Detecting Features from Confusion Matrices using Generalized Formal Concept Analysis

We claim that the confusion matrices of multiclass problems can be analyzed by means of a generalization of Formal Concept Analysis to obtain symbolic information about the feature sets of the underlying classification task.We prove our claims by analyzing the confusion matrices of human speech perception experiments and comparing our results to those elicited by experts.This work has been supported by Spanish Government-Comisión Interministerial de Ciencia y Tecnología TEC2008-02473/TEC y TEC2008-06382/TEC.Publicad

Comparison of four clinical risk scores in comatose patients after out-of-hospital cardiac arrest.

BACKGROUND AND AIMS Several different scoring systems for early risk stratification after out-of-hospital cardiac arrest have been developed, but few have been validated in large datasets. The aim of the present study was to compare the well-validated Out-of-hospital Cardiac Arrest (OHCA) and Cardiac Arrest Hospital Prognosis (CAHP)-scores to the less complex MIRACLE2- and Target Temperature Management (TTM)-scores. METHODS This was a post-hoc analysis of the Targeted Hypothermia versus Targeted Normothermia after Out-of-Hospital Cardiac Arrest (TTM2) trial. Missing data were handled by multiple imputation. The primary outcome was discriminatory performance assessed as the area under the receiver operating characteristics-curve (AUROC), with the outcome of interest being poor functional outcome or death (modified Rankin Scale 4-6) at 6 months after OHCA. RESULTS Data on functional outcome at 6 months were available for 1829 cases, which constituted the study population. The pooled AUROC for the MIRACLE2-score was 0.810 (95% CI 0.790 - 0.828), 0.835 (95% CI 0.816 - 0.852) for the TTM-score, 0.820 (95% CI 0.800 - 0.839) for the CAHP-score and 0.770 (95% CI 0.748 - 0.791) for the OHCA-score. At the cut-offs needed to achieve specificities >95%, sensitivities were <40 % for all four scoring systems. CONCLUSIONS The TTM-, MIRACLE2- and CAHP-scores are all capable of providing objective risk estimates accurate enough to be used as part of a holistic patient assessment after OHCA of a suspected cardiac origin. Due to its simplicity, the MIRACLE2-score could be a practical solution for both clinical application and risk stratification within trials

Quantitative Concept Analysis

Formal Concept Analysis (FCA) begins from a context, given as a binary relation between some objects and some attributes, and derives a lattice of concepts, where each concept is given as a set of objects and a set of attributes, such that the first set consists of all objects that satisfy all attributes in the second, and vice versa. Many applications, though, provide contexts with quantitative information, telling not just whether an object satisfies an attribute, but also quantifying this satisfaction. Contexts in this form arise as rating matrices in recommender systems, as occurrence matrices in text analysis, as pixel intensity matrices in digital image processing, etc. Such applications have attracted a lot of attention, and several numeric extensions of FCA have been proposed. We propose the framework of proximity sets (proxets), which subsume partially ordered sets (posets) as well as metric spaces. One feature of this approach is that it extracts from quantified contexts quantified concepts, and thus allows full use of the available information. Another feature is that the categorical approach allows analyzing any universal properties that the classical FCA and the new versions may have, and thus provides structural guidance for aligning and combining the approaches.Comment: 16 pages, 3 figures, ICFCA 201

Activating Generalized Fuzzy Implications from Galois Connections

This paper deals with the relation between fuzzy implications and Galois connections, trying to raise the awareness that the fuzzy implications are indispensable to generalise Formal Concept Analysis. The concrete goal of the paper is to make evident that Galois connections, which are at the heart of some of the generalizations of Formal Concept Analysis, can be interpreted as fuzzy incidents. Thus knowledge processing, discovery, exploration and visualization as well as data mining are new research areas for fuzzy implications as they are areas where Formal Concept Analysis has a niche.F.J. Valverde-Albacete—was partially supported by EU FP7 project LiMoSINe, (contract 288024). C. Peláez-Moreno—was partially supported by the Spanish Government-CICYT project 2011-268007/TEC.Publicad

