Related papers: Poset representation and similarity comparisons os…

It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular…

Cluster analysis of biological samples using gene expression measurements is a common task which aids the discovery of heterogeneous biological sub-populations having distinct mRNA profiles. Several model-based clustering algorithms have…

The nearest prototype classification is a less computationally intensive replacement for the $k$-NN method, especially when large datasets are considered. In metric spaces, centroids are often used as prototypes to represent whole clusters.…

In this article, we propose the use of partitioning and clustering methods as an alternative to Gaussian quadrature for stochastic collocation. The key idea is to use cluster centers as the nodes for collocation. In this way, we can extend…

Improving the explainability of the results from machine learning methods has become an important research goal. Here, we study the problem of making clusters more interpretable by extending a recent approach of [Davidson et al., NeurIPS…

In multi-objective decision planning and learning, much attention is paid to producing optimal solution sets that contain an optimal policy for every possible user preference profile. We argue that the step that follows, i.e, determining…

A poset can be regarded as a category in which there is at most one morphism between objects, and such that at most one of Hom(c,c') and Hom(c',c) is nonempty for c not equal to c'. If we keep in place the latter axiom but allow for more…

It has recently been argued that AI models' representations are becoming aligned as their scale and performance increase. Empirical analyses have been designed to support this idea and conjecture the possible alignment of different…

A paired comparison analysis is the simplest way to make comparative judgments between objects where objects may be goods, services or skills. For a set of problems, this technique helps to choose the most important problem to solve first…

A quantitative representation of discourse structure can be computed by measuring lexical cohesion relations among adjacent blocks of text. These representations have been proposed to deal with sub-topic text segmentation. In a parallel…

A good deal of science and technology concepts and methods rely on comparing and relating entities in quantitative terms. Among the several possible approaches, similarity indices allow some interesting features, especially the ability to…

Network clustering requires making many decisions manually, such as the number of groups and a statistical model to be used. Even after filtering using an information criterion or regularizing with a nonparametric framework, we are commonly…

Background: Pose estimation of rigid objects is a practical challenge in optical metrology and computer vision. This paper presents a novel stochastic-geometrical modeling framework for object pose estimation based on observing multiple…

A variety of possible extensions of mappings between posets to their Dedekind order completion is presented. One of such extensions has recently been used for solving large classes of nonlinear systems of partial differential equations with…

In this paper, the classification task for a family of sets representing the realisation of some random set models is solved. Both unsupervised and supervised classification methods are utilised using the similarity measure between two…

Multi-choice reading comprehension is a challenging task, which involves the matching between a passage and a question-answer pair. This paper proposes a new co-matching approach to this problem, which jointly models whether a passage can…

Recently, some contrastive learning methods have been proposed to simultaneously learn representations and clustering assignments, achieving significant improvements. However, these methods do not take the category information and…

Almost all representations considered in computable analysis are partial. We provide arguments in favor of total representations (by elements of the Baire space). Total representations make the well known analogy between numberings and…

Due to the availability of references of research papers and the rich information contained in papers, various citation analysis approaches have been proposed to identify similar documents for scholar recommendation. Despite of the success…

Posets are discrete mathematical structures which are ubiquitous in a broad range of data analysis and machine learning applications. Research connecting posets to the data science domain has been ongoing for many years. In this paper, a…