Principal Component Analysis Based on L1-Norm Maximization

By Nojun Kwak. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2008

750 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Control and Systems Engineering, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/f134f7976191ae4616342878dfbfc2ebe0c0c5c1

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In Analytical Chemistry

In Control and Systems Engineering

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Citations in the corpus

Efficient $l_{1}$ -Norm-Based Low-Rank Matrix Approximations for Large-Scale Problems Using Alternating Rectified Gradient Method (2015, background): “As an alternative, low-rank matrix approximation based on the l1-norm, which is more robust to outliers [1]–[3], [5], [6], has been proposed.”
Robust Computation of Linear Models by Convex Relaxation (2012, result): “], and it has been explored by many other authors [1,18,43,49,75].”
A Unifying Review of Deep and Shallow Anomaly Detection (2020, methodology): “For shallow methods, the problem is well studied, and we have many effective methods [5], [259], [326], [372], [374], [375], [471].”
Agnostic Estimation of Mean and Covariance (2016, background): “There have been attempts [25], [26] at achieving robustness by L1 minimization, but they don’t give any error bounds on the output produced.”
Robust (Semi) Nonnegative Graph Embedding (2014, background): “The function ‖ · ‖ denotes the norm of a matrix (or a vector).”
Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset (2015, methodology): “Experimental results [261] on the I2R dataset [217] show that LRMF-MOG outperforms SVD [111], RSL [371], PCP solved via IALM [45], CWM [206], PCA-l1 [206].”
Classification of Fruits Using Computer Vision and a Multiclass Support Vector Machine (2012, methodology): “Principal component analysis (PCA) is an efficient tool to reduce the dimensionality of a data set consisting of a large number of interrelated variables while retaining the most significant variations [17].”
On the Complexity of Robust PCA and ℓ1-norm Low-Rank Matrix Approximation (2015, background): “Although robust PCA and its variants are widely believed to be NP-hard (see, e.g., [26, 39]), it has, to the best of our knowledge, never been proved rigorously.”
Spatially Sparse Precoding in Millimeter Wave MIMO Systems (2013, background): “, the 1 norm of the diagonals [43], [67], [68].”
Few-Shot Adaptation of Generative Adversarial Networks (2020, methodology): “GANSpace applies PCA within the latent feature space of a pretrained GAN to discover semantically-interpretable directions for image editing in the latent space.”
Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision (2016, methodology): “…the classical singular value decomposition (SVD) under `2-norm loss, robust LRMF methods under `1-norm loss, and many probabilistic methods (Srebro et al, 2003; Buchanan and Fitzgibbon, 2005; Ke and Kanade, 2005; Mnih and Salakhutdinov, 2007; Kwak, 2008; Eriksson and Van Den Hengel, 2010).”
Robust Principal Component Analysis Based on Maximum Correntropy Criterion (2011, methodology): “Since the -norm based PCA is sensitive to outliers [ 10 ], -norm was applied in (1) to substitute the -norm.”
Statistical Inference for High-Dimensional Matrix-Variate Factor Models (2020, methodology): “In the community of image signal processing, model (1.1) and estimation methods such as (2 D ) 2 -PCA have been actively studied (Yang et al., 2004; Zhang and Zhou, 2005; Kong et al., 2005; Pang et al., 2008; Kwak, 2008; Li et al., 2010; Meng et al., 2012; Wang et al., 2015).”