Application of Soft Set Theory for Dimensionality Reduction Approach in Machine Learning

2021 ◽  
pp. 225-232
Author(s):  
P. D. Lanjewar ◽  
B. F. Momin
2012 ◽  
Vol 2 (4) ◽  
pp. 29-46 ◽  
Author(s):  
Bana Handaga ◽  
Tutut Herawan ◽  
Mustafa Mat Deris

Introduced is a new algorithm for the classification of numerical data using the theory of fuzzy soft set, named Fuzzy Soft Set Classifier (FSSC). The algorithm uses the fuzzy approach in the pre-processing stage to obtain features, and similarity concept in the process of classification. It can be applied not only to binary-valued datasets, but also be able to classify the data that consists of real numbers. Comparison tests on seven datasets from UCI Machine Learning Repository have been carried out. It is shown that the proposed algorithm provides better accuracy and higher accuracy as compared to the baseline algorithm using soft set theory.


Author(s):  
Susanto ◽  
Deris Stiawan ◽  
M. Agus Syamsul Arifin ◽  
Juli Rejito ◽  
Mohd. Yazid Idris ◽  
...  

Author(s):  
B. Elavarasan ◽  
G. Muhiuddin ◽  
K. Porselvi ◽  
Y. B. Jun

AbstractHuman endeavours span a wide spectrum of activities which includes solving fascinating problems in the realms of engineering, arts, sciences, medical sciences, social sciences, economics and environment. To solve these problems, classical mathematics methods are insufficient. The real-world problems involve many uncertainties making them difficult to solve by classical means. The researchers world over have established new mathematical theories such as fuzzy set theory and rough set theory in order to model the uncertainties that appear in various fields mentioned above. In the recent days, soft set theory has been developed which offers a novel way of solving real world issues as the issue of setting the membership function does not arise. This comes handy in solving numerous problems and many advancements are being made now-a-days. Jun introduced hybrid structure utilizing the ideas of a fuzzy set and a soft set. It is to be noted that hybrid structures are a speculation of soft set and fuzzy set. In the present work, the notion of hybrid ideals of a near-ring is introduced. Significant work has been carried out to investigate a portion of their significant properties. These notions are characterized and their relations are established furthermore. For a hybrid left (resp., right) ideal, different left (resp., right) ideal structures of near-rings are constructed. Efforts have been undertaken to display the relations between the hybrid product and hybrid intersection. Finally, results based on homomorphic hybrid preimage of a hybrid left (resp., right) ideals are proved.


2021 ◽  
pp. 1-15
Author(s):  
Monairah Alansari ◽  
Shehu Shagari Mohammed ◽  
Akbar Azam

As an improvement of fuzzy set theory, the notion of soft set was initiated as a general mathematical tool for handling phenomena with nonstatistical uncertainties. Recently, a novel idea of set-valued maps whose range set lies in a family of soft sets was inaugurated as a significant refinement of fuzzy mappings and classical multifunctions as well as their corresponding fixed point theorems. Following this new development, in this paper, the concepts of e-continuity and E-continuity of soft set-valued maps and αe-admissibility for a pair of such maps are introduced. Thereafter, we present some generalized quasi-contractions and prove the existence of e-soft fixed points of a pair of the newly defined non-crisp multivalued maps. The hypotheses and usability of these results are supported by nontrivial examples and applications to a system of integral inclusions. The established concepts herein complement several fixed point theorems in the framework of point-to-set-valued maps in the comparable literature. A few of these special cases of our results are highlighted and discussed.


2020 ◽  
Vol 79 (Suppl 1) ◽  
pp. 897.2-897
Author(s):  
M. Maurits ◽  
T. Huizinga ◽  
M. Reinders ◽  
S. Raychaudhuri ◽  
E. Karlson ◽  
...  

