1. CNN with a Fully Connected Layer¶

The conventional CNN can be conceptually divided into two parts. One part is feature extraction and the other is classification. In the feature extraction process, convolution is used to extract the features of the input data so that the classification can be performed well. The classification process classifies which group each input data belongs to by using the extracted features from the input data.

When we visually identify images, we do not look at the whole image; instead, we intuitively focus on the most important parts of the image. CNN learning is similar to the way humans focus. When its weights are optimized, the more important parts are given higher weights. But generally, we are not able to recognize this because the generic CNN goes through a fully connected layer and makes the features extracted by the convolution layer more abstract.

1.1. Issues on CNN (or Deep Learning)¶

Deep learning performs well comparing with any other existing algorithms
But works as a black box
- A classification result is simply returned without knowing how the classification results are derived → little interpretability
When we visually identify images, we do not look at the whole image
Instead, we intuitively focus on the most important parts of the image
When CNN weights are optimized, the more important parts are given higher weights
Class activation map (CAM)
- We can determine which parts of the image the model is focusing on, based on the learned weights
- Highlighting the importance of the image region to the prediction

2. CAM: CNN with a Global Average Pooling¶

shed light on how it explicitly enables the convolutional neural network to have remarkable localization ability
the heatmap is the class activation map, highlighting the importance of the image region to the prediction

The deep learning model is a black box model. When input data is received, a classification result of 1 or 0 is simply returned for the binary classification problem, without knowing how the classification results are derived. Meanwhile, The class activation map (CAM) is capable of interpreting the results of the classification. We can determine which parts of the image the model is focusing on. Through an analysis of which part of the image the model is focusing on, we are able to interpret which part of the image is considered important.

The class activation map (CAM) is a modified convolution layer. It directly highlights the important parts of the spatial grid of an image. As a result, we can see the emphasized parts of the model. The below figure describes the procedure for class activation mapping.

The feature maps of the last convolution layer can be interpreted as a collection of visual spatial locations focused on by the model. The CAM can be obtained by taking a linear sum of the features. They all have different weights and thus can obtain spatial locations according to various input images through a linear combination. For a given image, $f_k(x,y)$ represents the feature map of unit $k$ in the last convolution layer at spatial location $(x,y)$. For a given class $c$, the class score, $S_c$, is expressed as the following equation.

$$S_c = \sum_k \omega_k^c \sum_{x,y} f_k(x,y)= \sum_{x,y} \sum_k \omega_k^c \; f_k(x,y)$$

where $\omega_k^c$ the weight corresponding to class $c$ for unit $k$. The class activation map for class $c$ is denoted as $M_c$.

$$M_c(x,y) = \sum_k \omega_k^c \; f_k(x,y)$$

$M_c$ directly indicates the importance of the feature map at a spatial grid $(x,y)$ of the class $c$. Finally the output of the softmax for class $c$ is,

$$P_c = \frac{\exp\left(S_c\right)}{\sum_c \exp\left(S_c\right)}$$

In case of the CNN, the size of the feature map is reduced by the pooling layer. By simple up-sampling, it is possible to identify attention image regions for each label.

Limitations of Class Activation Maps (CAM)

Requires a Global Average Pooling layer
Unable to visualize feature maps from different layers (other than the last)

3. CAM with NEU¶

Download NEU steel surface defects images and labels

import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
import cv2

from google.colab import drive
drive.mount('/content/drive')

Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount("/content/drive", force_remount=True).

# Change file paths if necessary

train_x = np.load('/content/drive/MyDrive/DL_Colab/DL_data/NEU_train_imgs.npy')
train_y = np.load('/content/drive/MyDrive/DL_Colab/DL_data/NEU_train_labels.npy')

test_x = np.load('/content/drive/MyDrive/DL_Colab/DL_data/NEU_test_imgs.npy')
test_y = np.load('/content/drive/MyDrive/DL_Colab/DL_data/NEU_test_labels.npy')

n_train = train_x.shape[0]
n_test = test_x.shape[0]

print ("The number of training images : {}, shape : {}".format(n_train, train_x.shape))
print ("The number of testing images : {}, shape : {}".format(n_test, test_x.shape))

