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BP: Fachverband Biologische Physik

BP 21: High-Throughput Data and their Analysis

BP 21.4: Vortrag

Mittwoch, 28. März 2007, 19:00–19:15, H43

Efficient dimension reduction of large-scale biomedical time-series — •Fabian Theis — MPI for Dynamics and Self-Organisation, Göttingen, Germany

Dimension reduction considers the question of removing a noise subspace from a larger multivariate signal. It is a key preprocessing step in contemporary biomedical data analysis for example of EEG or fMRI. Classically, a signal is differentiated from noise by having a higher variance, and algorithms such as principal component analysis (PCA) remove the low-variance components thereby failing to capture signals that are deteriorated by noise of similar or stronger power.

In order to perform noisy dimension reduction, either higher-order statistics of the data or additional information such as temporal structure may be used. The former methods assume i.i.d. signals, whereas the latter deal with the more realistic assumption of a multivariate `colored' (in contrast to white) stochastic process. The proposed method, denoted by colored subspace analysis (CSA), distinguishes signal from noise by nontrivial autocovariances. The goal of CSA is to find such a projection onto a signal subspace of minimal dimension. We can prove that the signal subspace is unique, and an efficient algorithm can be proposed. Its complexity is in the order of twice the order of PCA, with an optional accuracy factor. The feasibility of the algorithm is illustrated when applied to fMRI. Independent of data dimension, a task-related subspace is robustly identified. In contrast, the necessary dimension of the PCA-based signal subspace is not invariant under increasing number of captured MRI frames.