scholarly journals Principal Graphs and Manifolds

2010 ◽  
pp. 28-59 ◽  
Author(s):  
Alexander N. Gorban ◽  
Andrei Y. Zinovyev
Keyword(s):  
Principal Component ◽  
Approximation Problem ◽  
Graph Grammar ◽  
Multidimensional Data ◽  
Data Set ◽  
Expectation Maximisation ◽  
The Family ◽  
Distance Approximation ◽  
Principal Points ◽  
Multidimensional Data Set

In many physical, statistical, biological and other investigations it is desirable to approximate a system of points by objects of lower dimension and/or complexity. For this purpose, Karl Pearson invented principal component analysis in 1901 and found ‘lines and planes of closest fit to system of points’. The famous k-means algorithm solves the approximation problem too, but by finite sets instead of lines and planes. This chapter gives a brief practical introduction into the methods of construction of general principal objects (i.e., objects embedded in the ‘middle’ of the multidimensional data set). As a basis, the unifying framework of mean squared distance approximation of finite datasets is selected. Principal graphs and manifolds are constructed as generalisations of principal components and k-means principal points. For this purpose, the family of expectation/maximisation algorithms with nearest generalisations is presented. Construction of principal graphs with controlled complexity is based on the graph grammar approach.

scholarly journals Clustering algorithms subjected to K-mean and gaussian mixture model on multidimensional data set

2019 ◽  
Vol 7 (2) ◽  
pp. 448 ◽  
Author(s):  
Saadaldeen Rashid Ahmed Ahmed ◽  
Israa Al Barazanchi ◽  
Zahraa A. Jaaz ◽  
Haider Rasheed Abdulshaheed
Keyword(s):  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Clustering Algorithms ◽  
Gaussian Mixture ◽  
Multidimensional Data ◽  
Data Set ◽  
Multidimensional Data Set

scholarly journals THE IMPACT OF REAL ESTATE INVESTMENTS ON THE PERFORMANCE OF THE ENTITIES LISTED AT THE BVB

2021 ◽  
Vol 30 (30 (1)) ◽  
pp. 177-186
Author(s):  
Silviu Cornel Virgil Chiriac
Keyword(s):  
Principal Component Analysis ◽  
Real Estate ◽  
Financial Performance ◽  
Descriptive Analysis ◽  
Composite Index ◽  
Principal Component ◽  
Component Analysis ◽  
Multidimensional Data ◽  
Data Set ◽  
The Impact

The current paper is part of a wider study which aims at identifying the determining factors of the performances of the entities in the real estate field and the setting up of a composite index of the companies’ performances based on a sample of 29 companies listed at the BVB Bucharest (Bucharest Stock Exchange) in the year 2019 using one of the multidimensional data analysis techniques, the principal component analysis. The descriptive analysis, the principal component analysis for setting up the composite index of the companies performances were applied within the study in order to highlight the most important companies from the point of view of the financial performance. The descriptive analysis of the data set highlights the overview within the companies selected for analysis. The study aims at building a synthetic indicator that will show the financial performance of the companies selected based on 9 financial indicators using the principal component analysis PCA. The 9 indicators considered for the analysis were selected based on specialised articles and they are: ROA – return on assets, which reflect the company’s capacity of using its assets productively, ROE – return on equity, which measures the efficiency of use of the stockholders’ capitals, rotation of total assets, general liquidity ratio, general solvency ratio, general dent-to-equity level, net profit margin, gross return of portfolio.

scholarly journals 3D Visualization of Sound Fields Perceived by an Acoustic Camera

2015 ◽  
Vol 15 (7) ◽  
pp. 45-57
Author(s):  
Nevena Popova ◽  
Georgi Shishkov ◽  
Petia Koprinkova-Hristova ◽  
Kiril Alexiev
Keyword(s):  
3D Visualization ◽  
Multidimensional Data ◽  
Sound Waves ◽  
Signal Processing Algorithm ◽  
Data Set ◽  
3 Dimensional ◽  
Sound Fields ◽  
Neuro Fuzzy ◽  
Real Time Visualization ◽  
Multidimensional Data Set

Abstract The paper summarizes the application results of a recently proposed neuro-fuzzy algorithm for multi-dimensional data clustering to 3-Dimensional (3D) visualization of dynamically perceived sound waves recorded by an acoustic camera. The main focus in the present work is on the developed signal processing algorithm adapted to the specificity of multidimensional data set recorded by the acoustic camera, as well as on the created software package for real-time visualization of the “observed” sound waves propagation.

scholarly journals A cognitive model for managing the national innovation system parameters based on international comparisons (the case of the EU countries)

2019 ◽  
Vol 17 (4) ◽  
pp. 153-162
Author(s):  
Igor Khanin ◽  
Gennadiy Shevchenko ◽  
Vladimir Bilozubenko ◽  
Maxim Korneyev
Keyword(s):  
Feature Vector ◽  
Cognitive Model ◽  
International Comparisons ◽  
Innovation System ◽  
Multidimensional Data ◽  
Data Set ◽  
Eu Countries ◽  
Global Innovation ◽  
Multidimensional Data Set ◽  
The Eu

To carry out a comparative analysis of the EU countries’ national innovation systems (NIS), a feature vector has been compiled, covering three modules, namely, science, education, and innovation. The feature vector is a valid multidimensional data set of sixteen official statistics indices and two sub-indices of the Global Innovation Index. The development of a cognitive model for managing the NIS parameters required a preliminary three-stage empirical study to determine its elements. In the first stage, cluster analysis was performed (the k-means, metric – Euclidean distance algorithm was used). As a result, the EU countries were divided into four clusters (following multidimensional scaling estimates). In the second stage, a classification analysis (using decision trees) was carried out, which allowed determining three parameters that distinguish clusters (or classes) optimally. These parameters are recognized as important ones in terms of positioning the countries in the general ranking; that is, they can be considered as a priority for the NIS development and improving the countries’ positions in international comparisons. In the third stage, based on the authors’ approach, the significance (information content) of each key parameter is estimated. As a result, a cognitive model was compiled, taking into account the parameter significance. The model can be used in managing the NIS parameters, seeking to increase the system performance and improve the international position of a specific country. The model can also be used by partner countries, for example, Ukraine, as it demonstrates the landscape of EU innovative development and outlines the directions for priority development of NIS towards the European progress.

scholarly journals WEB APPLICATION FOR LARGE-SCALE MULTIDIMENSIONAL DATA VISUALIZATION

2011 ◽  
Vol 16 (1) ◽  
pp. 273-285 ◽  
Author(s):  
Gintautas Dzemyda ◽  
Virginijus Marcinkevičius ◽  
Viktor Medvedev
Keyword(s):  
Data Mining ◽  
Data Visualization ◽  
Web Application ◽  
Large Scale ◽  
Visual Presentation ◽  
Multidimensional Data ◽  
Data Sets ◽  
Data Set ◽  
Multidimensional Data Visualization ◽  
Multidimensional Data Set

In this paper, we present an approach of the web application (as a service) for data mining oriented to the multidimensional data visualization. This paper focuses on visualization methods as a tool for the visual presentation of large-scale multidimensional data sets. The proposed implementation of such a web application obtains a multidimensional data set and as a result produces a visualization of this data set. It also supports different configuration parameters of the data mining methods used. Parallel computation has been used in the proposed implementation to run the algorithms simultaneously on different computers.

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