Alignment of Overlapping Locally Scaled Patches for Multidimensional Scaling and Dimensionality Reduction

2008 ◽  
Vol 30 (3) ◽  
pp. 438-450 ◽  
Author(s):  
Li Yang
Keyword(s):  
Multidimensional Scaling ◽  
Dimensionality Reduction

scholarly journals On the Complexity Analysis and Visualization of Musical Information

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 669 ◽  
Author(s):  
António M. Lopes ◽  
J. A. Tenreiro Machado
Keyword(s):  
Multidimensional Scaling ◽  
Dimensionality Reduction ◽  
Complexity Analysis ◽  
Computational Tools ◽  
Scaling Technique ◽  
Digital Representations ◽  
Musical Production ◽  
Musical Works ◽  
Visualization Techniques

This paper considers several distinct mathematical and computational tools, namely complexity, dimensionality-reduction, clustering, and visualization techniques, for characterizing music. Digital representations of musical works of four artists are analyzed by means of distinct indices and visualized using the multidimensional scaling technique. The results are then correlated with the artists’ musical production. The patterns found in the data demonstrate the effectiveness of the approach for assessing the complexity of musical information.

scholarly journals A visual approach for analysis and inference of molecular activity spaces

2019 ◽  
Vol 11 (1) ◽  
Author(s):  
Samina Kausar ◽  
Andre O. Falcao
Keyword(s):  
Multidimensional Scaling ◽  
Dimensionality Reduction ◽  
Biological Evaluation ◽  
Classification Model ◽  
Data Sets ◽  
Similarity Matrix ◽  
Data Set ◽  
Structure Activity ◽  
Reference Space ◽  
Sammon Mapping

Abstract Background Molecular space visualization can help to explore the diversity of large heterogeneous chemical data, which ultimately may increase the understanding of structure-activity relationships (SAR) in drug discovery projects. Visual SAR analysis can therefore be useful for library design, chemical classification for their biological evaluation and virtual screening for the selection of compounds for synthesis or in vitro testing. As such, computational approaches for molecular space visualization have become an important issue in cheminformatics research. The proposed approach uses molecular similarity as the sole input for computing a probabilistic surface of molecular activity (PSMA). This similarity matrix is transformed in 2D using different dimension reduction algorithms (Principal Coordinates Analysis ( PCooA), Kruskal multidimensional scaling, Sammon mapping and t-SNE). From this projection, a kernel density function is applied to compute the probability of activity for each coordinate in the new projected space. Results This methodology was tested over four different quantitative structure-activity relationship (QSAR) binary classification data sets and the PSMAs were computed for each. The generated maps showed internal consistency with active molecules grouped together for all data sets and all dimensionality reduction algorithms. To validate the quality of the generated maps, the 2D coordinates of test molecules were computed into the new reference space using a data transformation matrix. In total sixteen PSMAs were built, and their performance was assessed using the Area Under Curve (AUC) and the Matthews Coefficient Correlation (MCC). For the best projections for each data set, AUC testing results ranged from 0.87 to 0.98 and the MCC scores ranged from 0.33 to 0.77, suggesting this methodology can validly capture the complexities of the molecular activity space. All four mapping functions provided generally good results yet the overall performance of PCooA and t-SNE was slightly better than Sammon mapping and Kruskal multidimensional scaling. Conclusions Our result showed that by using an appropriate combination of metric space representation and dimensionality reduction applied over metric spaces it is possible to produce a visual PSMA for which its consistency has been validated by using this map as a classification model. The produced maps can be used as prediction tools as it is simple to project any molecule into this new reference space as long as the similarities to the molecules used to compute the initial similarity matrix can be computed.

scholarly journals An Efficient Kriging Modeling Method Based on Multidimensional Scaling for High-Dimensional Problems

Algorithms ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 3
Author(s):  
Yu Ge ◽  
Junjun Shi ◽  
Yaohui Li ◽  
Jingfang Shen
Keyword(s):  
Multidimensional Scaling ◽  
Dimensionality Reduction ◽  
Flight Control ◽  
Distance Matrix ◽  
Modeling Method ◽  
Inner Product ◽  
High Dimensional ◽  
Design Data ◽  
Field Problem ◽  
Product Matrix

Kriging-based modeling has been widely used in computationally intensive simulations. However, the Kriging modeling of high-dimensional problems not only takes more time, but also leads to the failure of model construction. To this end, a Kriging modeling method based on multidimensional scaling (KMDS) is presented to avoid the “dimensional disaster”. Under the condition of keeping the distance between the sample points before and after the dimensionality reduction unchanged, the KMDS method, which mainly calculates each element in the inner product matrix due to the mapping relationship between the distance matrix and the inner product matrix, completes the conversion of design data from high dimensional to low dimensional. For three benchmark functions with different dimensions and the aviation field problem of aircraft longitudinal flight control, the proposed method is compared with other dimensionality reduction methods. The KMDS method has better modeling efficiency while meeting certain accuracy requirements.

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