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Two-Dimensional Quaternion PCA and Sparse PCA
IEEE Transactions on Neural Networks and Learning Systems, 2019Benefited from quaternion representation that is able to encode the cross-channel correlation of color images, quaternion principle component analysis (QPCA) was proposed to extract features from color images while reducing the feature dimension. A quaternion covariance matrix (QCM) of input samples was constructed, and its eigenvectors were derived to
Xiaolin Xiao, Yicong Zhou
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Vector $l_0$ Sparse Variable PCA
IEEE Transactions on Signal Processing, 2011Principal component analysis (PCA) achieves dimension reduction by replacing the original measured variables with a smaller set of derived variables called the principal components. Sparse PCA improves this with sparsity. There are two kinds of sparse PCA; sparse loading PCA (slPCA) which keeps all the measured variables but zeroes out some of their ...
Magnus O Ulfarsson, Victor Solo
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PCA in Sparse Data-Dependent Noise
2018 IEEE International Symposium on Information Theory (ISIT), 2018In recent work, we obtained finite sample guarantees for the problem of Principal Component Analysis (PCA) in nonisotropic and data-dependent noise. In this work, we study an important special case of this: the problem of PCA in sparse data-dependent noise with the noise depending linearly on the signal (true data) at each time.
Namrata Vaswani, Praneeth Narayanamurthy
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Sparse PCA by iterative elimination algorithm
Advances in Computational Mathematics, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yang Wang 0020, Qiang Wu 0003
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Sparse Bayesian Learning for Robust PCA
ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019In this paper, we propose a new Bayesian model to solve the Robust PCA problem - recovering the underlying low-rank matrix and sparse matrix from their noisy compositions. We first derive and analyze a new objective function, which is proven to be equivalent to the fundamental minimizing "rank+sparsity" objective.
Jing Liu 0009 +2 more
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Comparing Classical and Robust Sparse PCA
2013The main drawback of principal component analysis (PCA) especially for applications in high dimensions is that the extracted components are linear combinations of all input variables. To facilitate the interpretability of PCA various sparse methods have been proposed recently.
Valentin Todorov, Peter Filzmoser
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Recovering PCA and sparse PCA via hybrid-\((\ell_1,\ell_2)\) sparse sampling of data elements
J. Mach. Learn. Res., 2017Summary: This paper addresses how well we can recover a data matrix when only given a few of its elements. We present a randomized algorithm that element-wise sparsifies the data, retaining only a few of its entries. Our new algorithm independently samples the data using probabilities that depend on both squares (\(\ell_2\) sampling) and absolute ...
Abhisek Kundu +2 more
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A communication-efficient and privacy-aware distributed algorithm for sparse PCA
Computational Optimization and Applications, 2023Xin Liu
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