Dimensionality Reduction of High-Dimensional Data with a NonLinear Principal Component Aligned Generative Topographic Mapping

2014 ◽  
Vol 36 (3) ◽  
pp. A1027-A1047 ◽  
Author(s):  
M. Griebel ◽  
A. Hullmann
Keyword(s):  
Dimensionality Reduction ◽  
High Dimensional Data ◽  
Principal Component ◽  
High Dimensional ◽  
Topographic Mapping ◽  
Generative Topographic Mapping

scholarly journals A novel metric reveals previously unrecognized distortion in dimensionality reduction of scRNA-Seq data

2019 ◽  
Author(s):  
Shamus M. Cooley ◽  
Timothy Hamilton ◽  
J. Christian J. Ray ◽  
Eric J. Deeds
Keyword(s):  
Dimensionality Reduction ◽  
Single Cells ◽  
High Dimensional Data ◽  
Three Dimensional ◽  
Principal Component ◽  
Cell Types ◽  
High Dimensional ◽  
Before And After ◽  
Downstream Analysis ◽  
High Level

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.

scholarly journals Performance Analysis of Dimensionality Reduction Techniques in the Context of Clustering

2019 ◽  
Vol 8 (S3) ◽  
pp. 66-71
Author(s):  
T. Sudha ◽  
P. Nagendra Kumar
Keyword(s):  
Principal Component Analysis ◽  
Dimensionality Reduction ◽  
High Dimensional Data ◽  
Principal Component ◽  
Component Analysis ◽  
High Dimensional ◽  
Reduction Techniques ◽  
Dimensionality Reduction Techniques ◽  
Low Dimensional ◽  
Probabilistic Principal Component Analysis

Data mining is one of the major areas of research. Clustering is one of the main functionalities of datamining. High dimensionality is one of the main issues of clustering and Dimensionality reduction can be used as a solution to this problem. The present work makes a comparative study of dimensionality reduction techniques such as t-distributed stochastic neighbour embedding and probabilistic principal component analysis in the context of clustering. High dimensional data have been reduced to low dimensional data using dimensionality reduction techniques such as t-distributed stochastic neighbour embedding and probabilistic principal component analysis. Cluster analysis has been performed on the high dimensional data as well as the low dimensional data sets obtained through t-distributed stochastic neighbour embedding and Probabilistic principal component analysis with varying number of clusters. Mean squared error; time and space have been considered as parameters for comparison. The results obtained show that time taken to convert the high dimensional data into low dimensional data using probabilistic principal component analysis is higher than the time taken to convert the high dimensional data into low dimensional data using t-distributed stochastic neighbour embedding.The space required by the data set reduced through Probabilistic principal component analysis is less than the storage space required by the data set reduced through t-distributed stochastic neighbour embedding.

scholarly journals High-dimensional data analysis with subspace comparison using matrix visualization

2017 ◽  
Vol 18 (1) ◽  
pp. 94-109 ◽  
Author(s):  
Junpeng Wang ◽  
Xiaotong Liu ◽  
Han-Wei Shen
Keyword(s):  
Dimensionality Reduction ◽  
Dimensional Space ◽  
High Dimensional Data ◽  
Principal Component ◽  
Data Exploration ◽  
High Dimensional ◽  
Data Sets ◽  
Subspace Analysis ◽  
Matrix Visualization ◽  
Fine Tune

Due to the intricate relationship between different dimensions of high-dimensional data, subspace analysis is often conducted to decompose dimensions and give prominence to certain subsets of dimensions, i.e. subspaces. Exploring and comparing subspaces are important to reveal the underlying features of subspaces, as well as to portray the characteristics of individual dimensions. To date, most of the existing high-dimensional data exploration and analysis approaches rely on dimensionality reduction algorithms (e.g. principal component analysis and multi-dimensional scaling) to project high-dimensional data, or their subspaces, to two-dimensional space and employ scatterplots for visualization. However, the dimensionality reduction algorithms are sometimes difficult to fine-tune and scatterplots are not effective for comparative visualization, making subspace comparison hard to perform. In this article, we aggregate high-dimensional data or their subspaces by computing pair-wise distances between all data items and showing the distances with matrix visualizations to present the original high-dimensional data or subspaces. Our approach enables effective visual comparisons among subspaces, which allows users to further investigate the characteristics of individual dimensions by studying their behaviors in similar subspaces. Through subspace comparisons, we identify dominant, similar, and conforming dimensions in different subspace contexts of synthetic and real-world high-dimensional data sets. Additionally, we present a prototype that integrates parallel coordinates plot and matrix visualization for high-dimensional data exploration and incremental dimensionality analysis, which also allows users to further validate the dimension characterization results derived from the subspace comparisons.

