English
Related papers

Related papers: L1-norm Principal-Component Analysis of Complex Da…

200 papers

We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can…

Methods for supervised principal component analysis (SPCA) aim to incorporate label information into principal component analysis (PCA), so that the extracted features are more useful for a prediction task of interest. Prior work on SPCA…

Machine Learning · Statistics 2022-08-18 Alexander Ritchie , Laura Balzano , Daniel Kessler , Chandra S. Sripada , Clayton Scott

Principal Component Analysis (PCA) finds the best linear representation of data, and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that…

Optimization and Control · Mathematics 2019-12-24 Raphael A. Hauser , Armin Eftekhari

Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…

Methodology · Statistics 2026-02-10 Enes Makalic , Daniel F. Schmidt

Robust Principal Component Analysis (RPCA) via rank minimization is a powerful tool for recovering underlying low-rank structure of clean data corrupted with sparse noise/outliers. In many low-level vision problems, not only it is known…

Computer Vision and Pattern Recognition · Computer Science 2019-02-18 Tae-Hyun Oh , Yu-Wing Tai , Jean-Charles Bazin , Hyeongwoo Kim , In So Kweon

It is well known that Sparse PCA (Sparse Principal Component Analysis) is NP-hard to solve exactly on worst-case instances. What is the complexity of solving Sparse PCA approximately? Our contributions include: 1) a simple and efficient…

Machine Learning · Statistics 2015-07-22 Siu On Chan , Dimitris Papailiopoulos , Aviad Rubinstein

We study the problem of high-dimensional Principal Component Analysis (PCA) with missing observations. In simple, homogeneous missingness settings with a noise level of constant order, we show that an existing inverse-probability weighted…

Methodology · Statistics 2019-07-01 Ziwei Zhu , Tengyao Wang , Richard J. Samworth

In the context of sparse principal component detection, we bring evidence towards the existence of a statistical price to pay for computational efficiency. We measure the performance of a test by the smallest signal strength that it can…

Statistics Theory · Mathematics 2013-04-29 Quentin Berthet , Philippe Rigollet

Most high-dimensional matrix recovery problems are studied under the assumption that the target matrix has certain intrinsic structures. For image data related matrix recovery problems, approximate low-rankness and smoothness are the two…

Machine Learning · Statistics 2021-04-08 Long Feng , Junhui Wang

Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…

Methodology · Statistics 2026-03-24 Daning Bi , Le Chang , Yanrong Yang

This paper uses network packet capture data to demonstrate how Robust Principal Component Analysis (RPCA) can be used in a new way to detect anomalies which serve as cyber-network attack indicators. The approach requires only a few…

Cryptography and Security · Computer Science 2018-01-08 Randy Paffenroth , Kathleen Kay , Les Servi

We propose a kernel-PCA based method to detect anomaly in chemical sensors. We use temporal signals produced by chemical sensors to form vectors to perform the Principal Component Analysis (PCA). We estimate the kernel-covariance matrix of…

Signal Processing · Electrical Eng. & Systems 2022-09-30 Hongyi Pan , Diaa Badawi , Ishaan Bassi , Sule Ozev , Ahmet Enis Cetin

Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which…

Machine Learning · Computer Science 2017-05-04 Zan Gao , Guotai Zhang , Feiping Nie , Hua Zhang

The network traffic matrix is widely used in network operation and management. It is therefore of crucial importance to analyze the components and the structure of the network traffic matrix, for which several mathematical approaches such…

Networking and Internet Architecture · Computer Science 2015-03-19 Zhe Wang , Kai Hu , Ke Xu , Baolin Yin , Xiaowen Dong

Principal component analysis (PCA) is a popular tool for linear dimensionality reduction and feature extraction. Kernel PCA is the nonlinear form of PCA, which better exploits the complicated spatial structure of high-dimensional features.…

Computer Vision and Pattern Recognition · Computer Science 2014-09-02 Quan Wang

Principal component analysis and factor analysis are fundamental multivariate analysis methods. In this paper a unified framework to connect them is introduced. Under a general latent variable model, we present matrix optimization problems…

Methodology · Statistics 2024-05-31 Shifeng Xiong

STEM XEDS spectrum images can be drastically denoised by application of the principal component analysis (PCA). This paper looks inside the PCA workflow step by step on an example of a complex semiconductor structure consisting of a number…

Image and Video Processing · Electrical Eng. & Systems 2019-10-16 Pavel Potapov , Axel Lubk

Singular Value Decomposition (and Principal Component Analysis) is one of the most widely used techniques for dimensionality reduction: successful and efficiently computable, it is nevertheless plagued by a well-known, well-documented…

Machine Learning · Computer Science 2011-01-04 Huan Xu , Constantine Caramanis , Sujay Sanghavi

Principal component analysis (PCA) is widely used to analyze high-dimensional data, but it is very sensitive to outliers. Robust PCA methods seek fits that are unaffected by the outliers and can therefore be trusted to reveal them. FastHCS…

Methodology · Statistics 2015-09-25 E. Schmitt , K. Vakili

A data table which is arranged according to two factors can often be considered as a compositional table. An example is the number of unemployed people, split according to gender and age classes. Analyzed as compositions, the relevant…

Methodology · Statistics 2019-04-12 Julie Rendlová , Karel Hron , Kamila Fačevicová , Peter Filzmoser