Deep Learning using Linear Support Vector Machines這篇論文主要用SVM分類器替代了softmax分類器，並用合頁損失替代了交叉熵損失，具體定義如下：

程式碼:

# Copyright 2017 Abien Fred Agarap

# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at

#    http://www.apache.org/licenses/LICENSE-2.0

# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

"""2 Convolutional Layers with Max Pooling CNN"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

__version__ = '0.1.0'
__author__ = 'Abien Fred Agarap'

import os
import tensorflow as tf
import time
import sys


class CNNSVM:

    def __init__(self, alpha, batch_size, num_classes, num_features, penalty_parameter):
        """Initializes the CNN-SVM model

        :param alpha: The learning rate to be used by the model.
        :param batch_size: The number of batches to use for training/validation/testing.
        :param num_classes: The number of classes in the dataset.
        :param num_features: The number of features in the dataset.
        :param penalty_parameter: The SVM C penalty parameter.
        """
        self.alpha = alpha
        self.batch_size = batch_size
        self.name = 'CNN-SVM'
        self.num_classes = num_classes
        self.num_features = num_features
        self.penalty_parameter = penalty_parameter

        def __graph__():

            with tf.name_scope('input'):
                # [BATCH_SIZE, NUM_FEATURES]
                x_input = tf.placeholder(dtype=tf.float32, shape=[None, num_features], name='x_input')

                # [BATCH_SIZE, NUM_CLASSES]
                y_input = tf.placeholder(dtype=tf.float32, shape=[None, num_classes], name='actual_label')

            # First convolutional layer
            first_conv_weight = self.weight_variable([5, 5, 1, 32])
            first_conv_bias = self.bias_variable([32])

            input_image = tf.reshape(x_input, [-1, 28, 28, 1])

            first_conv_activation = tf.nn.relu(self.conv2d(input_image, first_conv_weight) + first_conv_bias)
            first_conv_pool = self.max_pool_2x2(first_conv_activation)

            # Second convolutional layer
            second_conv_weight = self.weight_variable([5, 5, 32, 64])
            second_conv_bias = self.bias_variable([64])

            second_conv_activation = tf.nn.relu(self.conv2d(first_conv_pool, second_conv_weight) + second_conv_bias)
            second_conv_pool = self.max_pool_2x2(second_conv_activation)

            # Fully-connected layer (Dense Layer)
            dense_layer_weight = self.weight_variable([7 * 7 * 64, 1024])
            dense_layer_bias = self.bias_variable([1024])

            second_conv_pool_flatten = tf.reshape(second_conv_pool, [-1, 7 * 7 * 64])
            dense_layer_activation = tf.nn.relu(tf.matmul(second_conv_pool_flatten, dense_layer_weight) +
                                                dense_layer_bias)

            # Dropout, to avoid over-fitting
            keep_prob = tf.placeholder(tf.float32)
            h_fc1_drop = tf.nn.dropout(dense_layer_activation, keep_prob)

            # Readout layer
            readout_weight = self.weight_variable([1024, num_classes])
            readout_bias = self.bias_variable([num_classes])

            output = tf.matmul(h_fc1_drop, readout_weight) + readout_bias

            with tf.name_scope('svm'):
                regularization_loss = tf.reduce_mean(tf.square(readout_weight))
                hinge_loss = tf.reduce_mean(
                    tf.square(tf.maximum(tf.zeros([batch_size, num_classes]), 1 - y_input * output)))
                with tf.name_scope('loss'):
                    loss = regularization_loss + penalty_parameter * hinge_loss
            tf.summary.scalar('loss', loss)

            optimizer = tf.train.AdamOptimizer(learning_rate=alpha).minimize(loss)

            with tf.name_scope('accuracy'):
                output = tf.identity(tf.sign(output), name='prediction')
                correct_prediction = tf.equal(tf.argmax(output, 1), tf.argmax(y_input, 1))
                with tf.name_scope('accuracy'):
                    accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
            tf.summary.scalar('accuracy', accuracy)

            merged = tf.summary.merge_all()

            self.x_input = x_input
            self.y_input = y_input
            self.keep_prob = keep_prob
            self.output = output
            self.loss = loss
            self.optimizer = optimizer
            self.accuracy = accuracy
            self.merged = merged

        sys.stdout.write('\n<log> Building graph...')
        __graph__()
        sys.stdout.write('</log>\n')

    def train(self, checkpoint_path, epochs, log_path, train_data, test_data):
        """Trains the initialized model.

