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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…

机器学习 · 计算机科学 2021-11-30 Arpita Gang , Waheed U. Bajwa

Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…

统计理论 · 数学 2017-10-30 Raphael Hauser , Raul Kangro , Jüri Lember , Heinrich Matzinger

Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further…

In multiple-input multiple-output communications, channel estimation is paramount to keep base stations and users on track. This paper proposes a novel PCA-based-principal component analysis-channel estimation approach for MIMO orthogonal…

Principal component analysis (PCA) is known to be sensitive to outliers, so that various robust PCA variants were proposed in the literature. A recent model, called REAPER, aims to find the principal components by solving a convex…

数值分析 · 数学 2021-03-19 Robert Beinert , Gabriele Steidl

Retrieval-Augmented Generation (RAG) has emerged as a powerful paradigm for grounding large language models in external knowledge sources, improving the precision of agents responses. However, high-dimensional language model embeddings,…

机器学习 · 计算机科学 2025-04-14 Arman Khaledian , Amirreza Ghadiridehkordi , Nariman Khaledian

Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however,…

计算机视觉与模式识别 · 计算机科学 2010-02-11 Mingyu Fan , Nannan Gu , Hong Qiao , Bo Zhang

Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…

机器学习 · 统计学 2019-10-28 Jean P. Chereau , Bruno Scalzo Dees , Danilo P. Mandic

Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected…

机器学习 · 统计学 2022-09-05 Michael Weylandt , George Michailidis

Principal component analysis (PCA) is a classical feature extraction method, but it may be adversely affected by outliers, resulting in inaccurate learning of the projection matrix. This paper proposes a robust method to estimate both the…

机器学习 · 计算机科学 2024-08-23 Yingzhuo Deng , Ke Hu , Bo Li , Yao Zhang

This paper presents a method for detecting mispronunciations with the aim of improving Computer Assisted Language Learning (CALL) tools used by foreign language learners. The algorithm is based on Principle Component Analysis (PCA). It is…

声音 · 计算机科学 2016-02-29 Zhenhao Ge , Sudhendu R. Sharma , Mark J. T. Smith

Multivariate binary data is becoming abundant in current biological research. Logistic principal component analysis (PCA) is one of the commonly used tools to explore the relationships inside a multivariate binary data set by exploiting the…

统计方法学 · 统计学 2020-10-15 Yipeng Song , Johan A. Westerhuis , Age K. Smilde

Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…

统计计算 · 统计学 2011-12-23 Nathan Halko , Per-Gunnar Martinsson , Yoel Shkolnisky , Mark Tygert

Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…

机器学习 · 统计学 2023-07-21 Debolina Paul , Saptarshi Chakraborty , Swagatam Das

In this paper, we develop an algorithm for federated principal component analysis (PCA) with emphases on both communication efficiency and data privacy. Generally speaking, federated PCA algorithms based on direct adaptations of classic…

最优化与控制 · 数学 2024-10-29 Lei Wang , Xin Liu , Yin Zhang

We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems,…

机器学习 · 计算机科学 2020-06-09 Maksim Elizarev , Andrei Mukhin , Aleksey Khlyupin

Principal component analysis (PCA) is a well-established method commonly used to explore and visualise data. A classical PCA model is the fixed effect model where data are generated as a fixed structure of low rank corrupted by noise. Under…

统计方法学 · 统计学 2013-05-13 Marie Verbanck , Julie Josse , François Husson

Principal component regression (PCR) is a two-stage procedure: the first stage performs principal component analysis (PCA) and the second stage constructs a regression model whose explanatory variables are replaced by principal components…

机器学习 · 统计学 2021-11-22 Shuichi Kawano

At the crossway of machine learning and data analysis, anomaly detection aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…

统计方法学 · 统计学 2025-06-06 Romain Valla , Pavlo Mozharovskyi , Florence d'Alché-Buc

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…

机器学习 · 统计学 2022-08-18 Alexander Ritchie , Laura Balzano , Daniel Kessler , Chandra S. Sripada , Clayton Scott