Graph Embedding with Data Uncertainty

TL;DR

This paper introduces a novel graph embedding method that incorporates data uncertainty by modeling data points as probability distributions, improving the robustness of low-dimensional embeddings in the presence of measurement artifacts.

Contribution

It reformulates graph embedding to account for data uncertainty using Gaussian distributions and proposes two schemes for modeling this uncertainty in supervised and unsupervised settings.

Findings

Enhanced embedding robustness to measurement artifacts

Unified framework for distribution-based graph embedding

Improved performance in uncertain data scenarios

Abstract

spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. The main aim is to learn a meaningful low dimensional embedding of the data. However, most subspace learning methods do not take into consideration possible measurement inaccuracies or artifacts that can lead to data with high uncertainty. Thus, learning directly from raw data can be misleading and can negatively impact the accuracy. In this paper, we propose to model artifacts in training data using probability distributions; each data point is represented by a Gaussian distribution centered at the original data point and having a variance modeling its uncertainty. We reformulate the Graph Embedding framework to make it suitable for learning from distributions and we study as special cases the Linear Discriminant Analysis and the Marginal Fisher Analysis techniques. Furthermore, we propose two schemes for modeling data uncertainty based on pair-wise distances in an unsupervised and a supervised contexts.