Background:Heterogeneity in disease populations complicates discovery of risk factors. To identify risk factors for subpopulations of diseases, we need analytical methods that can deal with unidentified disease subgroups.Objectives:Inspired by successful approaches from the Big Data field, we developed a high-throughput approach to identify subpopulations within patients with heterogeneous, complex diseases using the wealth of information available in Electronic Medical Records (EMRs).Methods:We extracted longitudinal healthcare-interaction records coded by 1,853 PheCodes[1] of the 64,819 patients from the Boston’s Partners-Biobank. Through dimensionality reduction using t-SNE[2] we created a 2D embedding of 32,424 of these patients (set A). We then identified distinct clusters post-t-SNE using DBscan[3] and visualized the relative importance of individual PheCodes within them using specialized spectrographs. We replicated this procedure in the remaining 32,395 records (set B).Results:Summary statistics of both sets were comparable (Table 1).Table 1.Summary statistics of the total Partners Biobank dataset and the 2 partitions.Set-Aset-BTotalEntries12,200,31112,177,13124,377,442Patients32,42432,39564,819Patientyears369,546.33368,597.92738,144.2unique ICD codes25,05624,95326,305unique Phecodes1,8511,8531,853We found 284 clusters in set A and 295 in set B, of which 63.4% from set A could be mapped to a cluster in set B with a median (range) correlation of 0.24 (0.03 – 0.58).Clusters represented similar yet distinct clinical phenotypes; e.g. patients diagnosed with “other headache syndrome” were separated into four distinct clusters characterized by migraines, neurofibromatosis, epilepsy or brain cancer, all resulting in patients presenting with headaches (Fig. 1 & 2). Though EMR databases tend to be noisy, our method was also able to differentiate misclassification from true cases; SLE patients with RA codes clustered separately from true RA cases.Figure 1.Two dimensional representation of Set A generated using dimensionality reduction (tSNE) and clustering (DBScan).Figure 2.Phenotype Spectrographs (PheSpecs) of four clusters characterized by “Other headache syndromes”, driven by codes relating to migraine, epilepsy, neurofibromatosis or brain cancer.Conclusion:We have shown that EMR data can be used to identify and visualize latent structure in patient categorizations, using an approach based on dimension reduction and clustering machine learning techniques. Our method can identify misclassified patients as well as separate patients with similar problems into subsets with different associated medical problems. Our approach adds a new and powerful tool to aid in the discovery of novel risk factors in complex, heterogeneous diseases.References:[1] Denny, J.C. et al. Bioinformatics (2010)[2]van der Maaten et al. Journal of Machine Learning Research (2008)[3] Ester, M. et al. Proceedings of the Second International Conference on Knowledge Discovery and Data Mining. (1996)Disclosure of Interests:Marc Maurits: None declared, Thomas Huizinga Grant/research support from: Ablynx, Bristol-Myers Squibb, Roche, Sanofi, Consultant of: Ablynx, Bristol-Myers Squibb, Roche, Sanofi, Marcel Reinders: None declared, Soumya Raychaudhuri: None declared, Elizabeth Karlson: None declared, Erik van den Akker: None declared, Rachel Knevel: None declared


Author(s):  
Riccardo Capelli ◽  
Andrea Gardin ◽  
Charly Empereur-mot ◽  
Giovanni Doni ◽  
Giovanni M. Pavan

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 1822
Author(s):  
Norbert Huber

Nanoporous metals, with their complex microstructure, represent an ideal candidate for the development of methods that combine physics, data, and machine learning. The preparation of nanporous metals via dealloying allows for tuning of the microstructure and macroscopic mechanical properties within a large design space, dependent on the chosen dealloying conditions. Specifically, it is possible to define the solid fraction, ligament size, and connectivity density within a large range. These microstructural parameters have a large impact on the macroscopic mechanical behavior. This makes this class of materials an ideal science case for the development of strategies for dimensionality reduction, supporting the analysis and visualization of the underlying structure–property relationships. Efficient finite element beam modeling techniques were used to generate ~200 data sets for macroscopic compression and nanoindentation of open pore nanofoams. A strategy consisting of dimensional analysis, principal component analysis, and machine learning allowed for data mining of the microstructure–property relationships. It turned out that the scaling law of the work hardening rate has the same exponent as the Young’s modulus. Simple linear relationships are derived for the normalized work hardening rate and hardness. The hardness to yield stress ratio is not limited to 1, as commonly assumed for foams, but spreads over a large range of values from 0.5 to 3.


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