Department of Mathematics - Seminar on Statistics - Recovery of Timelabels in Noisy Dynamical Data

The study of dynamical data requires information on temporal labels, such as the stages in embryo development and angles in Cyro-EM molecule dynamics. However, in these applications, temporal labelling either requires huge manpower cost or is not available. In practice, the noise in the feature space makes this problem more challenging.

Our work develops spectral algorithms to recover the temporal labels from noisy data points. We first construct the graph Laplacian of the data, and then use the Fiedler vectors to recover the temporal labels. The construction and recovery steps vary on whether the dynamical system is periodic or non-periodic. Our method does not require certain monotone properties on the similarity matrix, which are commonly assumed in existing spectral seriation algorithms.

We analyze the l_infinity error of our estimators for the temporal labels and ranking, without assumptions on the eigengap. In numerical analysis, our method outperforms spectral seriation algorithms based on a similarity matrix. The performance of our algorithms is further demonstrated on  biomolecule data examples.