Hierarchical surrogate model with dimensionality reduction technique for high‐dimensional uncertainty propagation

2020 ◽  
Vol 121 (9) ◽  
pp. 2068-2085
Author(s):  
Kai Cheng ◽  
Zhenzhou Lu
Keyword(s):  
Dimensionality Reduction ◽  
Surrogate Model ◽  
Uncertainty Propagation ◽  
Reduction Technique ◽  
High Dimensional ◽  
Dimensionality Reduction Technique

scholarly journals Dimensionality Reduction by Weighted Connections between Neighborhoods

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Fuding Xie ◽  
Yutao Fan ◽  
Ming Zhou
Keyword(s):  
Dimensionality Reduction ◽  
Dimensional Space ◽  
High Dimensional Data ◽  
Reduction Technique ◽  
Experimental Results ◽  
High Dimensional ◽  
Reduced Dimensionality ◽  
Dimensionality Reduction Technique ◽  
Low Dimensionality ◽  
Local Topology

Dimensionality reduction is the transformation of high-dimensional data into a meaningful representation of reduced dimensionality. This paper introduces a dimensionality reduction technique by weighted connections between neighborhoods to improveK-Isomap method, attempting to preserve perfectly the relationships between neighborhoods in the process of dimensionality reduction. The validity of the proposal is tested by three typical examples which are widely employed in the algorithms based on manifold. The experimental results show that the local topology nature of dataset is preserved well while transforming dataset in high-dimensional space into a new dataset in low-dimensionality by the proposed method.

scholarly journals Evaluation of UMAP as an alternative to t-SNE for single-cell data

2018 ◽  
Author(s):  
Etienne Becht ◽  
Charles-Antoine Dutertre ◽  
Immanuel W. H. Kwok ◽  
Lai Guan Ng ◽  
Florent Ginhoux ◽  
...  
Keyword(s):  
Dimensionality Reduction ◽  
Single Cell ◽  
Rna Sequencing ◽  
Reduction Technique ◽  
High Dimensional ◽  
The Past ◽  
Dimensionality Reduction Technique ◽  
Single Cell Rna Sequencing ◽  
Linear Dimensionality Reduction ◽  
Cell Data

AbstractUniform Manifold Approximation and Projection (UMAP) is a recently-published non-linear dimensionality reduction technique. Another such algorithm, t-SNE, has been the default method for such task in the past years. Herein we comment on the usefulness of UMAP high-dimensional cytometry and single-cell RNA sequencing, notably highlighting faster runtime and consistency, meaningful organization of cell clusters and preservation of continuums in UMAP compared to t-SNE.

scholarly journals Explaining three-dimensional dimensionality reduction plots

2015 ◽  
Vol 15 (2) ◽  
pp. 154-172 ◽  
Author(s):  
Danilo B Coimbra ◽  
Rafael M Martins ◽  
Tácito TAT Neves ◽  
Alexandru C Telea ◽  
Fernando V Paulovich
Keyword(s):  
Dimensionality Reduction ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Original Data ◽  
Reduction Technique ◽  
High Dimensional ◽  
Dimensionality Reduction Technique ◽  
Visualization Techniques ◽  
High Dimensional Datasets ◽  
Three Dimensional Space

Understanding three-dimensional projections created by dimensionality reduction from high-variate datasets is very challenging. In particular, classical three-dimensional scatterplots used to display such projections do not explicitly show the relations between the projected points, the viewpoint used to visualize the projection, and the original data variables. To explore and explain such relations, we propose a set of interactive visualization techniques. First, we adapt and enhance biplots to show the data variables in the projected three-dimensional space. Next, we use a set of interactive bar chart legends to show variables that are visible from a given viewpoint and also assist users to select an optimal viewpoint to examine a desired set of variables. Finally, we propose an interactive viewpoint legend that provides an overview of the information visible in a given three-dimensional projection from all possible viewpoints. Our techniques are simple to implement and can be applied to any dimensionality reduction technique. We demonstrate our techniques on the exploration of several real-world high-dimensional datasets.

scholarly journals Decision Tree based Classification and Dimensionality Reduction of Cervical Cancer

2020 ◽  
Vol 9 (4) ◽  
pp. 1531-1535
Keyword(s):  
Cervical Cancer ◽  
Decision Tree ◽  
Dimensionality Reduction ◽  
Reduction Technique ◽  
High Dimensional ◽  
Biological Processes ◽  
Decision Tree Algorithm ◽  
Dimensionality Reduction Technique ◽  
C4.5 Algorithm ◽  
C4.5 Decision Tree

