scholarly journals Feature Level-Sets: Generalizing Iso-surfaces to Multi-variate Data

2021 ◽  
Author(s):  
Jochen Jankowai ◽  
Ingrid Hotz
Keyword(s):  
Large Class ◽  
Level Sets ◽  
Data Sets ◽  
Special Cases ◽  
Tensor Data ◽  
Simple Features ◽  
Attribute Space ◽  
Feature Visualization

Iso-surfaces or level-sets provide an effective and frequently used means for feature visualization. However, they are restricted to simple features for uni-variate data. The approach does not scale when moving to multi-variate data or when considering more complex feature definitions. In this paper, we introduce the concept of traits and feature level-sets, which can be understood as a generalization of level-sets as it includes iso-surfaces, and fiber surfaces as special cases. The concept is applicable to a large class of traits defined as subsets in attribute space, which can be arbitrary combinations of points, lines, surfaces and volumes. It is implemented into a system that provides an interface to define traits in an interactive way and multiple rendering options. We demonstrate the effectiveness of the approach using multi-variate data sets of different nature, including vector and tensor data, from different application domains.

Computing Cores for Existential Rules with the Standard Chase and ASP

2020 ◽  
Author(s):  
Markus Krötzsch
Keyword(s):  
Large Class ◽  
Data Exchange ◽  
Answer Set Programming ◽  
Query Answering ◽  
Universal Model ◽  
The Core ◽  
Universal Models ◽  
General Terms ◽  
Special Cases ◽  
The Many

To reason with existential rules (a.k.a. tuple-generating dependencies), one often computes universal models. Among the many such models of different structure and cardinality, the core is arguably the “best”. Especially for finitely satisfiable theories, where the core is the unique smallest universal model, it has advantages in query answering, non-monotonic reasoning, and data exchange. Unfortunately, computing cores is difficult and not supported by most reasoners. We therefore propose ways of computing cores using practically implemented methods from rule reasoning and answer set programming. Our focus is on cases where the standard chase algorithm produces a core. We characterise this desirable situation in general terms that apply to a large class of cores, derive concrete approaches for decidable special cases, and generalise these approaches to non-monotonic extensions of existential rules.

scholarly journals Stringy canonical forms and binary geometries from associahedra, cyclohedra and generalized permutohedra

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Song He ◽  
Zhenjie Li ◽  
Prashanth Raman ◽  
Chi Zhang
Keyword(s):  
Large Class ◽  
Configuration Space ◽  
Moduli Space ◽  
Cluster Algebras ◽  
Configuration Spaces ◽  
Minkowski Sum ◽  
Canonical Forms ◽  
Infinite Class ◽  
Special Cases ◽  
Generalized Associahedra

Abstract Stringy canonical forms are a class of integrals that provide α′-deformations of the canonical form of any polytopes. For generalized associahedra of finite-type cluster algebras, there exist completely rigid stringy integrals, whose configuration spaces are the so-called binary geometries, and for classical types are associated with (generalized) scattering of particles and strings. In this paper, we propose a large class of rigid stringy canonical forms for another class of polytopes, generalized permutohedra, which also include associahedra and cyclohedra as special cases (type An and Bn generalized associahedra). Remarkably, we find that the configuration spaces of such integrals are also binary geometries, which were suspected to exist for generalized associahedra only. For any generalized permutohedron that can be written as Minkowski sum of coordinate simplices, we show that its rigid stringy integral factorizes into products of lower integrals for massless poles at finite α′, and the configuration space is binary although the u equations take a more general form than those “perfect” ones for cluster cases. Moreover, we provide an infinite class of examples obtained by degenerations of type An and Bn integrals, which have perfect u equations as well. Our results provide yet another family of generalizations of the usual string integral and moduli space, whose physical interpretations remain to be explored.

Computation of Spatial Displacements From Redundant Geometric Features

1992 ◽  
Author(s):  
Q. J. Ge ◽  
B. Ravani
Keyword(s):  
Symmetric Matrix ◽  
Automatic Generation ◽  
Geometric Features ◽  
Least Eigenvalue ◽  
Special Cases ◽  
Minimum Number ◽  
Feature Information ◽  
Spatial Displacements ◽  
Simple Features ◽  
Cubic Function

