scholarly journals The experimental study of the effectiveness of Kohonen maps and autoassociative neural networks in the qualitative analysis of multidimensional data by the example of real data describing coal susceptibility to fluidal gasification

2020 ◽  
Vol 32 (18) ◽  
pp. 15221-15235 ◽  
Author(s):  
Dariusz Jamróz
Keyword(s):  
Neural Networks ◽  
Qualitative Analysis ◽  
Dimensional Space ◽  
Real Data ◽  
Multidimensional Data ◽  
Multidimensional Space ◽  
Specific Data ◽  
Kohonen Maps ◽  
Multidimensional Visualization ◽  
Autoassociative Neural Networks

Abstract The qualitative analysis of multidimensional data using their visualization allows to observe some characteristics of data in a way which is the most natural for a human, through the sense of sight. Thanks to such an approach, some characteristics of the analyzed data are simply visible. This allows to avoid using often complex algorithms allowing to examine specific data properties. Visualization of multidimensional data consists in using the representation transforming a multidimensional space into a two-dimensional space representing a computer screen. The important information which can be obtained in this way is the possibility to separate points belonging to different classes in the multidimensional space. Such information can be directly obtained if images of points belonging to different classes occupy other areas of the picture presenting these data. The paper presents the effectiveness of the qualitative analysis of multidimensional data conducted in this way through their visualization with the application of Kohonen maps and autoassociative neural networks. The obtained results were compared with results obtained using the perspective-based observational tunnels method, PCA, multidimensional scaling and relevance maps. Effectiveness tests of the above methods were performed using real seven-dimensional data describing coal samples in terms of their susceptibility to fluidal gasification. The methods’ effectiveness was compared using the criterion for the readability of the multidimensional visualization results, introduced in earlier papers.

scholarly journals The Use of the Visualisation of Multidimensional Data Using PCA to Evaluate Possibilities of the Division of Coal Samples Space Due to their Suitability for Fluidised Gasification

2016 ◽  
Vol 61 (3) ◽  
pp. 523-535
Author(s):  
Dariusz Jamróz ◽  
Tomasz Niedoba ◽  
Agnieszka Surowiak ◽  
Tadeusz Tumidajski
Keyword(s):  
Dimensional Space ◽  
Principal Component ◽  
Multidimensional Data ◽  
Multidimensional Space ◽  
Data Visualisation ◽  
Gasification Process ◽  
Pca Method ◽  
Optimal Subspace ◽  
Natural Way

AbstractMethods serving to visualise multidimensional data through the transformation of multidimensional space into two-dimensional space, enable to present the multidimensional data on the computer screen. Thanks to this, qualitative analysis of this data can be performed in the most natural way for humans, through the sense of sight. An example of such a method of multidimensional data visualisation is PCA (principal component analysis) method. This method was used in this work to present and analyse a set of seven-dimensional data (selected seven properties) describing coal samples obtained from Janina and Wieczorek coal mines. Coal from these mines was previously subjected to separation by means of a laboratory ring jig, consisting of ten rings. With 5 layers of both types of coal (with 2 rings each) were obtained in this way. It was decided to check if the method of multidimensional data visualisation enables to divide the space of such divided samples into areas with different suitability for the fluidised gasification process. To that end, the card of technological suitability of coal was used (Sobolewski et al., 2012; 2013), in which key, relevant and additional parameters, having effect on the gasification process, were described. As a result of analyses, it was stated that effective determination of coal samples suitability for the on-surface gasification process in a fluidised reactor is possible. The PCA method enables the visualisation of the optimal subspace containing the set requirements concerning the properties of coals intended for this process.

Refined qualitative analysis for a class of neural networks

2003 ◽  
Author(s):  
Mihaela-Hanako Matcovschi ◽  
Octavian Pastravanu
Keyword(s):  
Neural Networks ◽  
Qualitative Analysis

Structuring and visualization of indicators in multidimensional data cubes

2018 ◽  
pp. 79-87
Author(s):  
E. E. Akimkina
Keyword(s):  
Decision Making ◽  
Data Processing ◽  
Data Management ◽  
Multidimensional Data ◽  
End User ◽  
Processing Technologies ◽  
Data Cubes ◽  
Multidimensional Visualization ◽  
Multidimensional Data Cubes ◽  
Practical Recommendations

The problems of structuring of indicators in multidimensional data cubes with their subsequent processing with the help of end-user tools providing multidimensional visualization and data management are analyzed; the possibilities of multidimensional data processing technologies for managing and supporting decision making at a design and technological enterprise are shown; practical recommendations on the use of domestic computer environments for the structuring and visualization of multidimensional data cubes are given.

