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We present a numerical method to model dynamical systems from data. We use the recently introduced method Scalable Probabilistic Approximation (SPA) to project points from a Euclidean space to convex polytopes and represent these projected states of a system in new, lower-dimensional coordinates denoting their position in the polytope. We then introduce a specific nonlinear transformation to construct a model of the dynamics in the polytope and to transform back into the original state space. To overcome the potential loss of information from the projection to a lower-dimensional polytope, we use memory in the sense of the delay-embedding theorem of Takens. By construction, our method produces stable models. We illustrate the capacity of the method to reproduce even chaotic dynamics and attractors with multiple connected components on various examples.
Motivation: High-throughput proteomics techniques, such as mass spectrometry
(MS)-based approaches, produce very high-dimensional data-sets. In a clinical
setting one is often interested how MS spectra dier between patients of different
classes, for example spectra from healthy patients vs. spectra from patients
having a particular disease. Machine learning algorithms are needed to (a)
identify these discriminating features and (b) classify unknown spectra based on
this feature set. Since the acquired data is usually noisy, the algorithms should be
robust to noise and outliers, and the identied feature set should be as small as
possible.
Results: We present a new algorithm, Sparse Proteomics Analysis (SPA), based
on the theory of Compressed Sensing that allows to identify a minimal
discriminating set of features from mass spectrometry data-sets. We show how
our method performs on artificial and real-world data-sets.
Background: High-throughput proteomics techniques, such as mass spectrometry (MS)-based approaches, produce very high-dimensional data-sets. In a clinical setting one is often interested in how mass spectra differ between patients of different classes, for example spectra from healthy patients vs. spectra from patients having a particular disease. Machine learning algorithms are needed to (a) identify these discriminating features and (b) classify unknown spectra based on this feature set. Since the acquired data is usually noisy, the algorithms should be robust against noise and outliers, while the identified feature set should be as small as possible.
Results: We present a new algorithm, Sparse Proteomics Analysis (SPA),based on thet heory of compressed sensing that allows us to identify a minimal discriminating set of features from mass spectrometry data-sets. We show (1) how our method performs on artificial and real-world data-sets, (2) that its performance is competitive with standard (and widely used) algorithms for analyzing proteomics data, and (3) that it is robust against random and systematic noise. We further demonstrate the applicability of our algorithm to two previously published clinical data-sets.