scholarly journals Parallel Framework for Dimensionality Reduction of Large-Scale Datasets

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Sai Kiranmayee Samudrala ◽  
Jaroslaw Zola ◽  
Srinivas Aluru ◽  
Baskar Ganapathysubramanian
Keyword(s):  
Dimensionality Reduction ◽  
Organic Solar Cells ◽  
Large Scale ◽  
Parallel Implementation ◽  
High Dimensional Data ◽  
Real Life ◽  
Processing Parameters ◽  
High Dimensional ◽  
Morphology Evolution ◽  
Reduction Techniques

Dimensionality reduction refers to a set of mathematical techniques used to reduce complexity of the original high-dimensional data, while preserving its selected properties. Improvements in simulation strategies and experimental data collection methods are resulting in a deluge of heterogeneous and high-dimensional data, which often makes dimensionality reduction the only viable way to gain qualitative and quantitative understanding of the data. However, existing dimensionality reduction software often does not scale to datasets arising in real-life applications, which may consist of thousands of points with millions of dimensions. In this paper, we propose a parallel framework for dimensionality reduction of large-scale data. We identify key components underlying the spectral dimensionality reduction techniques, and propose their efficient parallel implementation. We show that the resulting framework can be used to process datasets consisting of millions of points when executed on a 16,000-core cluster, which is beyond the reach of currently available methods. To further demonstrate applicability of our framework we perform dimensionality reduction of 75,000 images representing morphology evolution during manufacturing of organic solar cells in order to identify how processing parameters affect morphology evolution.

scholarly journals Unsupervised Text Feature Learning via Deep Variational Auto-encoder

2020 ◽  
Vol 49 (3) ◽  
pp. 421-437
Author(s):  
Genggeng Liu ◽  
Lin Xie ◽  
Chi-Hua Chen
Keyword(s):  
Dimensionality Reduction ◽  
High Dimensional Data ◽  
Image Data ◽  
Original Data ◽  
Feature Representation ◽  
High Dimensional ◽  
Learning To Learn ◽  
Text Feature ◽  
Reduction Methods ◽  
Low Dimensional

Dimensionality reduction plays an important role in the data processing of machine learning and data mining, which makes the processing of high-dimensional data more efficient. Dimensionality reduction can extract the low-dimensional feature representation of high-dimensional data, and an effective dimensionality reduction method can not only extract most of the useful information of the original data, but also realize the function of removing useless noise. The dimensionality reduction methods can be applied to all types of data, especially image data. Although the supervised learning method has achieved good results in the application of dimensionality reduction, its performance depends on the number of labeled training samples. With the growing of information from internet, marking the data requires more resources and is more difficult. Therefore, using unsupervised learning to learn the feature of data has extremely important research value. In this paper, an unsupervised multilayered variational auto-encoder model is studied in the text data, so that the high-dimensional feature to the low-dimensional feature becomes efficient and the low-dimensional feature can retain mainly information as much as possible. Low-dimensional feature obtained by different dimensionality reduction methods are used to compare with the dimensionality reduction results of variational auto-encoder (VAE), and the method can be significantly improved over other comparison methods.

Glyphboard: Visual Exploration of High-Dimensional Data Combining Glyphs with Dimensionality Reduction

2020 ◽  
Vol 26 (4) ◽  
pp. 1661-1671 ◽  
Author(s):  
Dietrich Kammer ◽  
Mandy Keck ◽  
Thomas Grunder ◽  
Alexander Maasch ◽  
Thomas Thom ◽  
...  
Keyword(s):  
Dimensionality Reduction ◽  
High Dimensional Data ◽  
Visual Exploration ◽  
High Dimensional

High-Dimensional Data Dimension Reduction Based on KECA

2013 ◽  
Vol 303-306 ◽  
pp. 1101-1104 ◽  
Author(s):  
Yong De Hu ◽  
Jing Chang Pan ◽  
Xin Tan
Keyword(s):  
Principal Component Analysis ◽  
Dimension Reduction ◽  
High Dimensional Data ◽  
Principal Component ◽  
Good Method ◽  
Component Analysis ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Kernel Principal Component Analysis ◽  
High Dimensional

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.

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