Geometric representation of high dimension, low sample size data

2005 ◽  
Vol 67 (3) ◽  
pp. 427-444 ◽  
Author(s):  
Peter Hall ◽  
J. S. Marron ◽  
Amnon Neeman
Keyword(s):  
Sample Size ◽  
High Dimension ◽  
Geometric Representation ◽  
Size Data

Robust centroid based classification with minimum error rates for high dimension, low sample size data

2009 ◽  
Vol 139 (8) ◽  
pp. 2571-2580 ◽  
Author(s):  
Jiancheng Jiang ◽  
J.S. Marron ◽  
Xuejun Jiang
Keyword(s):  
Sample Size ◽  
High Dimension ◽  
Error Rates ◽  
Minimum Error ◽  
Size Data

scholarly journals On Perfect Clustering of High Dimension, Low Sample Size Data

2020 ◽  
Vol 42 (9) ◽  
pp. 2257-2272 ◽  
Author(s):  
Soham Sarkar ◽  
Anil K. Ghosh
Keyword(s):  
Sample Size ◽  
High Dimension ◽  
Size Data

scholarly journals On some graph-based two-sample tests for high dimension, low sample size data

2019 ◽  
Vol 109 (2) ◽  
pp. 279-306
Author(s):  
Soham Sarkar ◽  
Rahul Biswas ◽  
Anil K. Ghosh
Keyword(s):  
Sample Size ◽  
High Dimension ◽  
Size Data

Statistical inference for high-dimension, low-sample-size data

2017 ◽  
Vol 30 (2) ◽  
pp. 137-158
Author(s):  
Makoto Aoshima ◽  
Kazuyoshi Yata
Keyword(s):  
Sample Size ◽  
Statistical Inference ◽  
High Dimension ◽  
Size Data

scholarly journals Deep Neural Networks for High Dimension, Low Sample Size Data

2017 ◽  
Author(s):  
Bo Liu ◽  
Ying Wei ◽  
Yu Zhang ◽  
Qiang Yang
Keyword(s):  
Neural Networks ◽  
Sample Size ◽  
High Dimension ◽  
Deep Neural Networks ◽  
Genetic Data ◽  
High Dimensional ◽  
Large Sample Size ◽  
Prediction Problem ◽  
The Stability ◽  
Size Data

Deep neural networks (DNN) have achieved breakthroughs in applications with large sample size. However, when facing high dimension, low sample size (HDLSS) data, such as the phenotype prediction problem using genetic data in bioinformatics, DNN suffers from overfitting and high-variance gradients. In this paper, we propose a DNN model tailored for the HDLSS data, named Deep Neural Pursuit (DNP). DNP selects a subset of high dimensional features for the alleviation of overfitting and takes the average over multiple dropouts to calculate gradients with low variance. As the first DNN method applied on the HDLSS data, DNP enjoys the advantages of the high nonlinearity, the robustness to high dimensionality, the capability of learning from a small number of samples, the stability in feature selection, and the end-to-end training. We demonstrate these advantages of DNP via empirical results on both synthetic and real-world biological datasets.

scholarly journals Second Order Expansions for High-Dimension Low-Sample-Size Data Statistics in Random Setting

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1151
Author(s):  
Gerd Christoph ◽  
Vladimir V. Ulyanov
Keyword(s):  
Sample Size ◽  
High Dimension ◽  
Random Variable ◽  
Second Order ◽  
Multivariate Normal ◽  
Edgeworth Expansions ◽  
Sample Correlation ◽  
Data Statistics ◽  
Student’S T ◽  
Size Data

We consider high-dimension low-sample-size data taken from the standard multivariate normal distribution under assumption that dimension is a random variable. The second order Chebyshev–Edgeworth expansions for distributions of an angle between two sample observations and corresponding sample correlation coefficient are constructed with error bounds. Depending on the type of normalization, we get three different limit distributions: Normal, Student’s t-, or Laplace distributions. The paper continues studies of the authors on approximation of statistics for random size samples.

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