Abstract This paper follows a previous one on the computation of spatial displacements (Ravani and Ge, 1992). The first paper dealt with the problem of computing spatial displacements from a minimum number of simple features of points, lines, planes, and their combinations. The present paper deals with the same problem using a redundant set of the simple geometric features. The problem for redundant information is formulated as a least squares problem which includes all simple features. A Clifford algebra is used to unify the handling of various feature information. An algorithm for determining the best orientation is developed which involves finding the eigenvector associated with the least eigenvalue of a 4 × 4 symmetric matrix. The best translation is found to be a rational cubic function of the best orientation. Special cases are discussed which yield the best orientation in closed form. In addition, simple algorithms are provided for automatic generation of body-fixed coordinate frames from various feature information. The results have applications in robot and world model calibration for off-line programming and computer vision.

scholarly journals A New Family of Extended Lindley Models: Properties, Estimation and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2146
Author(s):  
Abdulrahman Abouammoh ◽  
Mohamed Kayid
Keyword(s):  
Power Distribution ◽  
Data Sets ◽  
Simulation Studies ◽  
Biological Engineering ◽  
Unified Approach ◽  
Right Censored Data ◽  
New Family ◽  
Special Cases ◽  
Life Distributions ◽  
And Behavior

There are many proposed life models in the literature, based on Lindley distribution. In this paper, a unified approach is used to derive a general form for these life models. The present generalization greatly simplifies the derivation of new life distributions and significantly increases the number of lifetime models available for testing and fitting life data sets for biological, engineering, and other fields of life. Several distributions based on the disparity of the underlying weights of Lindley are shown to be special cases of these forms. Some basic statistical properties and reliability functions are derived for the general forms. In addition, comparisons among various forms are investigated. Moreover, the power distribution of this generalization has also been considered. Maximum likelihood estimator for complete and right-censored data has been discussed and in simulation studies, the efficiency and behavior of it have been investigated. Finally, the proposed models have been fit to some data sets.

A Feature-Based Approach to Market Segmentation via Overlapping K-Centroids Clustering

1997 ◽  
Vol 34 (3) ◽  
pp. 370-377 ◽  
Author(s):  
Anil Chaturvedi ◽  
J. Douglas Carroll ◽  
Paul E. Green ◽  
John A. Rotondo
Keyword(s):  
Market Segmentation ◽  
Marketing Research ◽  
Large Data ◽  
Large Data Sets ◽  
Data Sets ◽  
Suggested Procedure ◽  
Overlapping Clusters ◽  
Special Cases ◽  
Feature Based ◽  
Distinct Partition

Nonhierarchical partitioning techniques are used widely in many marketing applications, particularly in the clustering of consumers, as opposed to brands. These techniques can be extremely sensitive to the presence of outliers, which might result in misinterpretations of the segments, and subsequently to inferring incorrect relationships of segments to independently defined, actionable variables. The authors propose a general approach to market segmentation based on the concept of overlapping clusters (Shepard and Arabie 1979), wherein each pattern of overlap can be interpreted as a distinct partition. Both K-means and K-medians clustering procedures are special cases of the proposed approach. The suggested procedure can handle relatively large data sets (e.g., 2000 entities), is easily programmable, and hence can be gainfully employed in marketing research.

scholarly journals Efficient Kernel Selection via Spectral Analysis

2017 ◽  
Author(s):  
Jian Li ◽  
Yong Liu ◽  
Hailun Lin ◽  
Yinliang Yue ◽  
Weiping Wang
Keyword(s):  
Spectral Measure ◽  
Fundamental Problem ◽  
Selection Criterion ◽  
Data Sets ◽  
Maximum Mean Discrepancy ◽  
Generalization Bounds ◽  
Kernel Selection ◽  
Special Cases ◽  
High Computational Efficiency ◽  
High Computational Complexity

Kernel selection is a fundamental problem of kernel methods. Existing measures for kernel selection either provide less theoretical guarantee or have high computational complexity. In this paper, we propose a novel kernel selection criterion based on a newly defined spectral measure of a kernel matrix, with sound theoretical foundation and high computational efficiency. We first show that the spectral measure can be used to derive generalization bounds for some kernel-based algorithms. By minimizing the derived generalization bounds, we propose the kernel selection criterion with spectral measure. Moreover, we demonstrate that the popular minimum graph cut and maximum mean discrepancy are two special cases of the proposed criterion. Experimental results on lots of data sets show that our proposed criterion can not only give the comparable results as the state-of-the-art criterion, but also significantly improve the efficiency.

scholarly journals tensorBF: an R package for Bayesian tensor factorization

2016 ◽  
Author(s):  
Suleiman A. Khan ◽  
Muhammad Ammad-ud-din
Keyword(s):  
Best Practices ◽  
Drug Response ◽  
R Package ◽  
Predictive Analysis ◽  
Data Sets ◽  
Tensor Factorization ◽  
Tensor Structure ◽  
Number Of Factors ◽  
Tensor Factorizations ◽  
Tensor Data

