Related papers: On random pairwise comparisons matrices and their …
This paper recalls the definition of consistency for pairwise comparison matrices and briefly presents the concept of inconsistency index in connection to other aspects of the theory of pairwise comparisons. By commenting on a recent…
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…
Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…
In this work, we study several variants of matrix reduction via Gaussian elimination that try to keep the reduced matrix sparse. The motivation comes from the growing field of topological data analysis where matrix reduction is the major…
Reparameterizing a probabilisitic system is common advice for improving the performance of a statistical algorithm like Markov chain Monte Carlo, even though in theory such reparameterizations should leave the system, and the performance of…
In this paper, we consider large-scale ranking problems where one is given a set of (possibly non-redundant) pairwise comparisons and the underlying ranking explained by those comparisons is desired. We show that stochastic gradient descent…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for…
Pairwise comparisons are used in a wide variety of decision situations where the importance of alternatives should be measured on a numerical scale. One popular method to derive the priorities is based on the right eigenvector of a…
Procedural material models have been gaining traction in many applications thanks to their flexibility, compactness, and easy editability. We explore the inverse rendering problem of procedural material parameter estimation from…
We present a robust method to find region-level correspondences between shapes, which are invariant to changes in geometry and applicable across multiple shape representations. We generate simplified shape graphs by jointly decomposing the…
The problem of completing high-dimensional matrices from a limited set of observations arises in many big data applications, especially, recommender systems. Existing matrix completion models generally follow either a memory- or a…
Mathematical analysis of the analytic hierarchy process (AHP) led to the development of a mathematical function, usually called the inconsistency index, which has the center role in measuring the inconsistency of the judgements in AHP.…
The pairwise comparisons method is a convenient tool used when the relative order of preferences among different concepts (alternatives) needs to be determined. There are several popular implementations of this method, including the…
We suggest two metrics for assessing the quality of atomistic configurations of disordered materials, both of which are based on quantifying the orientational distribution of neighbours around each atom in the configuration. The first…
We present a novel sparse modeling approach to non-rigid shape matching using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so…
Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying…
Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…
We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…
Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…