Rigorous optimisation of multilinear discriminant analysis with Tucker and PARAFAC structures

Abstract Background We propose rigorously optimised supervised feature extraction methods for multilinear data based on Multilinear Discriminant Analysis (MDA) and demonstrate their usage on Electroencephalography (EEG) and simulated data. While existing MDA methods use heuristic optimisation procedures based on an ambiguous Tucker structure, we propose a rigorous approach via optimisation on the cross-product of Stiefel manifolds. We also introduce MDA methods with the PARAFAC structure. We compare the proposed approaches to existing MDA methods and unsupervised multilinear decompositions. Results We find that manifold optimisation substantially improves MDA objective functions relative to existing methods and on simulated data in general improve classification performance. However, we find similar classification performance when applied to the electroencephalography data. Furthermore, supervised approaches substantially outperform unsupervised mulitilinear methods whereas methods with the PARAFAC structure perform similarly to those with Tucker structures. Notably, despite applying the MDA procedures to raw Brain-Computer Interface data, their performances are on par with results employing ample pre-processing and they extract discriminatory patterns similar to the brain activity known to be elicited in the investigated EEG paradigms. Conclusion The proposed usage of manifold optimisation constitutes the first rigorous and monotonous optimisation approach for MDA methods and allows for MDA with the PARAFAC structure. Our results show that MDA methods applied to raw EEG data can extract discriminatory patterns when compared to traditional unsupervised multilinear feature extraction approaches, whereas the proposed PARAFAC structured MDA models provide meaningful patterns of activity

Reported barriers to evaluation in chronic care: experiences in six European countries.

INTRODUCTION: The growing movement of innovative approaches to chronic disease management in Europe has not been matched by a corresponding effort to evaluate them. This paper discusses challenges to evaluation of chronic disease management as reported by experts in six European countries. METHODS: We conducted 42 semi-structured interviews with key informants from Austria, Denmark, France, Germany, The Netherlands and Spain involved in decision-making and implementation of chronic disease management approaches. Interviews were complemented by a survey on approaches to chronic disease management in each country. Finally two project teams (France and the Netherlands) conducted in-depth case studies on various aspects of chronic care evaluation. RESULTS: We identified three common challenges to evaluation of chronic disease management approaches: (1) a lack of evaluation culture and related shortage of capacity; (2) reluctance of payers or providers to engage in evaluation and (3) practical challenges around data and the heterogeity of IT infrastructure. The ability to evaluate chronic disease management interventions is influenced by contextual and cultural factors. CONCLUSIONS: This study contributes to our understanding of some of the most common underlying barriers to chronic care evaluation by highlighting the views and experiences of stakeholders and experts in six European countries. Overcoming the cultural, political and structural barriers to evaluation should be driven by payers and providers, for example by building in incentives such as feedback on performance, aligning financial incentives with programme objectives, collectively participating in designing an appropriate framework for evaluation, and making data use and accessibility consistent with data protection policies

Removal of muscular artifacts in EEG signals: a comparison of linear decomposition methods

Abstract The most common approach to reduce muscle artifacts in electroencephalographic signals is to linearly decompose the signals in order to separate artifactual from neural sources, using one of several variants of independent component analysis (ICA). Here we compare three of the most commonly used ICA methods (extended Infomax, FastICA and TDSEP) with two other linear decomposition methods (Fourier-ICA and spatio-spectral decomposition) suitable for the extraction of oscillatory activity. We evaluate the methods’ ability to remove event-locked muscle artifacts while maintaining event-related desynchronization in data from 18 subjects who performed self-paced foot movements. We find that all five analyzed methods drastically reduce the muscle artifacts. For the three ICA methods, adequately high-pass filtering is very important. Compared to the effect of high-pass filtering, differences between the five analyzed methods were small, with extended Infomax performing best

Additional file 2 of Rigorous optimisation of multilinear discriminant analysis with Tucker and PARAFAC structures

Appendix B - non-uniqueness of the tucker structure. Proof that the Tucker structure leads to non-unique solutions. (PDF 106 kb

Additional file 1 of Rigorous optimisation of multilinear discriminant analysis with Tucker and PARAFAC structures

Appendix A - Stationary points. Proof that the stationary points of the trace of matrix ratio and ratio of deteriminants objectives are the same. (PDF 92.7 kb