Formalized Conceptual Spaces with a Geometric Representation of Correlations

The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a similarity space and concepts are represented by convex regions in this space. After pointing out a problem with the convexity requirement, we propose a formalization of conceptual spaces based on fuzzy star-shaped sets. Our formalization uses a parametric definition of concepts and extends the original framework by adding means to represent correlations between different domains in a geometric way. Moreover, we define various operations for our formalization, both for creating new concepts from old ones and for measuring relations between concepts. We present an illustrative toy-example and sketch a research project on concept formation that is based on both our formalization and its implementation.Comment: Published in the edited volume "Conceptual Spaces: Elaborations and Applications". arXiv admin note: text overlap with arXiv:1706.06366, arXiv:1707.02292, arXiv:1707.0516

Generalized Matrix Factorizations as a Unifying Framework for Pattern Set Mining: Complexity Beyond Blocks

Abstract. Matrix factorizations are a popular tool to mine regularities from data. There are many ways to interpret the factorizations, but one particularly suited for data mining utilizes the fact that a matrix product can be interpreted as a sum of rank-1 matrices. Then the factorization of a matrix becomes the task of finding a small number of rank-1 matrices, sum of which is a good representation of the original matrix. Seen this way, it becomes obvious that many problems in data mining can be expressed as matrix factorizations with correct definitions of what a rank-1 matrix and a sum of rank-1 matrices mean. This paper develops a unified theory, based on generalized outer product operators, that encompasses many pattern set mining tasks. The focus is on the computational aspects of the theory and studying the computational complexity and approximability of many problems related to generalized matrix factorizations. The results immediately apply to a large number of data mining problems, and hopefully allow generalizing future results and algorithms, as well.

Diffusion and perfusion weighted magnetic resonance imaging for tumor volume definition in radiotherapy of brain tumors

Abstract Accurate target volume delineation is crucial for the radiotherapy of tumors. Diffusion and perfusion magnetic resonance imaging (MRI) can provide functional information about brain tumors, and they are able to detect tumor volume and physiological changes beyond the lesions shown on conventional MRI. This review examines recent studies that utilized diffusion and perfusion MRI for tumor volume definition in radiotherapy of brain tumors, and it presents the opportunities and challenges in the integration of multimodal functional MRI into clinical practice. The results indicate that specialized and robust post-processing algorithms and tools are needed for the precise alignment of targets on the images, and comprehensive validations with more clinical data are important for the improvement of the correlation between histopathologic results and MRI parameter images

Biomarkers of brain injury after cardiac arrest; a statistical analysis plan from the TTM2 trial biobank investigators

Background: Several biochemical markers in blood correlate with the magnitude of brain injury and may be used to predict neurological outcome after cardiac arrest. We present a protocol for the evaluation of prognostic accuracy of brain injury markers after cardiac arrest. The aim is to define the best predictive marker and to establish clinically useful cut-off levels for routine implementation. Methods: Prospective international multicenter trial within the Targeted Hypothermia versus Targeted Normothermia after Out-of-Hospital Cardiac Arrest (TTM2) trial in collaboration with Roche Diagnostics International AG. Samples were collected 0, 24, 48, and 72 hours after randomisation (serum) and 0 and 48 hours after randomisation (plasma), and pre-analytically processed at each site before storage in a central biobank. Routine markers neuron-specific enolase (NSE) and S100B, and neurofilament light, total-tau and glial fibrillary acidic protein will be batch analysed using novel Elecsys® electrochemiluminescence immunoassays on a Cobas e601 instrument. Results: Statistical analysis will be reported according to the Standards for Reporting Diagnostic accuracy studies (STARD) and will include comparisons for prediction of good versus poor functional outcome at six months post-arrest, by modified Rankin Scale (0–3 vs. 4–6), using logistic regression models and receiver operating characteristics curves, evaluation of mortality at six months according to biomarker levels and establishment of cut-off values for prediction of poor neurological outcome at 95–100% specificities. Conclusions: This prospective trial may establish a standard methodology and clinically appropriate cut-off levels for the optimal biomarker of brain injury which predicts poor neurological outcome after cardiac arrest