Facing the high-dimensions: Inverse projection with radial basis functions

Amorim, Elisa Portes dos Santos; Brazil, Emilio Vital; Mena‐Chalco, Jesús Pascual; Velho, Luiz; Nonato, Luís Gustavo; Samavati, Faramarz; Sousa, Mário Costa

doi:10.1016/j.cag.2015.02.009

Cited by 21 publications

(31 citation statements)

References 39 publications

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“…This limitation is well known and discussed in several works [21,[47][48][49]. The same limitations are shared by the inverse projection P −1 [12,20,50].…”

Section: Dense Map Filteringmentioning

confidence: 88%

Constructing and Visualizing High-Quality Classifier Decision Boundary Maps

et al. 2019

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Visualizing decision boundaries of machine learning classifiers can help in classifier design, testing and fine-tuning. Decision maps are visualization techniques that overcome the key sparsity-related limitation of scatterplots for this task. To increase the trustworthiness of decision map use, we perform an extensive evaluation considering the dimensionality-reduction (DR) projection techniques underlying decision map construction. We extend the visual accuracy of decision maps by proposing additional techniques to suppress errors caused by projection distortions. Additionally, we propose ways to estimate and visually encode the distance-to-decision-boundary in decision maps, thereby enriching the conveyed information. We demonstrate our improvements and the insights that decision maps convey on several real-world datasets.

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“…This limitation is well known and discussed in several works [21,[47][48][49]. The same limitations are shared by the inverse projection P −1 [12,20,50].…”

Section: Dense Map Filteringmentioning

confidence: 88%

Constructing and Visualizing High-Quality Classifier Decision Boundary Maps

et al. 2019

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“…For example, iLAMP [2] introduces a backprojection method for LAMP [30] using local neighborhoods and demonstrates its viability over synthetic datasets [2]. Researchers also investigated general backward-projection meth- ods based on radial basis functions [1,44], treating backward projection as an interpolation problem. Autoencoders [26], neural-network-based DR models, are a promising approach to computing backward projections.…”

Section: Backward Projectionmentioning

confidence: 99%

A Visual Interaction Framework for Dimensionality Reduction Based Data Exploration

Cavallo

Demiralp

2018

Proceedings of the 2018 CHI Conference on Human Factors in Computing Systems

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Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data. However, reasoning dynamically about the results of a dimensionality reduction is difficult. Dimensionality-reduction algorithms use complex optimizations to reduce the number of dimensions of a dataset, but these new dimensions often lack a clear relation to the initial data dimensions, thus making them difficult to interpret.Here we propose a visual interaction framework to improve dimensionality-reduction based exploratory data analysis. We introduce two interaction techniques, forward projection and backward projection, for dynamically reasoning about dimensionally reduced data. We also contribute two visualization techniques, prolines and feasibility maps, to facilitate the effective use of the proposed interactions.We apply our framework to PCA and autoencoder-based dimensionality reductions. Through data-exploration examples, we demonstrate how our visual interactions can improve the use of dimensionality reduction in exploratory data analysis.

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“…Also, let E be a 2D vector field ensemble, i.e., a 2-dimensional vector is defined at each spatial point in S r,c for V ∈ E. E can be viewed as a m-dimensional data set with m = r × c. As described by Amorim et al (2015), being Y ∈ R 2 the 2D projection of E, for any point p ∈ R 2 we want to find its m-dimensional representation, i.e., a point q ⊂ R m . Given the concept of RBF interpolation, we seek s(p):…”

Section: The Proposed Methodsmentioning

confidence: 99%

“…Dimensionality reduction, or multidimensional projection, is an approach used to represent a multidimensional data in a low-dimensional space. Its goal consists in providing an overview of similarities between instances of data in a projection space (Amorim et al, 2015), which can then be visually encoded and interpreted. Many algorithms for dimensionality reduction can be found in the literature.…”

Section: Vector Field Synthesismentioning

confidence: 99%

“…Recently, Amorim et al (2015) proposed an inverse projection technique based on RBF interpolation, providing a smooth and global mapping from low to high dimensions. In RBF interpolation, for N data points X i ∈ R m and their respective function values Y i ∈ R, an approximant s : R m → R is construct in such a way that is possible to derive the value y for any arbitrary point in x ∈ R m in such a way that:…”

Section: Inverse Projectionmentioning

confidence: 99%

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Uncertainty Analysis of 2d Vector Fields Through the Helmholtz-Hodge Decomposition

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Facing the high-dimensions: Inverse projection with radial basis functions

Cited by 21 publications

References 39 publications

Constructing and Visualizing High-Quality Classifier Decision Boundary Maps

Constructing and Visualizing High-Quality Classifier Decision Boundary Maps

A Visual Interaction Framework for Dimensionality Reduction Based Data Exploration

Uncertainty Analysis of 2d Vector Fields Through the Helmholtz-Hodge Decomposition

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