Package for multimodal autoencoders with Bregman divergences.

## Project description

Package for multimodal autoencoders with Bregman divergences.

## Description

This package contains an implementation of a flexible autoencoder that can take into account the noise distributions of multiple modalities. The autoencoder can be used to find a low-dimensional representation of multimodal data, taking advantage of the information that one modality provides about another.

Noise distributions are taken into account by means of Bregman divergences which correspond to particular exponential families such as Gaussian, Poisson or gamma distributions. Each modality can have its own Bregman divergence as loss function, thereby assuming a particular output noise distribution.

By default, the autoencoder network fusing multiple modalities consists of a variable number of ReLU layers that are densely connected. The number of layers and number of units per layer of the encoder and decoder networks are symmetric. Other network architectures can be easily implemented by overriding convenience methods.

## Requirements

The package is compatible with Python 2.7 and 3.x and additionally requires NumPy, Six and TensorFlow or Keras. It was tested with Python 2.7.17, Python 3.8.2, NumPy 1.18.4, Six 1.15.0, TensorFlow 2.2.0 and Keras 2.3.1.

## Installation

To install the mmae package with the TensorFlow back-end with GPU support, run:

pip install mmae[tensorflow-gpu]

To install the mmae package with the TensorFlow back-end without GPU support, run:

pip install mmae[tensorflow]

To install the mmae package with the Keras back-end, run:

pip install mmae[keras]

## Usage

The main class of this package is MultimodalAutoencoder which is implemented in the module mmae.multimodal_autoencoder. This class can be used to easily construct a multimodal autoencoder for dimensionality reduction. The main arguments for instantiation are input_shapes which is a list or dictionary of shapes for each modality, hidden_dims which is a list of the number of units per hidden layer of the encoder, and output_activations which is a list or dictionary of output activations for each modality.

The last element of hidden_dims is the dimensionality of the latent space representation. The other elements are mirrored for the decoder construction. For instance, if hidden_dims = [128, 64, 8] then the encoder will have hidden layers with 128 and 64 units and produce an 8 dimensional representation whereas the decoder will take the 8 dimensional representation, feed it into hidden layers with 64 and 128 units and produce multimodal outputs with shapes following input_shapes.

The method compile is used to set the model configuration for training. The main arguments are optimizer which is a Keras optimizer and loss which is a list or dictionary of loss functions for each modality. In addition to the standard Keras loss functions, regular Bregman divergences can be used. Current options are gaussian_divergence, gamma_divergence, bernoulli_divergence and poisson_divergence, corresponding to Gaussian, gamma, Bernoulli and Poisson noise models, respectively. Divergences corresponding to binomial and negative binomial distributions can be used by instantiating BinomialDivergence and NegativeBinomialDivergence, respectively, and passing the instance in loss. To implement other divergences, additional classes can be derived from BregmanDivergence where the abstract methods _phi and _phi_gradient need to be overridden. BregmanDivergence is implemented in the mmae.bregman_divergences module.

The following code fits a multimodal autoencoder to MNIST, where the images are treated as one modality and the number label is treated as another modality:

```
# Remove 'tensorflow.' from the next line if you use just Keras
from tensorflow.keras.datasets import mnist
from mmae.multimodal_autoencoder import MultimodalAutoencoder
# Load example data
(x_train, y_train), (x_validation, y_validation) = mnist.load_data()
# Scale pixel values to range [0, 1]
x_train = x_train.astype('float32') / 255.0
y_train = y_train.astype('float32') / 255.0
x_validation = x_validation.astype('float32') / 255.0
y_validation = y_validation.astype('float32') / 255.0
# Multimodal training data
data = [x_train, y_train]
# Multimodal validation data
validation_data = [x_validation, y_validation]
# Set network parameters
input_shapes = [x_train.shape[1:], (1,)]
# Number of units of each layer of encoder network
hidden_dims = [128, 64, 8]
# Output activation functions for each modality
output_activations = ['sigmoid', 'relu']
# Name of Keras optimizer
optimizer = 'adam'
# Loss functions corresponding to a noise model for each modality
loss = ['bernoulli_divergence', 'poisson_divergence']
# Construct autoencoder network
autoencoder = MultimodalAutoencoder(input_shapes, hidden_dims,
output_activations)
autoencoder.compile(optimizer, loss)
# Train model where input and output are the same
autoencoder.fit(data, epochs=100, batch_size=256,
validation_data=validation_data)
```

To obtain a latent representation of the training data:

`latent_data = autoencoder.encode(data)`

To decode the latent representation:

`reconstructed_data = autoencoder.decode(latent_data)`

Encoding and decoding can also be merged into the following single statement:

`reconstructed_data = autoencoder.predict(data)`

By default, the different modalities are fed directly into a densely connected fusion network. In order to pre- and post-process each modality, for instance using a convolutional neural network for the image data, the MultimodalAutoencoder methods _construct_unimodal_encoders and _construct_unimodal_decoders can be overridden. These methods add networks between the input and the fusion encoder and between the fusion decoder and the output, respectively.

## Source code

The source code of the mmae package is hosted on GitHub.

## License

Copyright (C) 2018-2020 Arno Onken

This file is part of the mmae package.

The mmae package is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

The mmae package is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, see <http://www.gnu.org/licenses/>.

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