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Inferring Proteolytic Processes from Mass Spectrometry Time Series Data Using Degradation Graphs
(2012)

Beating the Noise
(2006)

In the framework of time series analysis with recurrence networks, we introduce a self-adaptive method that determines the elusive recurrence threshold and identifies metastable states in complex real-world time series. As initial step, we introduce a way to set the embedding parameters used to reconstruct the state space from the time series. We set them as the ones giving the maximum Shannon entropy of the diagonal line length distribution for the first simultaneous minima of recurrence rate and Shannon entropy. To identify metastable states, as well as the transitions between them, we use a soft partitioning algorithm for module finding which is specifically developed for the case in which a system shows metastability. We illustrate our method with a complex time series example. Finally, we show the robustness of our method for identifying metastable states. Our results suggest that our method is robust for identifying metastable states in complex time series, even when introducing considerable levels of noise and missing data points.

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.

Most network clustering methods share the assumption that the network can be completely decomposed into modules, that is, every node belongs to (usually exactly one) module. Forcing this constraint can lead to misidentification of modules where none exist, while the true modules are drowned out in the noise, as has been observed e.g. for protein interaction networks. We thus propose a clustering model where networks contain both a modular region consisting of nodes that can be partitioned into modules, and a transition region containing nodes that lie between or outside modules. We propose two scores based on spectral properties to determine how well a network fits this model. We then evaluate three (partially adapted) clustering algorithms from the literature on random networks that fit our model, based on the scores and comparison to the ground truth. This allows to pinpoint the types of networks for which the different algorithms perform well.