Correlation Matrices with the Perron-Frobenius Property

2014 ◽  
Author(s):  
Phelim P. Boyle ◽  
Shui Feng ◽  
David Melkuev ◽  
Johnew Zhang
Keyword(s):  
Correlation Matrices

Sectoral Analysis of Foreign Direct Investment in India During First Generation Reform Period

2015 ◽  
Vol 4 (2) ◽  
Author(s):  
Manoj Kumar Sinha
Keyword(s):  
First Generation ◽  
Correlation Matrices ◽  
Foreign Investors ◽  
Industrial Policies ◽  
Sectoral Analysis ◽  
Industrial Sectors ◽  
Reform Period ◽  
Service Sectors ◽  
Almost All ◽  
Rank Dominance

Since 1991, India has cautiously and slowly opened almost all the sectors, except a few related to strategic importance, for foreign investors. Degree of openness of various industrial sectors for FDI has been increased to the extent of 100 percent by consistently liberalizing industrial policies of the sectors. The purpose of the paper is to study pattern and trends of sectoral distribution of FDI within the background of the first generation reforms and liberalized industrial policies during 1991-2001. The paper has used series of the dynamics and stylistic indices and statistical tools such as three level indices, index of rank dominance, and correlation matrices for explaining the pattern of FDI distribution across sectors during 1991-2001. The results show that electrical, transportation, chemical, telecommunication, and service sectors are most dominating sectors and represent almost 75 percent of total FDI received during 1991-2001. Index of rank dominance indicates distribution of FDI across the sectors is top heavy.

scholarly journals INQUIRY INTO VERTICAL MOVEMENTS OF THE EARTH‘S CRUST BASED ON SAMPLES FROM EASTERN LITHUANIA

2014 ◽  
Vol 40 (2) ◽  
pp. 58-67
Author(s):  
Ruta Puziene ◽  
Asta Anikeniene ◽  
Gitana Karsokiene
Keyword(s):  
Regression Models ◽  
Earth’S Crust ◽  
Movement Velocity ◽  
Correlation Matrices ◽  
Vertical Movements ◽  
Statistical Correlations ◽  
Horizontal Gradients ◽  
The Earth ◽  
Earth's Crust ◽  
Made In

In the research of vertical movements of the earth’s crust, examination of statistical correlations between the measured vertical movements of the earth’s crust and territorial geo-indexes is accomplished with the help of mathematical statistical analysis. Availability of the precise repeated levelling measuring data coupled with the preferred research methodology offer a chance to determine and predict recent vertical movements of the earth’s crust. For the inquiry into recent vertical movements of the earth’s crust, a Lithuanian class I vertical network levelling polygon was used. Drawing on measurements made in the polygon, vertical velocities of earth’s crust movements were calculated along the following levelling lines. For determining the relations shared by vertical movements of the earth’s crust and territorial geo-parameters, the following territory-defining parameters are accepted. Examination of the special qualities of relations shared by vertical movements of the earth’s crust and geo-parameters in the territory under research contributed to the computation of correlation matrices. Regression models are worked out taking into consideration only particular territory-defining geo-parameters, i.e. only those parameters which exhibit the following correlation coefficient value of the vertical earth’s crust movement velocity: r ≥ 0.50. A forecast of the velocities pertaining to vertical movements of the earth’s crust in the territory under examination was made with the application of regression models. Further in the process of this research, a map was compiled specifying the velocities of vertical movements of the earth’s crust in the territory. In the eastern part of this territory, the earth’s crust rises at a rate of up to 3 mm/year; while in the western part of it, the earth crust lowers at a rate of up to –1.5 mm/year. In order to pinpoint territories characterised by temperate and regular rising/lowering or intensive rising/lowering, a map of horizontal gradients of recent vertical earth crust movements in the territory enclosed by levelling polygon was compiled.

A Graphical Technique for Displaying Correlation Matrices

1997 ◽  
Vol 51 (4) ◽  
pp. 301 ◽  
Author(s):  
James A. Koziol ◽  
Joel E. Alexander ◽  
Lance O. Bauer ◽  
Samuel Kuperman ◽  
Sandra Morzorati ◽  
...  
Keyword(s):  
Correlation Matrices ◽  
Graphical Technique

scholarly journals Low-Rank Approximation of Difference between Correlation Matrices Using Inner Product

2021 ◽  
Vol 11 (10) ◽  
pp. 4582
Author(s):  
Kensuke Tanioka ◽  
Satoru Hiwa
Keyword(s):  
Dimensional Reduction ◽  
Low Rank ◽  
Inner Product ◽  
Low Rank Approximation ◽  
Correlation Matrices ◽  
Rank Matrix ◽  
Clustering Approach ◽  
Rank Approximation ◽  
The Difference ◽  
Low Rank Matrix

In the domain of functional magnetic resonance imaging (fMRI) data analysis, given two correlation matrices between regions of interest (ROIs) for the same subject, it is important to reveal relatively large differences to ensure accurate interpretation. However, clustering results based only on differences tend to be unsatisfactory and interpreting the features tends to be difficult because the differences likely suffer from noise. Therefore, to overcome these problems, we propose a new approach for dimensional reduction clustering. Methods: Our proposed dimensional reduction clustering approach consists of low-rank approximation and a clustering algorithm. The low-rank matrix, which reflects the difference, is estimated from the inner product of the difference matrix, not only from the difference. In addition, the low-rank matrix is calculated based on the majorize–minimization (MM) algorithm such that the difference is bounded within the range −1 to 1. For the clustering process, ordinal k-means is applied to the estimated low-rank matrix, which emphasizes the clustering structure. Results: Numerical simulations show that, compared with other approaches that are based only on differences, the proposed method provides superior performance in recovering the true clustering structure. Moreover, as demonstrated through a real-data example of brain activity measured via fMRI during the performance of a working memory task, the proposed method can visually provide interpretable community structures consisting of well-known brain functional networks, which can be associated with the human working memory system. Conclusions: The proposed dimensional reduction clustering approach is a very useful tool for revealing and interpreting the differences between correlation matrices, even when the true differences tend to be relatively small.

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