English
Related papers

Related papers: Joint Characterization of Multiscale Information i…

200 papers

In this paper, we consider clustering based on principal component analysis (PCA) for high-dimension, low-sample-size (HDLSS) data. We give theoretical reasons why PCA is effective for clustering HDLSS data. First, we derive a geometric…

Statistics Theory · Mathematics 2015-03-17 Kazuyoshi Yata , Makoto Aoshima

Principal Component Analysis (PCA) is well known for its capability of dimension reduction and data compression. However, when using PCA for compressing/reconstructing images, images need to be recast to vectors. The vectorization of images…

Computer Vision and Pattern Recognition · Computer Science 2021-05-04 Liang Liao , Xuechun Zhang , Xinqiang Wang , Sen Lin , Xin Liu

Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…

Computational Engineering, Finance, and Science · Computer Science 2021-06-09 Felipe L. Gewers , Gustavo R. Ferreira , Henrique F. de Arruda , Filipi N. Silva , Cesar H. Comin , Diego R. Amancio , Luciano da F. Costa

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…

Computation · Statistics 2016-01-29 Qiaoya Zhang , Yiyuan She

Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be…

Machine Learning · Statistics 2012-10-29 Youwei Zhang , Laurent El Ghaoui

Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration…

Methodology · Statistics 2021-04-06 Tiffany M. Tang , Genevera I. Allen

Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…

Machine Learning · Statistics 2021-09-10 Shaojie Xu , Joel Vaughan , Jie Chen , Agus Sudjianto , Vijayan Nair

Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method…

Machine Learning · Computer Science 2021-01-15 Yanjun Li , Bihan Wen , Hao Cheng , Yoram Bresler

Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting…

Methodology · Statistics 2015-06-16 A. A. Akinduko , A. N. Gorban

Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…

Machine Learning · Computer Science 2021-11-30 Arpita Gang , Waheed U. Bajwa

Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…

Machine Learning · Statistics 2019-08-21 Genevera I. Allen , Michael Weylandt

High dimensional data has introduced challenges that are difficult to address when attempting to implement classical approaches of statistical process control. This has made it a topic of interest for research due in recent years. However,…

Applications · Statistics 2019-04-23 Mohammad Nabhan , Yajun Mei , Jianjun Shi

t-Stochastic Neighbor Embedding (t-SNE) is a non-parametric data visualization method in classical machine learning. It maps the data from the high-dimensional space into a low-dimensional space, especially a two-dimensional plane, while…

Quantum Physics · Physics 2022-02-10 Yoshiaki Kawase , Kosuke Mitarai , Keisuke Fujii

In this paper, we tackle a significant challenge in PCA: heterogeneity. When data are collected from different sources with heterogeneous trends while still sharing some congruency, it is critical to extract shared knowledge while retaining…

Machine Learning · Computer Science 2025-08-25 Naichen Shi , Raed Al Kontar

Machine learning (ML) methods have proved to be a very successful tool in physical sciences, especially when applied to experimental data analysis. Artificial intelligence is particularly good at recognizing patterns in high dimensional…

Materials Science · Physics 2022-08-19 T. Tula , G. Möller , J. Quintanilla , S. R. Giblin , A. D. Hillier , E. E. McCabe , S. Ramos , D. S. Barker , S. Gibson

Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants…

Machine Learning · Statistics 2014-05-14 David Lopez-Paz , Suvrit Sra , Alex Smola , Zoubin Ghahramani , Bernhard Schölkopf

Predictive modeling from high-dimensional genomic data is often preceded by a dimension reduction step, such as principal components analysis (PCA). However, the application of PCA is not straightforward for multi-source data, wherein…

Quantitative Methods · Quantitative Biology 2017-07-19 Adam Kaplan , Eric F. Lock

Principal Component Analysis (PCA) is an important tool of dimension reduction especially when the dimension (or the number of variables) is very high. Asymptotic studies where the sample size is fixed, and the dimension grows [i.e., High…

Statistics Theory · Mathematics 2009-11-20 Sungkyu Jung , J. S. Marron

This paper addresses the challenge of spectral-spatial feature extraction for hyperspectral image classification by introducing a novel tensor-based framework. The proposed approach incorporates circular convolution into a tensor structure…

Computer Vision and Pattern Recognition · Computer Science 2024-12-10 Yuemei Ren , Liang Liao , Stephen John Maybank , Yanning Zhang , Xin Liu

Low-dimensional embeddings and visualizations are an indispensable tool for analysis of high-dimensional data. State-of-the-art methods, such as tSNE and UMAP, excel in unveiling local structures hidden in high-dimensional data and are…

Machine Learning · Computer Science 2023-02-01 Jonas Fischer , Rebekka Burkholz , Jilles Vreeken