The Influence of Initial Vector Selection on Tridiagonal Matrix Enhanced Multivariance Products Representation

2014 ◽  
Author(s):  
Cosar Gozukirmizi ◽  
Metin Demiralp
Keyword(s):  
Tridiagonal Matrix ◽  
Initial Vector

Automatic construction of academic profile: A case of information science domain

2021 ◽  
pp. 016555152199804
Author(s):  
Qian Geng ◽  
Ziang Chuai ◽  
Jian Jin
Keyword(s):  
Information Science ◽  
Binary Classification ◽  
Learning To Rank ◽  
Semantic Distance ◽  
Background Information ◽  
Training Dataset ◽  
Initial Vector ◽  
Specific Domain ◽  
Adaboost Algorithm ◽  
Domain Specific

To provide junior researchers with domain-specific concepts efficiently, an automatic approach for academic profiling is needed. First, to obtain personal records of a given scholar, typical supervised approaches often utilise structured data like infobox in Wikipedia as training dataset, but it may lead to a severe mis-labelling problem when they are utilised to train a model directly. To address this problem, a new relation embedding method is proposed for fine-grained entity typing, in which the initial vector of entities and a new penalty scheme are considered, based on the semantic distance of entities and relations. Also, to highlight critical concepts relevant to renowned scholars, scholars’ selective bibliographies which contain massive academic terms are analysed by a newly proposed extraction method based on logistic regression, AdaBoost algorithm and learning-to-rank techniques. It bridges the gap that conventional supervised methods only return binary classification results and fail to help researchers understand the relative importance of selected concepts. Categories of experiments on academic profiling and corresponding benchmark datasets demonstrate that proposed approaches outperform existing methods notably. The proposed techniques provide an automatic way for junior researchers to obtain organised knowledge in a specific domain, including scholars’ background information and domain-specific concepts.

scholarly journals A note on the eigenvalue free intervals of some classes of signed threshold graphs

2019 ◽  
Vol 7 (1) ◽  
pp. 218-225
Author(s):  
Milica Anđelić ◽  
Tamara Koledin ◽  
Zoran Stanić
Keyword(s):  
Tridiagonal Matrix ◽  
Constant Sign ◽  
Equitable Partition ◽  
Elementary Matrix ◽  
Matrix Operations ◽  
Threshold Graphs ◽  
The Matrix ◽  
Threshold Graph

Abstract We consider a particular class of signed threshold graphs and their eigenvalues. If Ġ is such a threshold graph and Q(Ġ ) is a quotient matrix that arises from the equitable partition of Ġ , then we use a sequence of elementary matrix operations to prove that the matrix Q(Ġ ) – xI (x ∈ ℝ) is row equivalent to a tridiagonal matrix whose determinant is, under certain conditions, of the constant sign. In this way we determine certain intervals in which Ġ has no eigenvalues.

scholarly journals Alternative proofs of some formulas for two tridiagonal determinants

2018 ◽  
Vol 10 (2) ◽  
pp. 287-297 ◽  
Author(s):  
Feng Qi ◽  
Ai-Qi Liu
Keyword(s):  
Chebyshev Polynomials ◽  
Tridiagonal Matrix ◽  
Fibonacci Polynomials ◽  
Detailed Proof ◽  
Delannoy Numbers ◽  
Appl Math ◽  
Math Phys

Abstract In the paper, the authors provide five alternative proofs of two formulas for a tridiagonal determinant, supply a detailed proof of the inverse of the corresponding tridiagonal matrix, and provide a proof for a formula of another tridiagonal determinant. This is a companion of the paper [F. Qi, V. Čerňanová,and Y. S. Semenov, Some tridiagonal determinants related to central Delannoy numbers, the Chebyshev polynomials, and the Fibonacci polynomials, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 81 (2019), in press.

On the Matrix With Elements 1/(r+s-1)

1974 ◽  
Vol 17 (2) ◽  
pp. 297-298 ◽  
Author(s):  
W. W. Sawyer
Keyword(s):  
Tridiagonal Matrix ◽  
The Matrix ◽  
Eigenvectors And Eigenvalues

A standard example of a matrix for which the computation of eigenvectors and eigenvalues is very awkward is the matrix A with ars=1/(r+s—1), 1≤r≤n, 1 ≤s≤n. It is therefore of interest that A commutes with a tridiagonal matrix.

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