前向算法（Forward Algorithm）是一种在机器学习中用于训练神经网络的方法。它的主要目的是通过计算梯度来调整网络中的权重和偏置，从而最小化损失函数。前向算法与其他优化算法（如梯度下降法、牛顿法等）结合使用，可以提高神经网络的性能和准确性。
前向算法的步骤如下：
- 初始化权重和偏置：在开始训练之前，需要为神经网络的每个权重和偏置赋初值。这些初值通常是随机生成的，以便在训练过程中更容易找到一个好的局部最小值。
- 前向传播：将训练数据输入到神经网络中，经过各层的计算，得到输出层的预测结果。这一过程称为前向传播。在前向传播过程中，每个神经元将接收到上一层神经元的输出信号，并根据激活函数（如 ReLU、Sigmoid、Softmax 等）计算自己的输出。
- 计算损失：根据预测结果和实际标签，计算损失函数（如交叉熵损失、均方误差损失等）。损失函数衡量了模型预测与实际标签之间的差距，用于评估模型性能。
- 计算梯度：使用链式法则计算损失函数关于每个权重和偏置的梯度。梯度是损失函数在每个参数上的局部最小值方向，可以利用梯度来更新权重和偏置，从而减小损失函数。
- 更新权重和偏置：根据计算出的梯度，使用优化算法（如梯度下降法、牛顿法等）来更新权重和偏置。这一过程会不断迭代，直到损失函数达到预设的阈值或达到最大迭代次数。
- 验证和测试：在训练过程中，可以使用验证集来评估模型性能，以便及时停止训练并避免过拟合。训练完成后，使用测试集来评估模型的最终性能。
总之，前向算法是机器学习中用于训练神经网络的一种方法，通过计算梯度来调整权重和偏置，从而最小化损失函数。它与其他优化算法结合使用，可以提高神经网络的性能和准确性。
Segmentation
Import libraries and define hyper-parameters:
import tensorflow as tf
import numpy as np
from bregman.suite import *
k = 2
segment_size = 50
max_iterations = 100
Define functions to get the chromogram and the dataset:
chromo = tf.placeholder(tf.float32)
max_freqs = tf.argmax(chromo, 0)
def get_chromogram(audio_file):
F = Chromagram(audio_file, nfft=16384, wfft=8192, nhop=2205)
return F.X
def get_dataset(sess, audio_file):
chromo_data = get_chromogram(audio_file)
print('chromo_data', np.shape(chromo_data))
chromo_length = np.shape(chromo_data)[1]
xs = []
for i in range(chromo_length/segment_size):
chromo_segment = chromo_data[:, i*segment_size:(i+1)*segment_size]
x = extract_feature_vector(sess, chromo_segment)
if len(xs) == 0:
xs = x
else:
xs = np.vstack((xs, x))
return xs
As required for the k-means algorithm, specify the assignment and re-centering code:
def initial_cluster_centroids(X, k):
return X[0:k, :]
def assign_cluster(X, centroids):
expanded_vectors = tf.expand_dims(X, 0)
expanded_centroids = tf.expand_dims(centroids, 1)
distances = tf.reduce_sum(tf.square(tf.subtract(expanded_vectors, expanded_centroids)), 2)
mins = tf.argmin(distances, 0)
return mins
def recompute_centroids(X, Y):
sums = tf.unsorted_segment_sum(X, Y, k)
counts = tf.unsorted_segment_sum(tf.ones_like(X), Y, k)
return sums / counts
Given a chromogram, extract a histogram of sound frequencies as our feature vector:
def extract_feature_vector(sess, chromo_data):
num_features, num_samples = np.shape(chromo_data)
freq_vals = sess.run(max_freqs, feed_dict={chromo: chromo_data})
hist, bins = np.histogram(freq_vals, bins=range(num_features + 1))
return hist.astype(float) / num_samples
In a session, segment an audio file using k-means:
with tf.Session() as sess:
X = get_dataset(sess, 'TalkingMachinesPodcast.wav')
print(np.shape(X))
centroids = initial_cluster_centroids(X, k)
i, converged = 0, False
# prev_Y = None
while not converged and i < max_iterations:
i += 1
Y = assign_cluster(X, centroids)
# if prev_Y == Y:
# converged = True
# break
# prev_Y = Y
centroids = sess.run(recompute_centroids(X, Y))
if i % 50 == 0:
print('iteration', i)
segments = sess.run(Y)
for i in range(len(segments)):
seconds = (i * segment_size) / float(20)
min, sec = divmod(seconds, 60)
time_str = str(min) + 'm ' + str(sec) + 's'
print(time_str, segments[i])
/usr/local/lib/python2.7/dist-packages/bregman/features_base.py:353: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
mxnorm = P.empty(self._cqtN) # Normalization coefficients
/usr/local/lib/python2.7/dist-packages/bregman/features_base.py:357: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
for i in P.arange(self._cqtN)])
('chromo_data', (12, 633))
(12, 12)
('iteration', 50)
('iteration', 100)
('0.0m 0.0s', 0)
('0.0m 2.5s', 1)
('0.0m 5.0s', 0)
('0.0m 7.5s', 1)
('0.0m 10.0s', 1)
('0.0m 12.5s', 1)
('0.0m 15.0s', 1)
('0.0m 17.5s', 0)
('0.0m 20.0s', 1)
('0.0m 22.5s', 1)
('0.0m 25.0s', 0)
('0.0m 27.5s', 0)
