Supervised t-Distributed Stochastic Neighbor Embedding for Data Visualization and Classification

2020 ◽  
Author(s):  
Yichen Cheng ◽  
Xinlei Wang ◽  
Yusen Xia
Keyword(s):  
Dimension Reduction ◽  
Sample Size ◽  
High Dimensional Data ◽  
Machine Learning Algorithms ◽  
High Dimensional ◽  
Data Sets ◽  
Wearable Electronics ◽  
Processing Technologies ◽  
Leibler Divergence ◽  
Supervised Dimension Reduction

We propose a novel supervised dimension-reduction method called supervised t-distributed stochastic neighbor embedding (St-SNE) that achieves dimension reduction by preserving the similarities of data points in both feature and outcome spaces. The proposed method can be used for both prediction and visualization tasks with the ability to handle high-dimensional data. We show through a variety of data sets that when compared with a comprehensive list of existing methods, St-SNE has superior prediction performance in the ultrahigh-dimensional setting in which the number of features p exceeds the sample size n and has competitive performance in the p ≤ n setting. We also show that St-SNE is a competitive visualization tool that is capable of capturing within-cluster variations. In addition, we propose a penalized Kullback–Leibler divergence criterion to automatically select the reduced-dimension size k for St-SNE. Summary of Contribution: With the fast development of data collection and data processing technologies, high-dimensional data have now become ubiquitous. Examples of such data include those collected from environmental sensors, personal mobile devices, and wearable electronics. High-dimensionality poses great challenges for data analytics routines, both methodologically and computationally. Many machine learning algorithms may fail to work for ultrahigh-dimensional data, where the number of the features p is (much) larger than the sample size n. We propose a novel method for dimension reduction that can (i) aid the understanding of high-dimensional data through visualization and (ii) create a small set of good predictors, which is especially useful for prediction using ultrahigh-dimensional data.

scholarly journals An analytic approach for interpretable predictive models in high dimensional data, in the presence of interactions with exposures

2017 ◽  
Author(s):  
Sahir Rai Bhatnagar ◽  
Yi Yang ◽  
Budhachandra Khundrakpam ◽  
Alan C Evans ◽  
Mathieu Blanchette ◽  
...  
Keyword(s):  
Variable Selection ◽  
Dimension Reduction ◽  
High Dimensional Data ◽  
Predictive Modelling ◽  
Original Data ◽  
High Dimensional ◽  
Data Sets ◽  
Imaging Studies ◽  
Modelling Framework ◽  
Network Properties

AbstractPredicting a phenotype and understanding which variables improve that prediction are two very challenging and overlapping problems in analysis of high-dimensional data such as those arising from genomic and brain imaging studies. It is often believed that the number of truly important predictors is small relative to the total number of variables, making computational approaches to variable selection and dimension reduction extremely important. To reduce dimensionality, commonly-used two-step methods first cluster the data in some way, and build models using cluster summaries to predict the phenotype.It is known that important exposure variables can alter correlation patterns between clusters of high-dimensional variables, i.e., alter network properties of the variables. However, it is not well understood whether such altered clustering is informative in prediction. Here, assuming there is a binary exposure with such network-altering effects, we explore whether use of exposure-dependent clustering relationships in dimension reduction can improve predictive modelling in a two-step framework. Hence, we propose a modelling framework called ECLUST to test this hypothesis, and evaluate its performance through extensive simulations.With ECLUST, we found improved prediction and variable selection performance compared to methods that do not consider the environment in the clustering step, or to methods that use the original data as features. We further illustrate this modelling framework through the analysis of three data sets from very different fields, each with high dimensional data, a binary exposure, and a phenotype of interest. Our method is available in the eclust CRAN package.

Mahalanobis distance informed by clustering

2018 ◽  
Vol 8 (2) ◽  
pp. 377-406
Author(s):  
Almog Lahav ◽  
Ronen Talmon ◽  
Yuval Kluger
Keyword(s):  
Mahalanobis Distance ◽  
High Dimensional Data ◽  
Hidden Variables ◽  
Real Data ◽  
Risk Groups ◽  
High Dimensional ◽  
Data Sets ◽  
Kaplan Meier ◽  
Data Points ◽  
Survival Plot