AbstractWith recent advancements in measurement technologies, many multi-way and tensor datasets have started to emerge. Exploiting the natural tensor structure in the data has been shown to be advantageous for both explorative and predictive studies in several application areas of bioinformatics and computational biology. Therefore, there has subsequently arisen a need for robust and flexible tools for effectively analyzing tensor data sets. We present the R package tensorBF, which is the first R package providing Bayesian factorization of a tensor. Our package implements a generative model that automatically identifies the number of factors needed to explain the tensor, overcoming a key limitation of traditional tensor factorizations. We also recommend best practices when using tensor factorizations for both, explorative and predictive analysis with an example application on drug response dataset. The package also implements tools related to the normalization of data, informative noise priors and visualization. Availability: The package is available at https://cran.r-project.org/package=tensorBF.

scholarly journals A map of decoy influence in human multi-alternative choice

2020 ◽  
Author(s):  
Tsvetomira Dumbalska ◽  
Vickie Li ◽  
Konstantinos Tsetsos ◽  
Christopher Summerfield
Keyword(s):  
Decision Making ◽  
Simple Model ◽  
Irrelevant Information ◽  
Incentive Compatible ◽  
Special Cases ◽  
Human Decision ◽  
Human Participants ◽  
Alternative Choice ◽  
Decoy Effects ◽  
Attribute Space

Human decisions can be biased by irrelevant information. For example, choices between two preferred alternatives can be swayed by a third option that is inferior or unavailable. Previous work has identified three classic biases, known as the attraction, similarity and compromise effects, which arise during choices between economic alternatives defined by two attributes. However, the reliability, interrelationship, and computational origin of these three biases has been controversial. Here, a large cohort of human participants made incentive-compatible choices among assets that varied in price and quality. Instead of focusing on the three classic effects, we sampled decoy stimuli exhaustively across bidimensional multi-attribute space and constructed a full map of decoy influence on choices between two otherwise preferred target items. Our analysis revealed that the decoy influence map was highly structured even beyond the three classic biases. We identified a very simple model that can fully reproduce the decoy influence map and capture its variability in individual participants. This model reveals that the three decoy effects are not distinct phenomena but are all special cases of a more general principle, by which attribute values are repulsed away from the context provided by rival options. The model helps understand why the biases are typically correlated across participants and allows us to validate a new prediction about their interrelationship. This work helps to clarify the origin of three of the most widely-studied biases in human decision-making.

On Critical Level Sets of Some two Degrees of Freedom Integrable Hamiltonian Systems

1998 ◽  
Vol 50 (1) ◽  
pp. 134-151
Author(s):  
Christine Médan
Keyword(s):  
Large Class ◽  
Hamiltonian Systems ◽  
Geodesic Flow ◽  
Level Sets ◽  
Degrees Of Freedom ◽  
Critical Level ◽  
Integrable Hamiltonian Systems ◽  
Two Degrees Of Freedom ◽  
Lagrange Top

AbstractWe prove that all Liouville's tori generic bifurcations of a large class of two degrees of freedom integrable Hamiltonian systems (the so called Jacobi–Moser– Mumford systems) are nondegenerate in the sense of Bott. Thus, for such systems, Fomenko's theory [4] can be applied (we give the example of Gel'fand–Dikii's system). We also check the Bott property for two interesting systems: the Lagrange top and the geodesic flow on an ellipsoid.

Estimation of the earthquake recurrence parameters for unequal observation periods for different magnitudes

1980 ◽  
Vol 70 (4) ◽  
pp. 1337-1346
Author(s):  
Dieter H. Weichert
Keyword(s):  
Least Squares ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Chi Square ◽  
Earthquake Parameters ◽  
Large Numbers ◽  
Special Cases ◽  
Weighting Methods ◽  
Asymptotic Forms

abstract Maximum likelihood estimation of the earthquake parameters No and β in the relation N = No exp (−βm) is extended to the case of events grouped in magnitude with each group observed over individual time periods. Asymptotic forms of the equation for β reduce to the estimators given for different special cases by Aki (1965), Utsu (1965, 1966), and Page (1968). The estimates of β are only approximately chi-square distributed. For sufficiently large numbers of events, they can be estimated from the curvature of the log-likelihood function. Sample calculations for three earthquake source zones in western Canada indicate that for well-constrained data sets, the often-used, least-squares estimation procedures lead to compatible results, but for less well-defined data sets, the effect of subjective plotting and weighting methods used for least-squares fitting leads to appreciably different parameters.

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