The number of training images : 1500, shape : (1500, 200, 200, 1)
The number of testing images : 300, shape : (300, 200, 200, 1)

model = tf.keras.models.Sequential([
    tf.keras.layers.Conv2D(filters = 32,
                           kernel_size = (3,3),
                           activation = 'relu',
                           padding = 'SAME',
                           input_shape = (200, 200, 1)),

    tf.keras.layers.MaxPool2D((2,2)),

    tf.keras.layers.Conv2D(filters = 64,
                           kernel_size = (3,3),
                           activation = 'relu',
                           padding = 'SAME',
                           input_shape = (100, 100, 32)),

    tf.keras.layers.MaxPool2D((2,2)),

    tf.keras.layers.Conv2D(filters = 64,
                           kernel_size = (3,3),
                           activation = 'relu',
                           padding = 'SAME',
                           input_shape = (50, 50, 64)),

    tf.keras.layers.MaxPool2D((2,2)),

    tf.keras.layers.Conv2D(filters = 64,
                           kernel_size = (3,3),
                           activation = 'relu',
                           padding = 'SAME',
                           input_shape = (25, 25, 64)),

    tf.keras.layers.GlobalAveragePooling2D(),

    tf.keras.layers.Dense(6, activation = 'softmax')
])

model.summary()

Model: "sequential"
_________________________________________________________________
 Layer (type)                Output Shape              Param #   
=================================================================
 conv2d (Conv2D)             (None, 200, 200, 32)      320       
                                                                 
 max_pooling2d (MaxPooling2  (None, 100, 100, 32)      0         
 D)                                                              
                                                                 
 conv2d_1 (Conv2D)           (None, 100, 100, 64)      18496     
                                                                 
 max_pooling2d_1 (MaxPoolin  (None, 50, 50, 64)        0         
 g2D)                                                            
                                                                 
 conv2d_2 (Conv2D)           (None, 50, 50, 64)        36928     
                                                                 
 max_pooling2d_2 (MaxPoolin  (None, 25, 25, 64)        0         
 g2D)                                                            
                                                                 
 conv2d_3 (Conv2D)           (None, 25, 25, 64)        36928     
                                                                 
 global_average_pooling2d (  (None, 64)                0         
 GlobalAveragePooling2D)                                         
                                                                 
 dense (Dense)               (None, 6)                 390       
                                                                 
=================================================================
Total params: 93062 (363.52 KB)
Trainable params: 93062 (363.52 KB)
Non-trainable params: 0 (0.00 Byte)
_________________________________________________________________

model.compile(optimizer = 'adam',
              loss = 'sparse_categorical_crossentropy',
              metrics = 'accuracy')

model.fit(train_x, train_y, epochs = 15)

Epoch 1/15
47/47 [==============================] - 10s 68ms/step - loss: 1.7321 - accuracy: 0.2100
Epoch 2/15
47/47 [==============================] - 2s 45ms/step - loss: 1.1566 - accuracy: 0.5353
Epoch 3/15
47/47 [==============================] - 2s 38ms/step - loss: 0.6805 - accuracy: 0.7527
Epoch 4/15
47/47 [==============================] - 2s 36ms/step - loss: 0.6311 - accuracy: 0.7533
Epoch 5/15
47/47 [==============================] - 2s 36ms/step - loss: 0.5192 - accuracy: 0.8047
Epoch 6/15
47/47 [==============================] - 2s 38ms/step - loss: 0.4316 - accuracy: 0.8380
Epoch 7/15
47/47 [==============================] - 2s 39ms/step - loss: 0.4138 - accuracy: 0.8447
Epoch 8/15
47/47 [==============================] - 2s 38ms/step - loss: 0.4769 - accuracy: 0.8280
Epoch 9/15
47/47 [==============================] - 2s 44ms/step - loss: 0.3368 - accuracy: 0.8813
Epoch 10/15
47/47 [==============================] - 2s 47ms/step - loss: 0.3436 - accuracy: 0.8740
Epoch 11/15
47/47 [==============================] - 2s 36ms/step - loss: 0.3365 - accuracy: 0.8787
Epoch 12/15
47/47 [==============================] - 2s 33ms/step - loss: 0.2938 - accuracy: 0.8913
Epoch 13/15
47/47 [==============================] - 2s 33ms/step - loss: 0.3180 - accuracy: 0.8847
Epoch 14/15
47/47 [==============================] - 2s 33ms/step - loss: 0.3724 - accuracy: 0.8633
Epoch 15/15
47/47 [==============================] - 2s 33ms/step - loss: 0.2569 - accuracy: 0.9080

<keras.src.callbacks.History at 0x7e41e206a500>

# accuracy test
test_loss, test_acc = model.evaluate(test_x, test_y)

10/10 [==============================] - 1s 41ms/step - loss: 0.2665 - accuracy: 0.9033

