MNIST dataset
The objective here is to classify the digit contained in a image.
Preparing the data
We can download the MNIST dataset using the dataset_mnist function available in the keras package.
# Downloading raw data
mnist <- dataset_mnist()We then need to extract the training and test data from the mnist object.
# Training data
train_images <- mnist$train$x
train_labels <- mnist$train$y
# Test data
test_images <- mnist$test$x
test_labels <- mnist$test$yThe code below shows that the train_images is a tensor with 3 axis, (samples, height, width). In this case, the channels axis was not necessary because the grey-scale images has only one channel.
str(train_images)## int [1:60000, 1:28, 1:28] 0 0 0 0 0 0 0 0 0 0 ...We can use slice operations to inspect specific images. Below we can see the content of the first training image.
train_images[1,,]## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## [1,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [6,] 0 0 0 0 0 0 0 0 0 0 0 0 3
## [7,] 0 0 0 0 0 0 0 0 30 36 94 154 170
## [8,] 0 0 0 0 0 0 0 49 238 253 253 253 253
## [9,] 0 0 0 0 0 0 0 18 219 253 253 253 253
## [10,] 0 0 0 0 0 0 0 0 80 156 107 253 253
## [11,] 0 0 0 0 0 0 0 0 0 14 1 154 253
## [12,] 0 0 0 0 0 0 0 0 0 0 0 139 253
## [13,] 0 0 0 0 0 0 0 0 0 0 0 11 190
## [14,] 0 0 0 0 0 0 0 0 0 0 0 0 35
## [15,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [16,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [17,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [18,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [19,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [20,] 0 0 0 0 0 0 0 0 0 0 0 0 39
## [21,] 0 0 0 0 0 0 0 0 0 0 24 114 221
## [22,] 0 0 0 0 0 0 0 0 23 66 213 253 253
## [23,] 0 0 0 0 0 0 18 171 219 253 253 253 253
## [24,] 0 0 0 0 55 172 226 253 253 253 253 244 133
## [25,] 0 0 0 0 136 253 253 253 212 135 132 16 0
## [26,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [27,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [28,] 0 0 0 0 0 0 0 0 0 0 0 0 0
## [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24]
## [1,] 0 0 0 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 0 0 0
## [5,] 0 0 0 0 0 0 0 0 0 0 0
## [6,] 18 18 18 126 136 175 26 166 255 247 127
## [7,] 253 253 253 253 253 225 172 253 242 195 64
## [8,] 253 253 253 253 251 93 82 82 56 39 0
## [9,] 253 198 182 247 241 0 0 0 0 0 0
## [10,] 205 11 0 43 154 0 0 0 0 0 0
## [11,] 90 0 0 0 0 0 0 0 0 0 0
## [12,] 190 2 0 0 0 0 0 0 0 0 0
## [13,] 253 70 0 0 0 0 0 0 0 0 0
## [14,] 241 225 160 108 1 0 0 0 0 0 0
## [15,] 81 240 253 253 119 25 0 0 0 0 0
## [16,] 0 45 186 253 253 150 27 0 0 0 0
## [17,] 0 0 16 93 252 253 187 0 0 0 0
## [18,] 0 0 0 0 249 253 249 64 0 0 0
## [19,] 0 46 130 183 253 253 207 2 0 0 0
## [20,] 148 229 253 253 253 250 182 0 0 0 0
## [21,] 253 253 253 253 201 78 0 0 0 0 0
## [22,] 253 253 198 81 2 0 0 0 0 0 0
## [23,] 195 80 9 0 0 0 0 0 0 0 0
## [24,] 11 0 0 0 0 0 0 0 0 0 0
## [25,] 0 0 0 0 0 0 0 0 0 0 0
## [26,] 0 0 0 0 0 0 0 0 0 0 0
## [27,] 0 0 0 0 0 0 0 0 0 0 0
## [28,] 0 0 0 0 0 0 0 0 0 0 0
## [,25] [,26] [,27] [,28]
## [1,] 0 0 0 0
## [2,] 0 0 0 0
## [3,] 0 0 0 0
## [4,] 0 0 0 0
## [5,] 0 0 0 0
## [6,] 0 0 0 0
## [7,] 0 0 0 0
## [8,] 0 0 0 0
## [9,] 0 0 0 0
## [10,] 0 0 0 0
## [11,] 0 0 0 0
## [12,] 0 0 0 0
## [13,] 0 0 0 0
## [14,] 0 0 0 0
## [15,] 0 0 0 0
## [16,] 0 0 0 0
## [17,] 0 0 0 0
## [18,] 0 0 0 0
## [19,] 0 0 0 0
## [20,] 0 0 0 0
## [21,] 0 0 0 0
## [22,] 0 0 0 0
## [23,] 0 0 0 0
## [24,] 0 0 0 0
## [25,] 0 0 0 0
## [26,] 0 0 0 0
## [27,] 0 0 0 0
## [28,] 0 0 0 0A plot can be made using the as.raster function.
# Plotting a digit
digit <- train_images[5,,]
plot(as.raster(digit, max = 255))
The train labels is a vector holding the digit that the respective image is representing, going from zero to nine.
table(train_labels)## train_labels
## 0 1 2 3 4 5 6 7 8 9
## 5923 6742 5958 6131 5842 5421 5918 6265 5851 5949Defining the model
In this case we are using a layer_dense which expects an input tensor of rank equal to two (sample, features) where each sample should contain 28*28=784 pixels.
network <- keras_model_sequential() %>%
layer_dense(units = 512, activation = "relu", input_shape = c(28*28)) %>%
layer_dense(units = 10, activation = "softmax")Compiling the model
network %>% compile(
optimizer = "rmsprop",
loss = "categorical_crossentropy",
metrics = c("accuracy")
)Data pre-processing
Before training, we’ll preprocess the data by reshaping it into the shape the network expects and scaling it so that all values are in the [0, 1] interval.
Previously, our training images, for instance, were stored in an array of shape (60000, 28, 28) of type integer with values in the [0, 255] interval. We transform it into a double array of shape (60000, 28 * 28) with values between 0 and 1.
# Processing the data
train_images <- array_reshape(train_images, c(60000, 28 * 28))
train_images <- train_images / 255
train_labels <- to_categorical(train_labels)
test_images <- array_reshape(test_images, c(10000, 28 * 28))
test_images <- test_images / 255
test_labels <- to_categorical(test_labels)Fitting the model
network %>% fit(train_images, train_labels, epochs = 5, batch_size = 128)Recommended exercise 1
Perform model validation (plot loss and accuracy metric) and model assessment (accuracy in the test dataset) for the model defined here.