Neural networks trained with high-dimensional functions approximation data in high-dimensional space

2021 ◽  
pp. 1-12
Author(s):  
Jian Zheng ◽  
Jianfeng Wang ◽  
Yanping Chen ◽  
Shuping Chen ◽  
Jingjin Chen ◽  
...  
Keyword(s):  
Neural Networks ◽  
Dimensional Space ◽  
Data Distribution ◽  
High Dimensional ◽  
Sufficient Information ◽  
Sufficient Data ◽  
High Dimensional Space ◽  
Positive Effects ◽  
The Neural Networks ◽  
Using Data

Neural networks can approximate data because of owning many compact non-linear layers. In high-dimensional space, due to the curse of dimensionality, data distribution becomes sparse, causing that it is difficulty to provide sufficient information. Hence, the task becomes even harder if neural networks approximate data in high-dimensional space. To address this issue, according to the Lipschitz condition, the two deviations, i.e., the deviation of the neural networks trained using high-dimensional functions, and the deviation of high-dimensional functions approximation data, are derived. This purpose of doing this is to improve the ability of approximation high-dimensional space using neural networks. Experimental results show that the neural networks trained using high-dimensional functions outperforms that of using data in the capability of approximation data in high-dimensional space. We find that the neural networks trained using high-dimensional functions more suitable for high-dimensional space than that of using data, so that there is no need to retain sufficient data for neural networks training. Our findings suggests that in high-dimensional space, by tuning hidden layers of neural networks, this is hard to have substantial positive effects on improving precision of approximation data.

Multicomponent microseismic data denoising by 3D shearlet transform

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. A45-A51 ◽  
Author(s):  
Chao Zhang ◽  
Mirko van der Baan
Keyword(s):  
Noise Suppression ◽  
Random Noise ◽  
Real Data ◽  
Fracture Initiation ◽  
Multidimensional Data ◽  
Data Sets ◽  
Denoising Method ◽  
Shearlet Transform ◽  
Microseismic Data ◽  
Significant Step

The low-magnitude microseismic signals generated by fracture initiation are generally buried in strong background noise, which complicates their interpretation. Thus, noise suppression is a significant step. We have developed an effective multicomponent, multidimensional microseismic-data denoising method by conducting a simplified polarization analysis in the 3D shearlet transform domain. The 3D shearlet transform is very competitive in dealing with multidimensional data because it captures details of signals at different scales and orientations, which benefits signal and noise separation. We have developed a novel processing strategy based on a signal-detection operator that can effectively identify signal coefficients in the shearlet domain by taking the correlation and energy distribution of 3C microseismic signals into account. We perform tests on synthetic and real data sets and determine that the proposed method can effectively remove random noise and preserve weak signals.

Effective approximation of high-dimensional space using neural networks

2021 ◽  
Author(s):  
Jian Zheng ◽  
Jianfeng Wang ◽  
Yanping Chen ◽  
Shuping Chen ◽  
Jingjin Chen ◽  
...  
Keyword(s):  
Neural Networks ◽  
Dimensional Space ◽  
High Dimensional ◽  
High Dimensional Space ◽  
Effective Approximation

scholarly journals Trivariate Empirical Mode Decomposition via Convex Optimization for Rolling Bearing Condition Identification

Sensors ◽  
2018 ◽  
Vol 18 (7) ◽  
pp. 2325 ◽  
Author(s):  
Yong Lv ◽  
Houzhuang Zhang ◽  
Cancan Yi
Keyword(s):  
Convex Optimization ◽  
Empirical Mode Decomposition ◽  
Dimensional Space ◽  
Real Data ◽  
Rolling Bearing ◽  
Low Rank ◽  
Data Matrix ◽  
Mode Decomposition ◽  
Uniform Sample ◽  
Local Mean

As a multichannel signal processing method based on data-driven, multivariate empirical mode decomposition (MEMD) has attracted much attention due to its potential ability in self-adaption and multi-scale decomposition for multivariate data. Commonly, the uniform projection scheme on a hypersphere is used to estimate the local mean. However, the unbalanced data distribution in high-dimensional space often conflicts with the uniform samples and its performance is sensitive to the noise components. Considering the common fact that the vibration signal is generated by three sensors located in different measuring positions in the domain of the structural health monitoring for the key equipment, thus a novel trivariate empirical mode decomposition via convex optimization was proposed for rolling bearing condition identification in this paper. For the trivariate data matrix, the low-rank matrix approximation via convex optimization was firstly conducted to achieve the denoising. It is worthy to note that the non-convex penalty function as a regularization term is introduced to enhance the performance. Moreover, the non-uniform sample scheme was determined by applying singular value decomposition (SVD) to the obtained low-rank trivariate data and then the approach used in conventional MEMD algorithm was employed to estimate the local mean. Numerical examples of synthetic defined by the fault model and real data generated by the fault rolling bearing on the experimental bench are provided to demonstrate the fruitful applications of the proposed method.

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