Data Preprocessing for Autoencoders

Before you can train your autoencoder to learn from data, that data needs to be properly prepared. This preparation, known as data preprocessing, involves transforming raw data into a clean and suitable format for your neural network. For autoencoders, which aim to accurately reconstruct their input, the quality and format of this input are especially significant. Just as a chef needs well-prepared ingredients, your autoencoder needs well-structured data to learn effectively and produce faithful reconstructions.

Why Preprocess Data for Autoencoders?

Feeding raw, unprepared data directly into a neural network can lead to a host of problems. It might train slowly, get stuck in suboptimal solutions, or produce unreliable results. Preprocessing helps to:

• Standardize Data: Ensures that all input features (like pixel values in an image) are on a consistent scale.
• Improve Model Performance: Well-preprocessed data often leads to faster training convergence and better model accuracy.
• Meet Network Expectations: Neural network layers often have specific requirements for the shape and type of input data.

For an autoencoder, since its target is to reproduce the input, ensuring the input is clean and well-formatted directly impacts its ability to learn this reconstruction task.

Common Preprocessing Steps for Image Data

When working with image datasets like MNIST for your autoencoder, several preprocessing steps are typically performed to prepare the data for the network. Let's walk through them.

1. Understanding Data Format and Range

First, it's important to know the characteristics of your raw data. For instance, the MNIST dataset, which is a common example for introductory image tasks, consists of grayscale images of handwritten digits.

• Pixel Values: Each image is made up of pixels, and each pixel has a value indicating its brightness. For MNIST, these are typically 8-bit integers, meaning pixel values range from 0 (representing black) to 255 (representing white).
• Data Shape: Each image has a specific height and width, 28x28 pixels for MNIST. If you have a collection of these images, say 60,000 for training, your dataset can be thought of as a large array of shape (60,000, 28, 28), where 60,000 is the number of samples, and each sample is a 28x28 matrix of pixel values.

Understanding these aspects is the first step before you can decide how to transform the data.

2. Normalization: Scaling Pixel Values

Neural networks, including autoencoders, generally perform better and train faster when the input numerical data falls within a consistent, small range. This process is called normalization.

• Why Normalize?

  • Better Gradient Flow: It helps prevent issues where some weights in the network update much faster than others simply because their corresponding input features have larger values. This leads to smoother and more stable training.
  • Faster Convergence: Optimization algorithms, which adjust the network's weights, can find good solutions more quickly when data is normalized.
  • Activation Function Compatibility: The activation function in the output layer of your decoder (often a sigmoid function for reconstructing normalized image data) expects its target values to be in the range [0, 1]. Normalizing your input to this range means your autoencoder is trying to reconstruct data in the same scale. This alignment is also beneficial when using loss functions like Mean Squared Error (MSE), as mentioned in the chapter introduction, $L(x, \hat{x}) = \frac{1}{N} \sum_{i=1}^{N} (x_i - \hat{x}_i)^2$ where both $x$ (input) and $\hat{x}$ (reconstruction) would be in the [0,1] range.

• How to Normalize for MNIST-like Images:

  • A very common method for images with pixel values from 0 to 255 is to scale them down to the [0, 1] range. You can achieve this by simply dividing every pixel value by 255.0.
  • If $x$ is an original pixel value, the normalized pixel $x_{norm}$ is calculated as: $x_{norm} = \frac{x}{255.0}$
  • Using 255.0 (a floating-point number) instead of 255 (an integer) ensures that the result of the division is also a floating-point number, which is what we typically need for neural network inputs.

3. Reshaping: Flattening Images for Dense Layers

The autoencoder architecture we'll be building in this chapter uses standard "dense" or "fully-connected" layers. These layers expect each input sample to be a flat, one-dimensional list (or vector) of numbers, not a 2D grid like an image.

• Why Reshape?
  • A 2D image (e.g., 28x28 pixels) needs to be transformed so that it can be fed into the input layer where each neuron typically corresponds to one feature in a 1D vector.
• How to Reshape:
  • This transformation is called "flattening." For a 28x28 pixel MNIST image, flattening converts it into a 1D vector with $28 \times 28 = 784$ elements.
  • So, if your dataset initially has a shape like (number of images, 28, 28), after flattening it will become (number of images, 784). Each image is now represented as a single row with 784 columns.
  • The network will then also learn to reconstruct this flattened 784-element vector.

Reshaping a 2D image matrix into a 1D vector. This flattened vector can then be fed into a dense input layer of an autoencoder.

4. Data Type Conversion

After performing arithmetic operations like normalization, it's a good habit to ensure your data is stored using an appropriate numerical data type. Most deep learning frameworks, such as TensorFlow and Keras, prefer data to be in a floating-point format for computations.

• Typically, float32 is a good choice. It offers a balance between numerical precision for the calculations involved in training a neural network and the memory required to store the data. If your original image data was stored as integers (e.g., uint8 for pixel values 0-255), the division by 255.0 in the normalization step usually handles the conversion to a float. However, explicitly setting the type (which you'll see in the coding examples) can prevent unexpected issues and ensures consistency.

Preparing Data Splits for Training and Evaluation

Although autoencoders are a form of unsupervised learning (meaning they learn from the data itself without explicit labels like 'cat' or 'dog'), it's still very important to divide your dataset. You'll typically create at least two splits: a training set and a testing set.

• Training Set: This is the bulk of your data. The autoencoder uses these examples to learn how to compress and then reconstruct the input. The model's weights are adjusted based on its performance on this set, specifically by trying to minimize the reconstruction error.
• Testing Set: This portion of the data is kept separate and is not shown to the model during the training phase. After the model is trained, you use the testing set to evaluate how well it performs on unseen data. For an autoencoder, this means checking the reconstruction quality for images it hasn't encountered before. This helps you understand if your model can generalize its learning or if it has merely "memorized" the training examples (a condition called overfitting).

It's essential that all preprocessing steps (normalization, reshaping, type conversion) are applied consistently across both the training and testing sets. This ensures that the model is evaluated on data that's in the same format as the data it was trained on.

With these preprocessing steps completed, your data is now in good shape. It's properly scaled, correctly dimensioned, and ready to be fed into your first autoencoder. In the next sections, we'll look at how to construct the model itself using TensorFlow and Keras, and then train it using this prepared data.