DCCA: Deep Canonical Correlation Analysis

This is an implementation of Deep Canonical Correlation Analysis (DCCA or Deep CCA) in Python. It needs Theano and Keras libraries to be installed.

DCCA is a non-linear version of CCA which uses neural networks as the mapping functions instead of linear transformers. DCCA is originally proposed in the following paper:

Galen Andrew, Raman Arora, Jeff Bilmes, Karen Livescu, "Deep Canonical Correlation Analysis.", ICML, 2013.

It uses the Keras library with the Theano backend, and does not work on the Tensorflow backend. Because the loss function of the network is written with Theano. The base modeling network can easily get substituted with a more efficient and powerful network like CNN.

Most of the configuration and parameters are set based on the following paper:

Weiran Wang, Raman Arora, Karen Livescu, and Jeff Bilmes. "On Deep Multi-View Representation Learning.", ICML, 2015.

Dataset

The model is evaluated on a noisy version of MNIST dataset. I built the dataset exactly like the way it is introduced in the paper. The train/validation/test split is the original split of MNIST.

The dataset was large and could not get uploaded on GitHub. So it is uploaded on another server. The first time that the code gets executed, the dataset gets downloaded automatically by the code. It will get saved under the datasets folder of user's Keras folder (normally under [Home Folder]/.keras/datasets/).

Differences with the original paper

The following are the differences between my implementation and the original paper (they are small):

• I used RMSProp (an adaptive version of gradient descent) instead of GD with momentum. It was so much faster in converging.
• Instead of a non-saturating version of sigmoid, I just used the standard sigmoid as the activation functions. Standard sigmoid is used in the MATLAB implementation too. It should not affect the performance significantly. However, if it is needed, it can get substituted by another non-saturating activation function like ReLU.
• Pre-training is not done in this implementation. However, it is not clear how much it can be useful.

Other Implementations

The following are the other implementations of DCCA in MATLAB and C++ from which I got help for the implementation. These codes are written by the authors of the original paper:

• C++ implementation from Galen Andrew's website (https://homes.cs.washington.edu/~galen/)

• MATLAB implementation from Weiran Wang's website (http://ttic.uchicago.edu/~wwang5/dccae.html)