Relations Between Two Sets of Variates

By H. Hotelling. 1936

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Citations in the corpus

The Bottom-up Evolution of Representations in the Transformer: A Study with Machine Translation and Language Modeling Objectives (2019, methodology): “To measure the inﬂuence of a token at l th layer on other tokens, we measure PWCCA distance between two versions of representations of other tokens in a sentence: ﬁrst after encoding as usual, second when encoding ﬁrst l − 1 layers as usual and masking out the inﬂuencing token at the l th layer.”
Fine-Grained Image Classification via Combining Vision and Language (2017, methodology): “Zhai et al. [24] propose to learn projection functions by the metric learning, and this method is further improved as Joint Representation Learning (JRL) [ 25] by adding other information such as semantic categories and semi-supervised information.”
Framing Image Description as a Ranking Task: Data, Models and Evaluation Metrics (2013, methodology): “KCCA is an extension of Canonical Correlation Analysis (Hotelling, 1936), which takes training data consisting of pairs of corresponding items x i , y i drawn from two different feature spaces (x i ∈ X , y i ∈ Y), and finds maximally correlated linear projections αx and βy of both sets of items into”
Flickr30k Entities: Collecting Region-to-Phrase Correspondences for Richer Image-to-Sentence Models (2015, methodology): “…and Fei-Fei 2015; Kiros et al. 2014; Mao et al. 2015b), using state-of-the-art text and image features with Canonical Correlation Analysis (CCA) (Hotelling 1936) continues to produce remarkable results (Gong et al. 2014b; Klein et al. 2014; Lev et al. 2015), and is also much faster to train…”
A Multi-View Embedding Space for Modeling Internet Images, Tags, and Their Semantics (2012, methodology): “…al., 2004; Hwang and Grauman, 2010, 2011; Rasiwasia et al., 2010) rely on canonical correlation analysis (CCA), a classic technique that maps two views, given by visual and and textual features, into a common latent space where the correlation between the two views is maximized (Hotelling, 1936).”
The Incomplete Rosetta Stone problem: Identifiability results for Multi-view Nonlinear ICA (2019, background): “At a high level, the model we consider in Section 3.2 is to CCA as nonlinear ICA is to PCA.”
Deep Multimodal Feature Analysis for Action Recognition in RGB+D Videos (2016, methodology): “As a baseline to the proposed method to perform the shared-specific analysis of the RGB+D inputs, we combined canonical correlation analysis (CCA) [19, 16] and reconstruction independent component analysis (RICA) [28], to extract correlated and independent components of input features.”
A Survey on Multi-view Learning (2013, methodology): “Hotelling (1936) introduced canonical correlation analysis (CCA) to describe the linear relation between two views which aims to compute a low-dimensional A Survey on Multi-view Learning shared embedding of both views of variables such that the correlations among the variables between the two views…”
Fisher Vectors Derived from Hybrid Gaussian-Laplacian Mixture Models for Image Annotation (2014, methodology): “This set is converted to a Fisher Vector based on one of the distributions: GMM, LMM, or HGLMM. Text to image matching is done using the Canonical Correlations Analysis algorithm [11].”
Kernel methods in machine learning (2007, neutral): “Given two samples X,Y , canonical correlation analysis (Hotelling [70]) aims at finding directions of projection u, v such that the correlation coefficient between X and Y is maximized.”
Learning Two-Branch Neural Networks for Image-Text Matching Tasks (2017, background): “One of the most popular baselines for image-text embedding is Canonical Correlation Analysis (CCA), which finds linear projections that maximize the correlation between projected vectors from the two views [21], [22].”
Learning Invariant Feature Spaces to Transfer Skills with Reinforcement Learning (2017, background): “We also compare to kernel-CCA (KCCA) which uses a kernel matrix to perform CCA, allowing the method to use an implied non-linear feature mapping of the data.”
Pattern recognition (1974, neutral): “In practice, the basic LBP labels are not much used because of the high dimensionality of the descriptor when the number of neighbors is large.”
Weakly-Supervised Alignment of Video with Text (2015, methodology): “Much of the work on joint representations of text and images makes use of canonical correlation analysis (CCA) [19].”
Automatic Description Generation from Images: A Survey of Models, Datasets, and Evaluation Measures (2016, methodology): “(2013) use KCCA, a kernelized version of CCA, Canonical Correlation Analysis (Hotelling, 1936), to learn the joint space.”
Bayesian group factor analysis with structured sparsity (2016, methodology): “…we can characterize canonical correlation analysis (CCA) as modeling paired observations y (1) i ∈ R p 1 ×1 and y (2) i ∈ R p 2 ×1 across n samples to identify a linear latent space for which the correlations between the two observations are maximized (Hotelling, 1936; Bach and Jordan, 2005).”
All-but-the-Top: Simple and Effective Postprocessing for Word Representations (2017, methodology): “While CCA-based spectral factorization methods have long been understood from a probabilistic (i.e., generative model) view point (Browne, 1979; Hotelling, 1936) and recently in the NLP context (Stratos et al., 2015), a corresponding effort for the PMI-based methods has only recently been conducted…”
Basic properties of strong mixing conditions. A survey and some open questions (2005, background): “The “maximal correlation” coefficient ρ(A,B) was first studied in the papers [74], [77], [86], [87], [109], in statistical contexts that had no particular connection”