id
	16393
Url
	https://chloe.cnr.it/s/BiDiAr/item/16393
Resource template
	Academic Article
Resource class
	bibo:AcademicArticle
Title
	Nonlinear Dimensionality Reduction for Data Visualization: An Unsupervised Fuzzy Rule-Based Approach
Creator
	Das, Suchismita
	Pal, Nikhil R.
Date
	2022
Language
	eng
Abstract
	In this article, we propose a general framework for the unsupervised fuzzy rule-based dimensionality reduction primarily for data visualization. This framework has the following important characteristics relevant to the dimensionality reduction for visualization: preserves neighborhood relationships; effectively handles data on nonlinear manifolds; capable of projecting out-of-sample test points; can reject test points, when it is appropriate; and interpretable to a reasonable extent. We use the first-order Takagi–Sugeno model. Typically, fuzzy rules are either provided by experts or extracted using an input–output training set. Here, neither the output data nor experts are available. This makes the problem challenging. We estimate the rule parameters minimizing a suitable objective function that preserves the interpoint geodesic distances (distances over the manifold) as Euclidean distances on the projected space. In this context, we propose a new variant of the geodesic c-means clustering algorithm. The proposed method is tested on several synthetic and real-world datasets and compared with the results of six state-of-the-art data visualization methods. The proposed method is the only method that performs equally well on all the datasets tried. Our method is found to be robust to the initial conditions. The predictability of the method is validated by suitable experiments. We also assess the ability of our method to reject test points when it should. The scalability issue of the scheme is also discussed. Due to the general nature of the framework, we can use different objective functions to obtain projections satisfying different goals. To the best of our knowledge, this is the first attempt to manifold learning using unsupervised fuzzy rule-based modeling.
Is Part Of
	IEEE Transactions on Fuzzy Systems
Doi
	https://doi.org/10.1109/TFUZZ.2021.3076583
Issn
	1941-0034
Issue
	7
Pages
	2157-2169
Short title
	Nonlinear Dimensionality Reduction for Data Visualization
Uri
	https://ieeexplore.ieee.org/document/9419710
Volume
	30
Homepage
	https://www.zotero.org/groups/5293298/bidiar/items/BGBHFNEDitem-list

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