Quantile-Quantile Embedding (QQE)

Paper

This is the code for the following paper:

• Benyamin Ghojogh, Fakhri Karray, Mark Crowley, "Quantile-Quantile Embedding for distribution transformation and manifold embedding with ability to choose the embedding distribution", Machine Learning with Applications, Elsevier, 2021.
• Link to paper: https://doi.org/10.1016/j.mlwa.2021.100088
• Link to arXiv version of paper: https://arxiv.org/abs/2006.11385
• Link to the Code Ocean Reproducible code of this project: https://codeocean.com/capsule/3352791/tree/v2

This code is for Quantile-Quantile Embedding (QQE).

Some manifold learning and dimensionality reduction methods, such as PCA, Isomap, and MDS, do not care about the distribution of embedding. Some other manifold learning and dimensionality reduction methods, such as SNE and t-SNE, force the distribution of embedding to a specific distribution. They do not give choice of embedding distribution to the user. QQE gives user the freedom to choose the distribution of embedding in manifold learning and dimensionality reduction. QQE can also be used for distribution transformation of data.

Using QQE for Distribution Transformation

Synthetic Data with Reference Sample

Synthetic Data with Reference CDF

Facial Image Data (Changing Distribution to Have Eye-Glasses)

Manifold Embedding

Synthetic Data

MNIST Digit Data

An Example of Progress of Algorithm

Use of QQE for Separation of Classes