Incremental Singular Value Decomposition of Uncertain Data with Missing Values

By Matthew Brand. 2002

597 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering

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Citations in the corpus

The Ideal Continual Learner: An Agent That Never Forgets (2023, methodology): “This is potentially numerically unstable; as Brand (2006) later commented:”
Face transfer with multilinear models (2005, methodology): “, PPCA [Tipping and Bishop 1999], SPCA [Roweis 1997], or ISVD [Brand 2002]).”
A PCA-based similarity measure for multivariate time series (2004, methodology): “On a PC witha 800MHz Pentium III CPU, a 64 × 64 matrix A can be decomposed in less than 0.04 second withone line MATLAB code, [a,b,c]=svd(A).”
Streaming PCA and Subspace Tracking: The Missing Data Case (2018, methodology): “Brand [15] replaces Sn−1 with λSn−1 where 0 λ < 1 is a scalar weight that diminishes the influence of previous singular values.”
Robust Rotation and Translation Estimation in Multiview Reconstruction (2007, methodology): “Note that the most time consuming operation is SVD applied to a 6 × 6 matrix irrespective of the number of points.”
A survey of appearance models in visual object tracking (2013, unknown): “Unlike the aforementioned robust PCA algorithm based on weighted residual errors, the incremental subspace learning algorithms [Levy and Lindenbaum 2000; Brand 2002] utilize incremental singular value decomposition (SVD) to obtain a closed-form solution to subspace learning.”
A Survey of Multi-View Representation Learning (2016, unknown): “Further, Golub and Zha [56] also provide a classical algorithm for computing CCA by first QR decomposition of the data matrices which whitens the data and then an SVD of the whitened covariance matrix.”
Person Identification Using Full-Body Motion and Anthropometric Biometrics from Kinect Videos (2012, background): “Since the computation complexity of the SVD and SVM algorithms are O(pq2 + p(2)q + q(3)) [21] and O(q2) [22] respectively, the computational complexity of the action classifier ≈ O(q3) where q = 2mn.”
Incremental Learning for Visual Tracking (2004, methodology): “Nume rous algorithms have been developed to update eigenbasis from a time-varying covaria nce matrix as more data arrive [6] [8] [11] [5].”
Bayesian reasoning and machine learning (2012, unknown): “When the matrix X is too large to store in memory, online SVD methods are available[52].”
Online Machine Learning in Big Data Streams (2018, methodology): “cipal component analysis (PCA) is a powerful tool for dimensionality reduction [128] based on matrix factorization. Online variants are based on ideas to incrementally update the matrix decomposition [37, 106, 36]. The ﬁrst PCA algorithms suitable for online learning are based on neural networks [17”
Incremental Learning for Robust Visual Tracking (2008, methodology): “Numerous, more-sophisticated algorithms have been developed to efficiently update an eigenbasis as more data arrive (Golub and Van Loan 1996; Hall et al. 1998; Levy and Lindenbaum 2000; Brand 2002).”
Subspace video stabilization (2011, methodology): “For an incomplete matrix, factorization is a nonlinear problem, but well-studied [Brand 2002; Buchanan and Fitzgibbon 2005; Chen 2008].”
Generalized Low Rank Approximations of Matrices (2004, methodology): “Several incremental algorithms have been proposed in the past ( Brand, 2002 ; G u &”