由于调参记录18依然存在过拟合，本文将自适应参数化ReLU激活函数中最后一层的神经元个数减少为1个，继续测试深度残差网络+自适应参数化ReLU激活函数在Cifar10数据集上的效果。
同时，迭代次数从调参记录18中的5000个epoch，减少到了500个epoch，因为5000次实在是太费时间了，差不多要四天才能跑完。
自适应参数化ReLU激活函数的基本原理如下：
Keras程序如下：
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue Apr 14 04:17:45 2020
Implemented using TensorFlow 1.0.1 and Keras 2.2.1
Minghang Zhao, Shisheng Zhong, Xuyun Fu, Baoping Tang, Shaojiang Dong, Michael Pecht,
Deep Residual Networks with Adaptively Parametric Rectifier Linear Units for Fault Diagnosis,
IEEE Transactions on Industrial Electronics, 2020, DOI: 10.1109/TIE.2020.2972458
@author: Minghang Zhao
"""
from __future__ import print_function
import keras
import numpy as np
from keras.datasets import cifar10
from keras.layers import Dense, Conv2D, BatchNormalization, Activation, Minimum
from keras.layers import AveragePooling2D, Input, GlobalAveragePooling2D, Concatenate, Reshape
from keras.regularizers import l2
from keras import backend as K
from keras.models import Model
from keras import optimizers
from keras.preprocessing.image import ImageDataGenerator
from keras.callbacks import LearningRateScheduler
K.set_learning_phase(1)
# The data, split between train and test sets
(x_train, y_train), (x_test, y_test) = cifar10.load_data()
# Noised data
x_train = x_train.astype('float32') / 255.
x_test = x_test.astype('float32') / 255.
x_test = x_test-np.mean(x_train)
x_train = x_train-np.mean(x_train)
print('x_train shape:', x_train.shape)
print(x_train.shape[0], 'train samples')
print(x_test.shape[0], 'test samples')
# convert class vectors to binary class matrices
y_train = keras.utils.to_categorical(y_train, 10)
y_test = keras.utils.to_categorical(y_test, 10)
# Schedule the learning rate, multiply 0.1 every 150 epoches
def scheduler(epoch):
if epoch % 150 == 0 and epoch != 0:
lr = K.get_value(model.optimizer.lr)
K.set_value(model.optimizer.lr, lr * 0.1)
print("lr changed to {}".format(lr * 0.1))
return K.get_value(model.optimizer.lr)
# An adaptively parametric rectifier linear unit (APReLU)
def aprelu(inputs):
# get the number of channels
channels = inputs.get_shape().as_list()[-1]
# get a zero feature map
zeros_input = keras.layers.subtract([inputs, inputs])
# get a feature map with only positive features
pos_input = Activation('relu')(inputs)
# get a feature map with only negative features
neg_input = Minimum()([inputs,zeros_input])
# define a network to obtain the scaling coefficients
scales_p = GlobalAveragePooling2D()(pos_input)
scales_n = GlobalAveragePooling2D()(neg_input)
scales = Concatenate()([scales_n, scales_p])
scales = Dense(channels//16, activation='linear', kernel_initializer='he_normal', kernel_regularizer=l2(1e-4))(scales)
scales = BatchNormalization(momentum=0.9, gamma_regularizer=l2(1e-4))(scales)
scales = Activation('relu')(scales)
scales = Dense(1, activation='linear', kernel_initializer='he_normal', kernel_regularizer=l2(1e-4))(scales)
scales = BatchNormalization(momentum=0.9, gamma_regularizer=l2(1e-4))(scales)
scales = Activation('sigmoid')(scales)
scales = Reshape((1,1,1))(scales)
# apply a paramtetric relu
neg_part = keras.layers.multiply([scales, neg_input])
return keras.layers.add([pos_input, neg_part])
# Residual Block
def residual_block(incoming, nb_blocks, out_channels, downsample=False,
downsample_strides=2):
residual = incoming
in_channels = incoming.get_shape().as_list()[-1]