        :param checkpoint_path: The path where to save the trained model.
        :param epochs: The number of passes through the entire dataset.
        :param log_path: The path where to save the TensorBoard logs.
        :param train_data: The training dataset.
        :param test_data: The testing dataset.
        :return: None
        """

        if not os.path.exists(path=log_path):
            os.mkdir(log_path)

        if not os.path.exists(path=checkpoint_path):
            os.mkdir(checkpoint_path)

        saver = tf.train.Saver(max_to_keep=4)

        init = tf.global_variables_initializer()

        timestamp = str(time.asctime())

        train_writer = tf.summary.FileWriter(logdir=log_path + timestamp + '-training', graph=tf.get_default_graph())

        with tf.Session() as sess:
            sess.run(init)

            checkpoint = tf.train.get_checkpoint_state(checkpoint_path)

            if checkpoint and checkpoint.model_checkpoint_path:
                saver = tf.train.import_meta_graph(checkpoint.model_checkpoint_path + '.meta')
                saver.restore(sess, tf.train.latest_checkpoint(checkpoint_path))

            for index in range(epochs):
                # train by batch
                batch_features, batch_labels = train_data.next_batch(self.batch_size)
                batch_labels[batch_labels == 0] = -1

                # input dictionary with dropout of 50%
                feed_dict = {self.x_input: batch_features, self.y_input: batch_labels, self.keep_prob: 0.5}
                
                # run the train op
                summary, _, loss = sess.run([self.merged, self.optimizer, self.loss], feed_dict=feed_dict)
                
                # every 100th step and at 0,
                if index % 100 == 0:
                    feed_dict = {self.x_input: batch_features, self.y_input: batch_labels, self.keep_prob: 1.0}
                    
                    # get the accuracy of training
                    train_accuracy = sess.run(self.accuracy, feed_dict=feed_dict)
                    
                    # display the training accuracy
                    print('step: {}, training accuracy : {}, training loss : {}'.format(index, train_accuracy, loss))

                    train_writer.add_summary(summary=summary, global_step=index)

                    saver.save(sess, save_path=os.path.join(checkpoint_path, self.name), global_step=index)

            test_features = test_data.images
            test_labels = test_data.labels
            test_labels[test_labels == 0] = -1

            feed_dict = {self.x_input: test_features, self.y_input: test_labels, self.keep_prob: 1.0}

            test_accuracy = sess.run(self.accuracy, feed_dict=feed_dict)

            print('Test Accuracy: {}'.format(test_accuracy))

    @staticmethod
    def weight_variable(shape):
        """Returns a weight matrix consisting of arbitrary values.

        :param shape: The shape of the weight matrix to create.
        :return: The weight matrix consisting of arbitrary values.
        """
        initial = tf.truncated_normal(shape, stddev=0.1)
        return tf.Variable(initial)

    @staticmethod
    def bias_variable(shape):
        """Returns a bias matrix consisting of 0.1 values.

        :param shape: The shape of the bias matrix to create.
        :return: The bias matrix consisting of 0.1 values.
        """
        initial = tf.constant(0.1, shape=shape)
        return tf.Variable(initial)

    @staticmethod
    def conv2d(features, weight):
        """Produces a convolutional layer that filters an image subregion

        :param features: The layer input.
        :param weight: The size of the layer filter.
        :return: Returns a convolutional layer.
        """
        return tf.nn.conv2d(features, weight, strides=[1, 1, 1, 1], padding='SAME')

    @staticmethod
    def max_pool_2x2(features):
        """Downnsamples the image based on convolutional layer

        :param features: The input to downsample.
        :return: Downsampled input.
        """
        return tf.nn.max_pool(features, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='SAME')0
 

# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.


"""Implementation of the CNN classes"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function


__version__ = '0.1.0'
__author__ = 'Abien Fred Agarap'


import argparse
from model.cnn_softmax import CNN
from model.cnn_svm import CNNSVM
from tensorflow.examples.tutorials.mnist import input_data




def parse_args():
    parser = argparse.ArgumentParser(description='CNN & CNN-SVM for Image Classification')
    group = parser.add_argument_group('Arguments')
    group.add_argument('-m', '--model', required=True, type=str,
                       help='[1] CNN-Softmax, [2] CNN-SVM')
    group.add_argument('-d', '--dataset', required=True, type=str,
                       help='path of the MNIST dataset')
    group.add_argument('-p', '--penalty_parameter', required=False, type=int,
                       help='the SVM C penalty parameter')
    group.add_argument('-c', '--checkpoint_path', required=True, type=str,
                       help='path where to save the trained model')
    group.add_argument('-l', '--log_path', required=True, type=str,
                       help='path where to save the TensorBoard logs')
    arguments = parser.parse_args()
    return arguments




if __name__ == '__main__':
    args = parse_args()


    mnist = input_data.read_data_sets(args.dataset, one_hot=True)
    num_classes = mnist.train.labels.shape[1]
    sequence_length = mnist.train.images.shape[1]
    model_choice = args.model


    assert model_choice == '1' or model_choice == '2', "Invalid choice: Choose between 1 and 2 only."


    if model_choice == '1':
        model = CNN(alpha=1e-3, batch_size=128, num_classes=num_classes, num_features=sequence_length)
        model.train(checkpoint_path=args.checkpoint_path, epochs=10000, log_path=args.log_path,
                    train_data=mnist.train, test_data=mnist.test)
    elif model_choice == '2':
        model = CNNSVM(alpha=1e-3, batch_size=128, num_classes=num_classes, num_features=sequence_length,
                       penalty_parameter=args.penalty_parameter)
        model.train(checkpoint_path=args.checkpoint_path, epochs=10000, log_path=args.log_path,
                    train_data=mnist.train, test_data=mnist.test)
 

這裡合頁損失的使用可以採用，tf.reduce_sum() 和tf.reduce_mean(）兩種，效果可能不一樣，對不同的應用。