Out-of-Sample Extension for Dimensionality Reduction of Noisy Time Series

TL;DR

This paper introduces a novel out-of-sample extension method for manifold learning that incorporates temporal information to improve robustness and accuracy in noisy time series data, outperforming existing approaches.

Contribution

The paper presents the first out-of-sample extension framework for manifold embeddings that explicitly leverages timing information, enhancing robustness to noise in sequential data.

Findings

Improved robustness and accuracy in noisy image data embeddings.

Superior performance in eye-gaze estimation tasks.

Effective handling of artifacts in sequential data.

Abstract

This paper proposes an out-of-sample extension framework for a global manifold learning algorithm (Isomap) that uses temporal information in out-of-sample points in order to make the embedding more robust to noise and artifacts. Given a set of noise-free training data and its embedding, the proposed framework extends the embedding for a noisy time series. This is achieved by adding a spatio-temporal compactness term to the optimization objective of the embedding. To the best of our knowledge, this is the first method for out-of-sample extension of manifold embeddings that leverages timing information available for the extension set. Experimental results demonstrate that our out-of-sample extension algorithm renders a more robust and accurate embedding of sequentially ordered image data in the presence of various noise and artifacts when compared to other timing-aware embeddings. Additionally, we show that an out-of-sample extension framework based on the proposed algorithm outperforms the state of the art in eye-gaze estimation.