Autoencoders
An Autoencoder is a type of artificial neural network used for unsupervised learning of efficient codings of input data. The goal of an autoencoder is to learn a compressed representation (encoding) for a set of data, typically for dimensionality reduction, feature learning, or data denoising. It does this by training the network to ignore insignificant data (“noise”). Autoencoders are composed of two main parts: an encoder and a decoder. The encoder compresses the input into a latent-space representation, and the decoder reconstructs the input data from this representation.
The architecture is split into two parts:
- Encoder: The encoder transforms the input data \mathbf{x} into a lower-dimensional representation \mathbf{z}, also known as the latent space or bottleneck layer. This is achieved through one or more layers of neurons with activation functions that introduce non-linearity, such as ReLU or sigmoid functions.
\mathbf{z} = f_{\text{encoder}}(\mathbf{x}) = \sigma(\mathbf{W}_e \mathbf{x} + \mathbf{b}_e)
where:
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\mathbf{W}_e and \mathbf{b}_e are the weights and biases of the encoder.
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\sigma is the activation function.
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Decoder: The decoder aims to reconstruct the original input data \mathbf{x} from the encoded representation \mathbf{z}. It mirrors the encoder’s architecture but in reverse, expanding the data back to the original input dimensions.
\mathbf{\hat{x}} = f_{\text{decoder}}(\mathbf{z}) = \sigma(\mathbf{W}_d \mathbf{z} + \mathbf{b}_d)
where:
- \mathbf{W}_d and \mathbf{b}_d are the weights and biases of the decoder.
- \mathbf{\hat{x}} is the reconstructed input.
Autoencoders are a fundamental tool in the field of unsupervised learning, enabling the discovery of efficient data representations. They serve as the building blocks for more advanced models and have wide-ranging applications across different domains. By learning to compress and reconstruct data, autoencoders facilitate tasks like dimensionality reduction, feature extraction, anomaly detection, and generative modeling, contributing significantly to advancements in machine learning and artificial intelligence.
Some use case are the following:
- Image Compression: Reducing image sizes by encoding them into lower-dimensional representations without significant loss of quality.
- Recommender Systems: Learning user and item representations for personalized recommendations.
- Biomedical Signal Processing: Analyzing ECG or EEG signals for patterns indicative of health conditions.
- Fraud Detection: Identifying unusual transaction patterns by detecting deviations from learned normal behavior.
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