Error bounds for correlation clustering

Author(s):  
Thorsten Joachims ◽  
John Hopcroft
2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Elena E. Berdysheva ◽  
Nira Dyn ◽  
Elza Farkhi ◽  
Alona Mokhov

AbstractWe introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet kernel using the newly defined weighted metric integral. We derive error bounds for these approximants. As a consequence, we prove that the sequence of the partial sums converges pointwisely in the Hausdorff metric to the values of the approximated set-valued function at its points of continuity, or to a certain set described in terms of the metric selections of the approximated multifunction at a point of discontinuity. Our error bounds are obtained with the help of the new notions of one-sided local moduli and quasi-moduli of continuity which we discuss more generally for functions with values in metric spaces.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Mario Zanfardino ◽  
Rossana Castaldo ◽  
Katia Pane ◽  
Ornella Affinito ◽  
Marco Aiello ◽  
...  

AbstractAnalysis of large-scale omics data along with biomedical images has gaining a huge interest in predicting phenotypic conditions towards personalized medicine. Multiple layers of investigations such as genomics, transcriptomics and proteomics, have led to high dimensionality and heterogeneity of data. Multi-omics data integration can provide meaningful contribution to early diagnosis and an accurate estimate of prognosis and treatment in cancer. Some multi-layer data structures have been developed to integrate multi-omics biological information, but none of these has been developed and evaluated to include radiomic data. We proposed to use MultiAssayExperiment (MAE) as an integrated data structure to combine multi-omics data facilitating the exploration of heterogeneous data. We improved the usability of the MAE, developing a Multi-omics Statistical Approaches (MuSA) tool that uses a Shiny graphical user interface, able to simplify the management and the analysis of radiogenomic datasets. The capabilities of MuSA were shown using public breast cancer datasets from TCGA-TCIA databases. MuSA architecture is modular and can be divided in Pre-processing and Downstream analysis. The pre-processing section allows data filtering and normalization. The downstream analysis section contains modules for data science such as correlation, clustering (i.e., heatmap) and feature selection methods. The results are dynamically shown in MuSA. MuSA tool provides an easy-to-use way to create, manage and analyze radiogenomic data. The application is specifically designed to guide no-programmer researchers through different computational steps. Integration analysis is implemented in a modular structure, making MuSA an easily expansible open-source software.


2019 ◽  
Vol 17 (1) ◽  
pp. 1599-1614
Author(s):  
Zhiwu Hou ◽  
Xia Jing ◽  
Lei Gao

Abstract A new error bound for the linear complementarity problem (LCP) of Σ-SDD matrices is given, which depends only on the entries of the involved matrices. Numerical examples are given to show that the new bound is better than that provided by García-Esnaola and Peña [Linear Algebra Appl., 2013, 438, 1339–1446] in some cases. Based on the obtained results, we also give an error bound for the LCP of SB-matrices. It is proved that the new bound is sharper than that provided by Dai et al. [Numer. Algor., 2012, 61, 121–139] under certain assumptions.


Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1288
Author(s):  
Silvestru Sever Dragomir

In this paper we establish some error bounds in approximating the integral by general trapezoid type rules for Fréchet differentiable functions with values in Banach spaces.


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