Analysis of a complex of statistical variables into principal components.

By H. Hotelling. 1933

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In Optimization & Training

Citations in the corpus

UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction (2018, methodology): “Algorithms such as PCA [8], MDS [9], and Sammon mapping [20] fall into the former category while t-SNE [15] [26], Isomap [24], LargeVis [22], Laplacian eigenmaps [1] [2], diffusion maps [4], NeRV [28], and JSE [12] all fall into the latter category.”
Representation Learning: A Review and New Perspectives (2012, methodology): “c, auto-encoder, and manifold learning) discussed here. Principal Components Analysis We will use probably the oldest feature extraction algorithm, principal components analysis (PCA) (Pearson, 1901; Hotelling, 1933), to illustrate the probabilistic, auto-encoder and manifold views of representation”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “Many classical learning algorithms—such as the perceptron (Rosenblatt 1958), support vector machine (SVM) (Cortes and Vapnik 1995), and principal component analysis (PCA) (Pearson 1901, Hotelling 1933)—employ data instances, e.g., x,x′ ∈ X , only through an inner product 〈x,x′〉, which basically is a”
Interpreting Deep Classifier by Visual Distillation of Dark Knowledge (2018, methodology): “Classical methods from statistics include principal components analysis (Hotelling, 1933) and multidimensional scaling (Cox & Cox, 2000).”
A practical tutorial on autoencoders for nonlinear feature fusion: Taxonomy, models, software and guidelines (2018, methodology): “Principal component analysis is a statistical technique developed geometrically by Pearson [29] and algebraically by Hotelling [30].”
Principal Component Analysis (2003, positive): “The first two PCs, PC1 and PC2, using the coefficients defined by the first two eigenvectors, given in (1) and (2), were used in Fig.”
Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks (2019, methodology): “Each node feature is generated by extracting bag-of-word features from the product descriptions followed by Principal Component Analysis [7] to reduce the dimension to be 100.”
Bayesian group factor analysis with structured sparsity (2016, methodology): “For example, in structured sparse PCA, the loading matrix is constrained to have specific patterns (Jenatton et al., 2010).”
Guided Variational Autoencoder for Disentanglement Learning (2020, methodology): “From a different angle, principal component analysis (PCA) family [22, 27, 7] can also be viewed as representation learning.”
Variational learning for latent Gaussian model of discrete data (2012, background): “It can also be interpreted as the orthogonal projection of the data vectors onto a lower dimensional space such that the variance of the projection is maximized [Hotelling, 1933].”
Signed Laplacian Embedding for Supervised Dimension Reduction (2014, methodology): “Zhang et al. (2009) proposed a patch alignment framework which summarizes various dimension reduction algorithms into one uniﬁed formulation, such as PCA (Hotelling 1933), LLE (Roweis and Saul 2000), LPP (He and Niyogi 2004), and DLA (Zhang et al. 2009).”
Convergence Rates of the POD–Greedy Method (2013, methodology): “This method was ori ginally introduced in probability theory as Karhunen-Loeve transformation [12, 15], or ev en earlier in statistics as Hotelling transformation [9].”
Introduction to Data Compression (2005, methodology): “The first transform to provide decorrelation for discrete data was presented by Hotelling [179] in the Journal of Educational Psychology in 1933.”
Diagnosing network-wide traffic anomalies (2004, methodology): “PCA is a coordinate transformation method that maps a given set of data points onto new axes [ 15 ].”
PPCA-Based Missing Data Imputation for Traffic Flow Volume: A Systematical Approach (2009, methodology): “If the likelihood function can correctly be estimated from the sampled data, then the missing data can be estimated according to the obtained likelihood function [25]–[29].”
Compressive Sensing and Low-Rank Libraries for Classification of Bifurcation Regimes in Nonlinear Dynamical Systems (2013, methodology): “POD is sometimes referred to as principal component analysis [38], the Karhunen–Loève decomposition, empirical orthogonal functions [33], or the Hotelling transform [27].”