Quantile-Quantile Embedding for Distribution Transformation and Manifold Embedding with Ability to Choose the Embedding Distribution

Abstract

We propose a new embedding method, named Quantile-Quantile Embedding (QQE), for distribution transformation and manifold embedding with the ability to choose the embedding distribution. QQE, which uses the concept of quantile-quantile plot from visual statistical tests, can transform the distribution of data to any theoretical desired distribution or empirical reference sample. Moreover, QQE gives the user a choice of embedding distribution in embedding the manifold of data into the low dimensional embedding space. It can also be used for modifying the embedding distribution of other dimensionality reduction methods, such as PCA, t-SNE, and deep metric learning, for better representation or visualization of data. We propose QQE in both unsupervised and supervised forms. QQE can also transform a distribution to either an exact reference distribution or its shape. We show that QQE allows for better discrimination of classes in some cases. Our experiments on different synthetic and image datasets show the effectiveness of the proposed embedding method.

Published in Machine Learning with Applications, Elsevier, Volume 6, Pages 100088, 2021

References in corpus (9)

• Generative Moment Matching Networks
• A Kernel Method for the Two-Sample Problem
• SoftTriple Loss: Deep Metric Learning Without Triplet Sampling
• Comparison of multivariate distributions using quantile-quantile plots and related tests
• Fisher Discriminant Triplet and Contrastive Losses for Training Siamese Networks
• Unsupervised and Supervised Principal Component Analysis: Tutorial
• Fisher and Kernel Fisher Discriminant Analysis: Tutorial
• Sampling Algorithms, from Survey Sampling to Monte Carlo Methods: Tutorial and Literature Review
• Batch-Incremental Triplet Sampling for Training Triplet Networks Using Bayesian Updating Theorem