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Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are…

Optimization and Control · Mathematics 2024-11-11 Yuqing He , Guanyi Wang , Yu Yang

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

Privacy-preserving data mining has become an important topic. People have built several multi-party-computation (MPC)-based frameworks to provide theoretically guaranteed privacy, the poor performance of real-world algorithms have always…

Cryptography and Security · Computer Science 2021-05-18 Xiaoyu Fan , Guosai Wang , Kun Chen , Xu He , Wei Xu

We apply unsupervised machine learning techniques, mainly principal component analysis (PCA), to compare and contrast the phase behavior and phase transitions in several classical spin models - the square and triangular-lattice Ising…

Statistical Mechanics · Physics 2017-06-23 Wenjian Hu , Rajiv R. P. Singh , Richard T. Scalettar

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…

Machine Learning · Computer Science 2012-06-22 Alfredo Kalaitzis , Neil Lawrence

For multimode processes, one generally establishes local monitoring models corresponding to local modes. However, the significant features of previous modes may be catastrophically forgotten when a monitoring model for the current mode is…

Machine Learning · Statistics 2021-05-31 Jingxin Zhang , Donghua Zhou , Maoyin Chen

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…

Machine Learning · Statistics 2023-07-21 Debolina Paul , Saptarshi Chakraborty , Swagatam Das

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…

Machine Learning · Statistics 2011-06-23 Alfredo A. Kalaitzis , Neil D. Lawrence

Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests.…

Optimization and Control · Mathematics 2017-10-09 Chris Junchi Li , Mengdi Wang , Han Liu , Tong Zhang

Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…

Methodology · Statistics 2026-03-17 Liangliang Yuan , Lei Wang , Quan Kong , Liuhua Peng

Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…

Statistics Theory · Mathematics 2009-08-26 Arash A. Amini , Martin J. Wainwright

Principal Component Analysis (PCA) is a powerful and popular dimensionality reduction technique. However, due to its linear nature, it often fails to capture the complex underlying structure of real-world data. While Kernel PCA (kPCA)…

Machine Learning · Computer Science 2026-02-05 Thomas Uriot , Elise Chung

The study of stability and sensitivity of statistical methods or algorithms with respect to their data is an important problem in machine learning and statistics. The performance of the algorithm under resampling of the data is a…

Statistics Theory · Mathematics 2023-02-15 Haoyu Wang

We propose a novel exemplar selection approach based on Principal Component Analysis (PCA) and median sampling, and a neural network training regime in the setting of class-incremental learning. This approach avoids the pitfalls due to…

Machine Learning · Computer Science 2023-12-18 Sahil Nokhwal , Nirman Kumar

We consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute its computation. For this purpose, we reformulate the problem in the sparse…

Machine Learning · Statistics 2015-05-13 Ami Wiesel , Alfred O. Hero

Integrated principal components analysis, or iPCA, is an unsupervised learning technique for grouped vector data recently defined by Tang and Allen. Like PCA, iPCA computes new axes that best explain the variance of the data, but iPCA is…

Statistics Theory · Mathematics 2023-07-04 Cole Franks , Visu Makam

Probabilistic Component Latent Analysis (PLCA) is a statistical modeling method for feature extraction from non-negative data. It has been fruitfully applied to various research fields of information retrieval. However, the EM-solved…

Methodology · Statistics 2017-03-16 D. Cazau , G. Nuel

We develop a new principal components analysis (PCA) type dimension reduction method for binary data. Different from the standard PCA which is defined on the observed data, the proposed PCA is defined on the logit transform of the success…

Applications · Statistics 2010-11-17 Seokho Lee , Jianhua Z. Huang , Jianhua Hu

Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…

Computation · Statistics 2018-11-06 Victor Minden , Cengiz Pehlevan , Dmitri B. Chklovskii

Principal component analysis (PCA) is a widely used dimension reduction method, but its performance is known to be non-robust to outliers. Recently, product-PCA (PPCA) has been shown to possess the efficiency-loss free ordering-robustness…

Statistics Theory · Mathematics 2024-12-17 Hung Hung , Chi-Chun Yeh , Su-Yun Huang