The data revolution in medicines and biology have increased our fundamental understandings of biological processes and determining the factors causing any disease, but it has also posed a challenge towards their analysis. After breast cancer, most of the deaths among women are due to cervical cancer. According to IARC, alone in 2012 a noticeable number of cases estimated 7095 of cervical cancer were reported. 16.5% of the deaths were due to the cervical cancer with the total deaths of 28,711 among women. To analyze the high dimensional data with high accuracy and in less amount of time, their dimensionality needs to be reduced to remove irrelevant features. The classification is performed using the recent iteration in Quinlan’s C4.5 decision tree algorithm i.e. C5.0 algorithm and PCA as Dimensionality Reduction technique. Our proposed methodology has shown a significant improvement in the account of time taken by both algorithms. This shows that C5.0 algorithm is superior to C4.5 algorithm.

Capturing discrete latent structures: choose LDs over PCs

Biostatistics ◽  
2021 ◽  
Author(s):  
Theresa A Alexander ◽  
Rafael A Irizarry ◽  
Héctor Corrada Bravo
Keyword(s):  
Dimensionality Reduction ◽  
Biological Data ◽  
Reduction Technique ◽  
Latent Structure ◽  
High Dimensional ◽  
Underlying Structure ◽  
Linear Transformations ◽  
Latent Structures ◽  
Low Dimensional ◽  
Discriminatory Information

Summary High-dimensional biological data collection across heterogeneous groups of samples has become increasingly common, creating high demand for dimensionality reduction techniques that capture underlying structure of the data. Discovering low-dimensional embeddings that describe the separation of any underlying discrete latent structure in data is an important motivation for applying these techniques since these latent classes can represent important sources of unwanted variability, such as batch effects, or interesting sources of signal such as unknown cell types. The features that define this discrete latent structure are often hard to identify in high-dimensional data. Principal component analysis (PCA) is one of the most widely used methods as an unsupervised step for dimensionality reduction. This reduction technique finds linear transformations of the data which explain total variance. When the goal is detecting discrete structure, PCA is applied with the assumption that classes will be separated in directions of maximum variance. However, PCA will fail to accurately find discrete latent structure if this assumption does not hold. Visualization techniques, such as t-Distributed Stochastic Neighbor Embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP), attempt to mitigate these problems with PCA by creating a low-dimensional space where similar objects are modeled by nearby points in the low-dimensional embedding and dissimilar objects are modeled by distant points with high probability. However, since t-SNE and UMAP are computationally expensive, often a PCA reduction is done before applying them which makes it sensitive to PCAs downfalls. Also, tSNE is limited to only two or three dimensions as a visualization tool, which may not be adequate for retaining discriminatory information. The linear transformations of PCA are preferable to non-linear transformations provided by methods like t-SNE and UMAP for interpretable feature weights. Here, we propose iterative discriminant analysis (iDA), a dimensionality reduction technique designed to mitigate these limitations. iDA produces an embedding that carries discriminatory information which optimally separates latent clusters using linear transformations that permit post hoc analysis to determine features that define these latent structures.

Dimensionality and Its Reduction

2014 ◽  
Author(s):  
Andrew J. Connolly ◽  
Jacob T. VanderPlas ◽  
Alexander Gray ◽  
Andrew J. Connolly ◽  
Jacob T. VanderPlas ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Reduction Technique ◽  
High Dimensional ◽  
Data Sets ◽  
Data Set ◽  
Gaussian Distributions ◽  
Dimensionality Reduction Technique ◽  
Alternative Techniques ◽  
New Generation

With the dramatic increase in data available from a new generation of astronomical telescopes and instruments, many analyses must address the question of the complexity as well as size of the data set. This chapter deals with how we can learn which measurements, properties, or combinations thereof carry the most information within a data set. It describes techniques that are related to concepts discussed when describing Gaussian distributions, density estimation, and the concepts of information content. The chapter begins with an exploration of the problems posed by high-dimensional data. It then describes the data sets used in this chapter, and introduces perhaps the most important and widely used dimensionality reduction technique, principal component analysis (PCA). The remainder of the chapter discusses several alternative techniques which address some of the weaknesses of PCA.

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