# get max pooling layer and fully connected layer
conv_layer = model.get_layer(index = 6)
fc_layer = model.layers[8].get_weights()[0]

# Class activation map
my_map = tf.matmul(conv_layer.output, fc_layer)
CAM = tf.keras.Model(inputs = model.inputs, outputs = my_map)

test_idx = [7]
test_image = test_x[test_idx]

pred = np.argmax(model.predict(test_image), axis = 1)
predCAM = CAM.predict(test_image)

attention = predCAM[:,:,:,pred]
attention = np.abs(np.reshape(attention,(25,25)))

resized_attention = cv2.resize(attention,
                               (200*5, 200*5),
                               interpolation = cv2.INTER_CUBIC)

resized_test_x = cv2.resize(test_image.reshape(200,200),
                            (200*5, 200*5),
                            interpolation = cv2.INTER_CUBIC)

plt.figure(figsize = (6, 9))
plt.subplot(3,2,1)
plt.imshow(test_x[test_idx].reshape(200,200), 'gray')
plt.axis('off')
plt.subplot(3,2,2)
plt.imshow(attention)
plt.axis('off')
plt.subplot(3,2,3)
plt.imshow(resized_test_x, 'gray')
plt.axis('off')
plt.subplot(3,2,4)
plt.imshow(resized_attention, 'jet', alpha = 0.5)
plt.axis('off')
plt.subplot(3,2,6)
plt.imshow(resized_test_x, 'gray')
plt.imshow(resized_attention, 'jet', alpha = 0.5)
plt.axis('off')
plt.show()

1/1 [==============================] - 0s 190ms/step
1/1 [==============================] - 0s 63ms/step

4. Grad-CAM: Gradient-weighted Class Activation Maps¶

Does not require a particular architecture (as long as we can differentiate)

Uses gradients to determine weighting of each feature map

CAM

$$\sum_k \omega^c_k f_k$$

Grad-CAM

$$ReLU \left(\sum_{k} \alpha^c_k f_k \right) \quad \text{where} \quad \alpha^c_k = \frac{1}{Z} \sum_{x,y} \frac{\partial z_c}{\partial f_k(x,y)}$$

model = tf.keras.models.Sequential([
    tf.keras.layers.Conv2D(filters = 32,
                           kernel_size = (3,3),
                           activation = 'relu',
                           padding = 'SAME',
                           input_shape = (200, 200, 1)),

    tf.keras.layers.MaxPool2D((2,2)),

    tf.keras.layers.Conv2D(filters = 64,
                           kernel_size = (3,3),
                           activation = 'relu',
                           padding = 'SAME',
                           input_shape = (100, 100, 32)),

    tf.keras.layers.MaxPool2D((2,2)),

    tf.keras.layers.Conv2D(filters = 64,
                           kernel_size = (3,3),
                           activation = 'relu',
                           padding = 'SAME',
                           input_shape = (50, 50, 64)),

    tf.keras.layers.MaxPool2D((2,2)),

    tf.keras.layers.Conv2D(filters = 64,
                           kernel_size = (3,3),
                           activation = 'relu',
                           padding = 'SAME',
                           input_shape = (25, 25, 64)),

    tf.keras.layers.MaxPool2D((2,2)),

    tf.keras.layers.Flatten(),
    tf.keras.layers.Dense(units=64,activation='relu'),
    tf.keras.layers.Dense(units=6,activation='softmax')
])

model.compile(optimizer = 'adam',
              loss = 'sparse_categorical_crossentropy',
              metrics = 'accuracy')

model.fit(train_x, train_y, epochs = 15)

