  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.