Abstract A fundamental question in data analysis, machine learning and signal processing is how to compare between data points. The choice of the distance metric is specifically challenging for high-dimensional data sets, where the problem of meaningfulness is more prominent (e.g. the Euclidean distance between images). In this paper, we propose to exploit a property of high-dimensional data that is usually ignored, which is the structure stemming from the relationships between the coordinates. Specifically, we show that organizing similar coordinates in clusters can be exploited for the construction of the Mahalanobis distance between samples. When the observable samples are generated by a nonlinear transformation of hidden variables, the Mahalanobis distance allows the recovery of the Euclidean distances in the hidden space. We illustrate the advantage of our approach on a synthetic example where the discovery of clusters of correlated coordinates improves the estimation of the principal directions of the samples. Our method was applied to real data of gene expression for lung adenocarcinomas (lung cancer). By using the proposed metric we found a partition of subjects to risk groups with a good separation between their Kaplan–Meier survival plot.

scholarly journals Scalable hierarchical clustering by composition rank vector encoding and tree structure

2020 ◽  
Author(s):  
Xiao Lai ◽  
Pu Tian
Keyword(s):  
Machine Learning ◽  
Hierarchical Clustering ◽  
Clustering Algorithm ◽  
High Dimensional Data ◽  
Machine Learning Algorithms ◽  
Tree Structure ◽  
Supervised Machine Learning ◽  
High Dimensional ◽  
Rank Vector ◽  
Nonlinear Correlations

AbstractSupervised machine learning, especially deep learning based on a wide variety of neural network architectures, have contributed tremendously to fields such as marketing, computer vision and natural language processing. However, development of un-supervised machine learning algorithms has been a bottleneck of artificial intelligence. Clustering is a fundamental unsupervised task in many different subjects. Unfortunately, no present algorithm is satisfactory for clustering of high dimensional data with strong nonlinear correlations. In this work, we propose a simple and highly efficient hierarchical clustering algorithm based on encoding by composition rank vectors and tree structure, and demonstrate its utility with clustering of protein structural domains. No record comparison, which is an expensive and essential common step to all present clustering algorithms, is involved. Consequently, it achieves linear time and space computational complexity hierarchical clustering, thus applicable to arbitrarily large datasets. The key factor in this algorithm is definition of composition, which is dependent upon physical nature of target data and therefore need to be constructed case by case. Nonetheless, the algorithm is general and applicable to any high dimensional data with strong nonlinear correlations. We hope this algorithm to inspire a rich research field of encoding based clustering well beyond composition rank vector trees.

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.

scholarly journals Double-Arc Parallel Coordinates and its Axes re-Ordering Methods

2020 ◽  
Vol 25 (4) ◽  
pp. 1376-1391
Author(s):  
Liangfu Lu ◽  
Wenbo Wang ◽  
Zhiyuan Tan
Keyword(s):  
High Dimensional Data ◽  
Two Dimensions ◽  
High Dimensional ◽  
Data Sets ◽  
Parallel Coordinates ◽  
Practical Applications ◽  
Data Volume ◽  
Visual Clutter ◽  
Correlation Information ◽  
Value Decomposition

AbstractThe Parallel Coordinates Plot (PCP) is a popular technique for the exploration of high-dimensional data. In many cases, researchers apply it as an effective method to analyze and mine data. However, when today’s data volume is getting larger, visual clutter and data clarity become two of the main challenges in parallel coordinates plot. Although Arc Coordinates Plot (ACP) is a popular approach to address these challenges, few optimization and improvement have been made on it. In this paper, we do three main contributions on the state-of-the-art PCP methods. One approach is the improvement of visual method itself. The other two approaches are mainly on the improvement of perceptual scalability when the scale or the dimensions of the data turn to be large in some mobile and wireless practical applications. 1) We present an improved visualization method based on ACP, termed as double arc coordinates plot (DACP). It not only reduces the visual clutter in ACP, but use a dimension-based bundling method with further optimization to deals with the issues of the conventional parallel coordinates plot (PCP). 2)To reduce the clutter caused by the order of the axes and reveal patterns that hidden in the data sets, we propose our first dimensional reordering method, a contribution-based method in DACP, which is based on the singular value decomposition (SVD) algorithm. The approach computes the importance score of attributes (dimensions) of the data using SVD and visualize the dimensions from left to right in DACP according the score in SVD. 3) Moreover, a similarity-based method, which is based on the combination of nonlinear correlation coefficient and SVD algorithm, is proposed as well in the paper. To measure the correlation between two dimensions and explains how the two dimensions interact with each other, we propose a reordering method based on non-linear correlation information measurements. We mainly use mutual information to calculate the partial similarity of dimensions in high-dimensional data visualization, and SVD is used to measure global data. Lastly, we use five case scenarios to evaluate the effectiveness of DACP, and the results show that our approaches not only do well in visualizing multivariate dataset, but also effectively alleviate the visual clutter in the conventional PCP, which bring users a better visual experience.

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