Epoch 1/15
47/47 [==============================] - 4s 33ms/step - loss: 1.7092 - accuracy: 0.2200
Epoch 2/15
47/47 [==============================] - 2s 32ms/step - loss: 1.1546 - accuracy: 0.5287
Epoch 3/15
47/47 [==============================] - 2s 34ms/step - loss: 0.7600 - accuracy: 0.7233
Epoch 4/15
47/47 [==============================] - 2s 33ms/step - loss: 0.5364 - accuracy: 0.8067
Epoch 5/15
47/47 [==============================] - 2s 33ms/step - loss: 0.2964 - accuracy: 0.9007
Epoch 6/15
47/47 [==============================] - 2s 32ms/step - loss: 0.2367 - accuracy: 0.9127
Epoch 7/15
47/47 [==============================] - 2s 32ms/step - loss: 0.1665 - accuracy: 0.9420
Epoch 8/15
47/47 [==============================] - 1s 32ms/step - loss: 0.1637 - accuracy: 0.9487
Epoch 9/15
47/47 [==============================] - 2s 32ms/step - loss: 0.2170 - accuracy: 0.9140
Epoch 10/15
47/47 [==============================] - 2s 32ms/step - loss: 0.1179 - accuracy: 0.9607
Epoch 11/15
47/47 [==============================] - 2s 32ms/step - loss: 0.1644 - accuracy: 0.9387
Epoch 12/15
47/47 [==============================] - 2s 33ms/step - loss: 0.1116 - accuracy: 0.9653
Epoch 13/15
47/47 [==============================] - 2s 34ms/step - loss: 0.1251 - accuracy: 0.9593
Epoch 14/15
47/47 [==============================] - 2s 33ms/step - loss: 0.4703 - accuracy: 0.8693
Epoch 15/15
47/47 [==============================] - 1s 32ms/step - loss: 0.1523 - accuracy: 0.9513

<keras.src.callbacks.History at 0x7e4195b05510>

model.summary()

Model: "sequential_1"
_________________________________________________________________
 Layer (type)                Output Shape              Param #   
=================================================================
 conv2d_4 (Conv2D)           (None, 200, 200, 32)      320       
                                                                 
 max_pooling2d_3 (MaxPoolin  (None, 100, 100, 32)      0         
 g2D)                                                            
                                                                 
 conv2d_5 (Conv2D)           (None, 100, 100, 64)      18496     
                                                                 
 max_pooling2d_4 (MaxPoolin  (None, 50, 50, 64)        0         
 g2D)                                                            
                                                                 
 conv2d_6 (Conv2D)           (None, 50, 50, 64)        36928     
                                                                 
 max_pooling2d_5 (MaxPoolin  (None, 25, 25, 64)        0         
 g2D)                                                            
                                                                 
 conv2d_7 (Conv2D)           (None, 25, 25, 64)        36928     
                                                                 
 max_pooling2d_6 (MaxPoolin  (None, 12, 12, 64)        0         
 g2D)                                                            
                                                                 
 flatten (Flatten)           (None, 9216)              0         
                                                                 
 dense_1 (Dense)             (None, 64)                589888    
                                                                 
 dense_2 (Dense)             (None, 6)                 390       
                                                                 
=================================================================
Total params: 682950 (2.61 MB)
Trainable params: 682950 (2.61 MB)
Non-trainable params: 0 (0.00 Byte)
_________________________________________________________________

test_idx = [7]
test_image = test_x[test_idx]

conv_layer = model.get_layer(index = 6)
grad_model = tf.keras.models.Model(inputs = model.inputs, outputs = [conv_layer.output, model.output])

with tf.GradientTape() as tape:
    desired_conv_layer_output, preds = grad_model(test_image)

    pred_index = tf.argmax(preds[0])
    class_channel = preds[:, pred_index]

# compute gradient via tensorflow GradientTape()
grads = tape.gradient(class_channel, desired_conv_layer_output)

pooled_grads = tf.reduce_mean(grads, axis = (0, 1, 2))

heatmap = tf.matmul(desired_conv_layer_output[0], pooled_grads[..., tf.newaxis])
heatmap = tf.squeeze(heatmap)

attention_grad = np.abs(np.reshape(heatmap,(25,25)))

resized_attention_grad = cv2.resize(attention_grad,
                                    (200*5,200*5),
                                    interpolation = cv2.INTER_CUBIC)

resized_test_x = cv2.resize(test_image.reshape(200,200),
                            (200*5, 200*5),
                            interpolation = cv2.INTER_CUBIC)

plt.figure(figsize = (6, 9))
plt.subplot(3,2,1)
plt.imshow(test_x[test_idx].reshape(200,200), 'gray')
plt.axis('off')
plt.subplot(3,2,2)
plt.imshow(attention_grad)
plt.axis('off')
plt.subplot(3,2,3)
plt.imshow(resized_test_x, 'gray')
plt.axis('off')
plt.subplot(3,2,4)
plt.imshow(resized_attention_grad, 'jet', alpha = 0.5)
plt.axis('off')
plt.subplot(3,2,6)
plt.imshow(resized_test_x, 'gray')
plt.imshow(resized_attention_grad, 'jet', alpha = 0.5)
plt.axis('off')
plt.show()

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