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Phase transitions in sparse PCA [PDF]

2015 IEEE International Symposium on Information Theory (ISIT), 2015
We study optimal estimation for sparse principal component analysis when the number of non-zero elements is small but on the same order as the dimension of the data. We employ approximate message passing (AMP) algorithm and its state evolution to analyze what is the information theoretically minimal mean-squared error and the one achieved by AMP in the
Lesieur, Thibault, Krzakala, Florent, Zdeborova, Lenka +2 more
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Sparse PCA for compositional data

, 2014
A great number of procedures for sparse principal component analysis (PCA) were proposed in the last decade. However, they cannot be applied directly for PCA of compositional data (CoDa). We introduce a new procedure for sparse PCA which takes into account the additional constraints specific for CoDa.
Trendafilov N, GALLO, Michele
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Subexponential-Time Algorithms for Sparse PCA

Foundations of Computational Mathematics, 2023
We study the computational cost of recovering a unit-norm sparse principal component $x \in \mathbb{R}^n$ planted in a random matrix, in either the Wigner or Wishart spiked model (observing either $W + λxx^\top$ with $W$ drawn from the Gaussian orthogonal ensemble, or $N$ independent samples from $\mathcal{N}(0, I_n + βxx^\top)$, respectively).
Yunzi Ding +3 more
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Information-theoretically optimal sparse PCA [PDF]

2014 IEEE International Symposium on Information Theory, 2014
Sparse Principal Component Analysis (PCA) is a dimensionality reduction technique wherein one seeks a low-rank representation of a data matrix with additional sparsity constraints on the obtained representation. We consider two probabilistic formulations of sparse PCA: a spiked Wigner and spiked Wishart (or spiked covariance) model.
Yash Deshpande, Andrea Montanari
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Clustering Algorithm for High-Dimensional Data Under New Dimensionality Reduc-tion Criteria

Jisuanji kexue yu tansuo, 2020
In order to solve the problem that principal component analysis (PCA) algorithm can??t deal with the reduction of clustering accuracy after high dimensional data reduction, a new attribute space concept is proposed.
WAN Jing, WU Fan, HE Yunbin, LI Song
doaj +1 more source

Sparse PCA on fixed-rank matrices [PDF]

Mathematical Programming, 2022
Sparse PCA is the optimization problem obtained from PCA by adding a sparsity constraint on the principal components. Sparse PCA is NP-hard and hard to approximate even in the single-component case. In this paper we settle the computational complexity of sparse PCA with respect to the rank of the covariance matrix.
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Sparse PCA with Multiple Components [PDF]

Operations Research
Sparse PCA with Multiple Components As the dimension of data sets increases, analysts often rely on principal component analysis (PCA) to summarize data via a small number of informative principal components (PCs). Sparse PCA makes those directions easier to interpret by using only selected variables, but computing several sparse ...
Ryan Cory-Wright, Jean Pauphilet
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Performing Sparse Regularization and Dimension Reduction Simultaneously in Multimodal Data Fusion

Frontiers in Neuroscience, 2019
Collecting multiple modalities of neuroimaging data on the same subject is increasingly becoming the norm in clinical practice and research. Fusing multiple modalities to find related patterns is a challenge in neuroimaging analysis.
Zhengshi Yang +539 more
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Probabilistic power flow calculation using principal component analysis-based compressive sensing

Frontiers in Energy Research, 2023
The increasing scale of the injection of renewable energy has brought about great uncertainty to the operation of power grid. In this situation, probabilistic power flow (PPF) calculation has been introduced to mitigate the low accuracy of traditional ...
Tonghe Wang +4 more
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Effective Feature Extraction via Folded-Sparse-PCA for Hyperspectral Image Classification

, 2023
Effective Feature Extraction via Folded-Sparse-PCA for Hyperspectral Image ...
MI Afjal (15370294) +5 more
core +1 more source

principal component analysis
principal component analysis pca
pca

sparse representation
sparse principal component analysis
dimensionality reduction

compressive sensing
medicine