 0.4, 0.1], [0.1, 0.3, 0.6]])
    hmm = HMM(initial_prob=initial_prob, trans_prob=trans_prob, obs_prob=obs_prob)

    observations = [0, 1, 1, 2, 1]
    with tf.Session() as sess:
        prob = forward_algorithm(sess, hmm, observations)
        print('Probability of observing {} is {}'.format(observations, prob))

        seq = viterbi_decode(sess, hmm, observations)
        print('Most likely hidden states are {}'.format(seq))
Probability of observing [0, 1, 1, 2, 1] is 0.0046421488
Most likely hidden states are [0, 0, 0, 1, 1]