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

arXiv: https://arxiv.org/abs/1606.08282 · HTML: https://mlsanity.com/paper/1606.08282/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2016.

## Built on by (most cited first, 2 of 2)

- [Neural FIM for learning Fisher Information Metrics from point cloud data](https://mlsanity.com/paper/2306.06062/) (2023)
- [Density-based Isometric Mapping](https://mlsanity.com/paper/2403.02531/) (2024)

## Abstract (arXiv)

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.