CNN autoencoder is trained on the MNIST numbers dataset for image reconstruction. Anomaly detection is carried out by calculating the Z-score. The Machine Learning framework used is Keras.

An autoencoder is a special type of neural network that is trained to copy its input to its output. An autoencoder first encodes the image into a lower dimensional latent representation, then decodes the latent representation back to an image. An autoencoder learns to compress the data while minimizing the reconstruction error.

The data set used for this project is the MNIST data set. The MNIST database (Modified National Institute of Standards and Technology database) is a large database of handwritten digits and fashion images.

The model architecture used for image reconstruction is the Convolution Neural network Autoencoder. There are two key components in an autoencoder: -Encoder: Learns how to compress the original input into a small encoding -Decoder: Learns how to restore the original data from that encoding generated by the Encoder

The encoder model consists of two convolution layers followed by a max-pooling subsampling. The 3 x 3 kernels and ReLU activations are also used. The decoder takes the tensor having the sizes of (None, 4, 4, 8) from the encoder and passes it through convolutional layers followed by up-sampling. The reconstructed tensor has the same size as that of the input image.

CNN autoencoder is trained on the MNIST data set . Model is compiled and trained with Adam optimizer, binary cross-entropy error loss, and a batch size of 60 for 50 epochs.

As mentioned above that the MNIST handwritten digits data set has been used to carry out image reconstruction, the fashion MNIST data set has been used as an anomaly in order to perform anomaly detection and calculate the accuracy of our algorithm.

The process of anomaly detection was carried out through the calculation of Z-score. Based on the reconstruction error for each image, the Z-score is calculated using the following calculations.

mean = summation of all the reconstruction errors/ number of input image samples
standard deviation = sqrt[( reconstruction error - mean) * ( reconstruction error - mean)]
Threshold (upper limit) = mean + (3 * standard deviation)
Threshold (lower limit) = mean - (3 * standard deviation)
reconstruction error = binary cross-entropy loss between the original image and reconstructed image.
If reconstruction error < Threshold (lower limit) OR reconstruction error > Threshold (upper limit) the anomaly is detected.

A normal distribution is used to plot the reconstruction error for all images. Through the calculations above, we calculate the Threshold.