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

TL;DR

Quantile-Quantile Embedding (QQE) is a novel method that transforms data distributions and offers flexible embedding distribution choices, improving data visualization and class discrimination in manifold learning.

Contribution

The paper introduces QQE, a new embedding technique that utilizes quantile-quantile plots for flexible distribution transformation and manifold embedding, applicable in both supervised and unsupervised settings.

Findings

QQE effectively transforms data to desired distributions.

QQE improves class discrimination in embeddings.

Experiments demonstrate QQE's effectiveness on synthetic and image datasets.

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.