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  "Title": "Canonical Correlation Analysis via Reduced Rank Regression",
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  "Date": "2026-04-10",
  "Authors@R": "c(\nperson(\"Claire\", \"Donnat\", , \"cdonnat@uchicago.edu\",\nrole = c(\"aut\", \"cre\"),\ncomment = c(ORCID = \"https://orcid.org/0000-0001-7079-8060\")),\nperson(\"Elena\", \"Tuzhilina\", , \"elena.tuzhilina@utoronto.ca\",\nrole = \"aut\",\ncomment = c(ORCID = \"https://orcid.org/0000-0002-1898-6010\")),\nperson(\"Zixuan\", \"Wu\", , \"zixuanwu@uchicago.edu\",\nrole = \"aut\",\ncomment = c(ORCID = \"https://orcid.org/0009-0006-4745-0000\")))",
  "Author": "Claire Donnat [aut, cre] (ORCID:\n<https://orcid.org/0000-0001-7079-8060>), Elena Tuzhilina [aut]\n(ORCID: <https://orcid.org/0000-0002-1898-6010>), Zixuan Wu\n[aut] (ORCID: <https://orcid.org/0009-0006-4745-0000>)",
  "Maintainer": "Claire Donnat <cdonnat@uchicago.edu>",
  "Description": "Canonical correlation analysis (CCA) via reduced-rank\nregression with support for regularization and\ncross-validation. Several methods for estimating CCA in\nhigh-dimensional settings are implemented. The first set of\nmethods, cca_rrr() (and variants: cca_group_rrr() and\ncca_graph_rrr()), assumes that one dataset is high-dimensional\nand the other is low-dimensional, while the second, ecca() (for\nEfficient CCA) assumes that both datasets are high-dimensional.\nFor both methods, standard l1 regularization as well as\ngroup-lasso regularization are available. cca_graph_rrr further\nsupports total variation regularization when there is a known\ngraph structure among the variables of the high-dimensional\ndataset. In this case, the loadings of the canonical directions\nof the high-dimensional dataset are assumed to be smooth on the\ngraph. For more details see Donnat and Tuzhilina (2024)\n<doi:10.48550/arXiv.2405.19539> and Wu, Tuzhilina and Donnat\n(2025) <doi:10.48550/arXiv.2507.11160>.",
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    "TPR",
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    {
      "page": "cca_graph_rrr",
      "title": "Graph-regularized Reduced-Rank Regression for Canonical Correlation Analysis",
      "topics": [
        "cca_graph_rrr"
      ]
    },
    {
      "page": "cca_graph_rrr_cv",
      "title": "Graph-regularized Reduced-Rank Regression for Canonical Correlation Analysis with cross validation",
      "topics": [
        "cca_graph_rrr_cv"
      ]
    },
    {
      "page": "cca_group_rrr",
      "title": "Group-Sparse Canonical Correlation via Reduced-Rank Regression",
      "topics": [
        "cca_group_rrr"
      ]
    },
    {
      "page": "cca_group_rrr_cv",
      "title": "Group-Sparse Canonical Correlation via Reduced-Rank Regression with CV",
      "topics": [
        "cca_group_rrr_cv"
      ]
    },
    {
      "page": "cca_rrr",
      "title": "Canonical Correlation Analysis via Reduced Rank Regression (RRR)",
      "topics": [
        "cca_rrr"
      ]
    },
    {
      "page": "cca_rrr_cv",
      "title": "Cross-validated Canonical Correlation Analysis via RRR",
      "topics": [
        "cca_rrr_cv"
      ]
    },
    {
      "page": "ecca",
      "title": "Efficient CCA for Two High-Dimensional Views",
      "topics": [
        "ecca"
      ]
    },
    {
      "page": "ecca.cv",
      "title": "Cross-Validated Efficient CCA",
      "topics": [
        "ecca.cv"
      ]
    },
    {
      "page": "FPR",
      "title": "False Positive Rate (TPR)",
      "topics": [
        "FPR"
      ]
    },
    {
      "page": "get_edge_incidence",
      "title": "Return the edge incidence matrix of an igraph graph",
      "topics": [
        "get_edge_incidence"
      ]
    },
    {
      "page": "principal_angles",
      "title": "Metrics for subspaces",
      "topics": [
        "principal_angles"
      ]
    },
    {
      "page": "regular_cca",
      "title": "Function to perform regular (low dimensional) canonical correlation analysis (CCA",
      "topics": [
        "regular_cca"
      ]
    },
    {
      "page": "SCCA_Parkhomenko",
      "title": "Function to perform Sparse CCA based on Waaijenborg et al. (2008) REFERENCE Parkhomenko et al. (2009), \"Sparse Canonical Correlation Anlaysis with Application to Genomic Data Integration\" in Statistical Applications in Genetics and Molecular Biology, Volume 8, Issue 1, Article 1",
      "topics": [
        "SCCA_Parkhomenko"
      ]
    },
    {
      "page": "sinTheta",
      "title": "SinTheta distance between subspaces",
      "topics": [
        "sinTheta"
      ]
    },
    {
      "page": "sparse_CCA_benchmarks",
      "title": "Additional Benchmarks for Sparse CCA Methods",
      "topics": [
        "sparse_CCA_benchmarks"
      ]
    },
    {
      "page": "SparseCCA",
      "title": "Function to perform Sparse CCA based on Wilms and Croux (2018) REFERENCE Wilms, I., & Croux, C. (2018). Sparse canonical correlation analysis using alternating regressions. Journal of Computational and Graphical Statistics, 27(1), 1-10.",
      "topics": [
        "SparseCCA"
      ]
    },
    {
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      "title": "Subdistance between subspaces",
      "topics": [
        "subdistance"
      ]
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      "title": "True Negative Rate (TNR)",
      "topics": [
        "TNR"
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      "title": "True Positive Rate (TPR)",
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        "TPR"
      ]
    },
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      "title": "Sparse CCA by Witten and Tibshirani (2009)",
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      ]
    }
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