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

Dadkhahi, Hamid, Marco F. Duarte, and Benjamin M. Marlin. "Out-of-Sample Extension for Dimensionality Reduction of Noisy Time Series." IEEE Transactions on Image Processing. 26 (2017): 5435-5446.


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 with 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.

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