for i in range(nb_blocks):
identity = residual
if not downsample:
downsample_strides = 1
residual = BatchNormalization(momentum=0.9, gamma_regularizer=l2(1e-4))(residual)
residual = aprelu(residual)
residual = Conv2D(out_channels, 3, strides=(downsample_strides, downsample_strides),
padding='same', kernel_initializer='he_normal',
kernel_regularizer=l2(1e-4))(residual)
residual = BatchNormalization(momentum=0.9, gamma_regularizer=l2(1e-4))(residual)
residual = aprelu(residual)
residual = Conv2D(out_channels, 3, padding='same', kernel_initializer='he_normal',
kernel_regularizer=l2(1e-4))(residual)
# Downsampling
if downsample_strides > 1:
identity = AveragePooling2D(pool_size=(1,1), strides=(2,2))(identity)
# Zero_padding to match channels
if in_channels != out_channels:
zeros_identity = keras.layers.subtract([identity, identity])
identity = keras.layers.concatenate([identity, zeros_identity])
in_channels = out_channels
residual = keras.layers.add([residual, identity])
return residual
# define and train a model
inputs = Input(shape=(32, 32, 3))
net = Conv2D(16, 3, padding='same', kernel_initializer='he_normal', kernel_regularizer=l2(1e-4))(inputs)
net = residual_block(net, 9, 32, downsample=False)
net = residual_block(net, 1, 32, downsample=True)
net = residual_block(net, 8, 32, downsample=False)
net = residual_block(net, 1, 64, downsample=True)
net = residual_block(net, 8, 64, downsample=False)
net = BatchNormalization(momentum=0.9, gamma_regularizer=l2(1e-4))(net)
net = aprelu(net)
net = GlobalAveragePooling2D()(net)
outputs = Dense(10, activation='softmax', kernel_initializer='he_normal', kernel_regularizer=l2(1e-4))(net)
model = Model(inputs=inputs, outputs=outputs)
sgd = optimizers.SGD(lr=0.1, decay=0., momentum=0.9, nesterov=True)
model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])
# data augmentation
datagen = ImageDataGenerator(
# randomly rotate images in the range (deg 0 to 180)
rotation_range=30,
# Range for random zoom
zoom_range = 0.2,
# shear angle in counter-clockwise direction in degrees
shear_range = 30,
# randomly flip images
horizontal_flip=True,
# randomly shift images horizontally
width_shift_range=0.125,
# randomly shift images vertically
height_shift_range=0.125)
reduce_lr = LearningRateScheduler(scheduler)
# fit the model on the batches generated by datagen.flow().
model.fit_generator(datagen.flow(x_train, y_train, batch_size=100),
validation_data=(x_test, y_test), epochs=500,
verbose=1, callbacks=[reduce_lr], workers=4)
# get results
K.set_learning_phase(0)
DRSN_train_score = model.evaluate(x_train, y_train, batch_size=100, verbose=0)
print('Train loss:', DRSN_train_score[0])
print('Train accuracy:', DRSN_train_score[1])
DRSN_test_score = model.evaluate(x_test, y_test, batch_size=100, verbose=0)
print('Test loss:', DRSN_test_score[0])
print('Test accuracy:', DRSN_test_score[1])实验结果如下：
Train loss: 0.1304543605595827
Train accuracy: 0.9980800018310547
Test loss: 0.3480722904205322
Test accuracy: 0.9396000015735626相较于调参记录18，训练准确率和测试准确率都降了一点。同时，训练准确率比测试准确率大概高了6%，说明依然存在过拟合。
Minghang Zhao, Shisheng Zhong, Xuyun Fu, Baoping Tang, Shaojiang Dong, Michael Pecht, Deep Residual Networks with Adaptively Parametric Rectifier Linear Units for Fault Diagnosis, IEEE Transactions on Industrial Electronics, 2020, DOI: 10.1109/TIE.2020.2972458
https://ieeexplore.ieee.org/document/8998530