scholarly journals When and Why are Principal Component Scores a Good Tool for Visualizing High-dimensional Data?

2017 ◽  
Vol 44 (3) ◽  
pp. 581-597 ◽  
Author(s):  
Kristoffer H. Hellton ◽  
Magne Thoresen
2013 ◽  
Vol 303-306 ◽  
pp. 1101-1104 ◽  
Author(s):  
Yong De Hu ◽  
Jing Chang Pan ◽  
Xin Tan

Kernel entropy component analysis (KECA) reveals the original data’s structure by kernel matrix. This structure is related to the Renyi entropy of the data. KECA maintains the invariance of the original data’s structure by keeping the data’s Renyi entropy unchanged. This paper described the original data by several components on the purpose of dimension reduction. Then the KECA was applied in celestial spectra reduction and was compared with Principal Component Analysis (PCA) and Kernel Principal Component Analysis (KPCA) by experiments. Experimental results show that the KECA is a good method in high-dimensional data reduction.


2010 ◽  
Vol 38 (6) ◽  
pp. 3605-3629 ◽  
Author(s):  
Seunggeun Lee ◽  
Fei Zou ◽  
Fred A. Wright

2011 ◽  
Vol 54 (1) ◽  
pp. 94-107 ◽  
Author(s):  
Guo-Chun Ding ◽  
Kornelia Smalla ◽  
Holger Heuer ◽  
Siegfried Kropf

2019 ◽  
Author(s):  
Shamus M. Cooley ◽  
Timothy Hamilton ◽  
J. Christian J. Ray ◽  
Eric J. Deeds

AbstractHigh-dimensional data are becoming increasingly common in nearly all areas of science. Developing approaches to analyze these data and understand their meaning is a pressing issue. This is particularly true for the rapidly growing field of single-cell RNA-Seq (scRNA-Seq), a technique that simultaneously measures the expression of tens of thousands of genes in thousands to millions of single cells. The emerging consensus for analysis workflows reduces the dimensionality of the dataset before performing downstream analysis, such as assignment of cell types. One problem with this approach is that dimensionality reduction can introduce substantial distortion into the data; consider the familiar example of trying to represent the three-dimensional earth as a two-dimensional map. It is currently unclear if such distortion affects analysis of scRNA-Seq data sets. Here, we introduce a straightforward approach to quantifying this distortion by comparing the local neighborhoods of points before and after dimensionality reduction. We found that popular techniques like t-SNE and UMAP introduce substantial distortion even for relatively simple geometries such as simulated hyperspheres. For scRNA-Seq data, we found the distortion in local neighborhoods was often greater than 95% in the representations typically used for downstream analysis. This high level of distortion can readily introduce important errors into cell type identification, pseudotime ordering, and other analyses that rely on local relationships. We found that principal component analysis can generate accurate embeddings of the data, but only when using dimensionalities that are much higher than typically used in scRNA-Seq analysis. We suggest approaches to take these findings into account and call for a new generation of dimensional reduction algorithms that can accurately embed high dimensional data in its true latent dimension.


2011 ◽  
Vol 20 (4) ◽  
pp. 852-873 ◽  
Author(s):  
Vadim Zipunnikov ◽  
Brian Caffo ◽  
David M. Yousem ◽  
Christos Davatzikos ◽  
Brian S. Schwartz ◽  
...  

Metabolites ◽  
2019 ◽  
Vol 9 (7) ◽  
pp. 133 ◽  
Author(s):  
Tessa Schillemans ◽  
Lin Shi ◽  
Xin Liu ◽  
Agneta Åkesson ◽  
Rikard Landberg ◽  
...  

Metabolomics has emerged as a promising technique to understand relationships between environmental factors and health status. Through comprehensive profiling of small molecules in biological samples, metabolomics generates high-dimensional data objectively, reflecting exposures, endogenous responses, and health effects, thereby providing further insights into exposure-disease associations. However, the multivariate nature of metabolomics data contributes to high complexity in analysis and interpretation. Efficient visualization techniques of multivariate data that allow direct interpretation of combined exposures, metabolome, and disease risk, are currently lacking. We have therefore developed the ‘triplot’ tool, a novel algorithm that simultaneously integrates and displays metabolites through latent variable modeling (e.g., principal component analysis, partial least squares regression, or factor analysis), their correlations with exposures, and their associations with disease risk estimates or intermediate risk factors. This paper illustrates the framework of the ‘triplot’ using two synthetic datasets that explore associations between dietary intake, plasma metabolome, and incident type 2 diabetes or BMI, an intermediate risk factor for lifestyle-related diseases. Our results demonstrate advantages of triplot over conventional visualization methods in facilitating interpretation in multivariate risk modeling with high-dimensional data. Algorithms, synthetic data, and tutorials are open source and available in the R package ‘triplot’.


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