A nonparametric probabilistic method to enhance PGD solutions with data-driven approach, application to the automated tape placement process

A nonparametric method assessing the error and variability margins in solutions depicted in a separated form using experimental results is illustrated in this work. The method assess the total variability of the solution including the modeling error and the truncation error when experimental results are available. The illustrated method is based on the use of the PGD separated form solutions, enriched by transforming a part of the PGD basis vectors into probabilistic one. The constructed probabilistic vectors are restricted to the physical solution’s Stiefel manifold. The result is a real-time parametric PGD solution enhanced with the solution variability and the confidence intervals.

Clustering of cancer data based on Stiefel manifold for multiple views

Background In recent years, various sequencing techniques have been used to collect biomedical omics datasets. It is usually possible to obtain multiple types of omics data from a single patient sample. Clustering of omics data plays an indispensable role in biological and medical research, and it is helpful to reveal data structures from multiple collections. Nevertheless, clustering of omics data consists of many challenges. The primary challenges in omics data analysis come from high dimension of data and small size of sample. Therefore, it is difficult to find a suitable integration method for structural analysis of multiple datasets. Results In this paper, a multi-view clustering based on Stiefel manifold method (MCSM) is proposed. The MCSM method comprises three core steps. Firstly, we established a binary optimization model for the simultaneous clustering problem. Secondly, we solved the optimization problem by linear search algorithm based on Stiefel manifold. Finally, we integrated the clustering results obtained from three omics by using k-nearest neighbor method. We applied this approach to four cancer datasets on TCGA. The result shows that our method is superior to several state-of-art methods, which depends on the hypothesis that the underlying omics cluster class is the same. Conclusion Particularly, our approach has better performance than compared approaches when the underlying clusters are inconsistent. For patients with different subtypes, both consistent and differential clusters can be identified at the same time.

Understanding the Variability in Graph Data Sets through Statistical Modeling on the Stiefel Manifold

Network analysis provides a rich framework to model complex phenomena, such as human brain connectivity. It has proven efficient to understand their natural properties and design predictive models. In this paper, we study the variability within groups of networks, i.e., the structure of connection similarities and differences across a set of networks. We propose a statistical framework to model these variations based on manifold-valued latent factors. Each network adjacency matrix is decomposed as a weighted sum of matrix patterns with rank one. Each pattern is described as a random perturbation of a dictionary element. As a hierarchical statistical model, it enables the analysis of heterogeneous populations of adjacency matrices using mixtures. Our framework can also be used to infer the weight of missing edges. We estimate the parameters of the model using an Expectation-Maximization-based algorithm. Experimenting on synthetic data, we show that the algorithm is able to accurately estimate the latent structure in both low and high dimensions. We apply our model on a large data set of functional brain connectivity matrices from the UK Biobank. Our results suggest that the proposed model accurately describes the complex variability in the data set with a small number of degrees of freedom.

Clustering of Cancer Data Based on Stiefel Manifold for Multiple Views

Background: In recent years, various sequencing techniques have been used to collect biomedical omics datasets. It is usually possible to obtain multiple types of omics data from a single patient sample. Clustering of these datasets has proved to be valuable for biological and medical research and helpful to reveal data structures from multiple collections. However, such data often have small sample size and high dimension. It is difficult to find a suitable integration method for structural analysis of multiple datasets. Results: In this paper, a multi-view clustering based on Stiefel manifold method (MCSM) is proposed. Firstly, we established a binary optimization model for the simultaneous clustering problem. Secondly, the optimization problem solved by linear search algorithm based on Stiefel manifold. Finally, we integrated the clustering results obtained from three omics by using k-nearest neighbor method. We applied this approach to four cancer datasets on TCGA. The result shows that our method is superior to several state-of-art methods, which depends on the hypothesis that the underlying omics cluster class is the same.Conclusion: Particularly, our approach has better performs when the underlying clusters are inconsistent. For patients with different subtypes, both consistent and differential clusters can be identified at the same time.