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  "Title": "Linear Optimal Low-Rank Projection",
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  "Date": "2020-06-20",
  "Authors@R": "c(person(\"Eric\", \"Bridgeford\", role = c(\"aut\", \"cre\"),\nemail = \"ericwb95@gmail.com\"),\nperson(\"Minh\", \"Tang\", role=\"ctb\",\nemail=\"minh@jhu.edu\"),\nperson(\"Jason\", \"Yim\", role = \"ctb\",\nemail = \"jasonkyuyim@gmail.com\"),\nperson(\"Joshua\", \"Vogelstein\", role = \"ths\",\nemail = \"jovo@jhu.edu\"))",
  "Maintainer": "Eric Bridgeford <ericwb95@gmail.com>",
  "Description": "Supervised learning techniques designed for the situation\nwhen the dimensionality exceeds the sample size have a tendency\nto overfit as the dimensionality of the data increases. To\nremedy this High dimensionality; low sample size (HDLSS)\nsituation, we attempt to learn a lower-dimensional\nrepresentation of the data before learning a classifier. That\nis, we project the data to a situation where the dimensionality\nis more manageable, and then are able to better apply standard\nclassification or clustering techniques since we will have\nfewer dimensions to overfit. A number of previous works have\nfocused on how to strategically reduce dimensionality in the\nunsupervised case, yet in the supervised HDLSS regime, few\nworks have attempted to devise dimensionality reduction\ntechniques that leverage the labels associated with the data.\nIn this package and the associated manuscript Vogelstein et al.\n(2017) <arXiv:1709.01233>, we provide several methods for\nfeature extraction, some utilizing labels and some not, along\nwith easily extensible utilities to simplify cross-validative\nefforts to identify the best feature extraction method.\nAdditionally, we include a series of adaptable benchmark\nsimulations to serve as a standard for future investigative\nefforts into supervised HDLSS. Finally, we produce a\ncomprehensive comparison of the included algorithms across a\nrange of benchmark simulations and real data applications.",
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  "URL": "https://github.com/neurodata/lol",
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  "Author": "Eric Bridgeford [aut, cre],\nMinh Tang [ctb],\nJason Yim [ctb],\nJoshua Vogelstein [ths]",
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    "message": "updated xval\n",
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      "date": "2018-04-13"
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      "date": "2020-06-26"
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    "lol.classify.nearestCentroid",
    "lol.classify.randomChance",
    "lol.classify.randomGuess",
    "lol.embed",
    "lol.project.bayes_optimal",
    "lol.project.dp",
    "lol.project.lol",
    "lol.project.lrcca",
    "lol.project.lrlda",
    "lol.project.pca",
    "lol.project.pls",
    "lol.project.rp",
    "lol.sims.cigar",
    "lol.sims.cross",
    "lol.sims.fat_tails",
    "lol.sims.khump",
    "lol.sims.kident",
    "lol.sims.mean_diff",
    "lol.sims.qdtoep",
    "lol.sims.rev_rtrunk",
    "lol.sims.rtrunk",
    "lol.sims.toep",
    "lol.sims.xor2",
    "lol.xval.eval",
    "lol.xval.optimal_dimselect",
    "lol.xval.split"
  ],
  "_help": [
    {
      "page": "lol.classify.nearestCentroid",
      "title": "Nearest Centroid Classifier Training",
      "topics": [
        "lol.classify.nearestCentroid"
      ]
    },
    {
      "page": "lol.classify.rand",
      "title": "Random Classifier Utility",
      "topics": [
        "lol.classify.rand"
      ]
    },
    {
      "page": "lol.classify.randomChance",
      "title": "Randomly Chance Classifier Training",
      "topics": [
        "lol.classify.randomChance"
      ]
    },
    {
      "page": "lol.classify.randomGuess",
      "title": "Randomly Guessing Classifier Training",
      "topics": [
        "lol.classify.randomGuess"
      ]
    },
    {
      "page": "lol.embed",
      "title": "Embedding",
      "topics": [
        "lol.embed"
      ]
    },
    {
      "page": "lol.project.bayes_optimal",
      "title": "Bayes Optimal",
      "topics": [
        "lol.project.bayes_optimal"
      ]
    },
    {
      "page": "lol.project.dp",
      "title": "Data Piling",
      "topics": [
        "lol.project.dp"
      ]
    },
    {
      "page": "lol.project.lol",
      "title": "Linear Optimal Low-Rank Projection (LOL)",
      "topics": [
        "lol.project.lol"
      ]
    },
    {
      "page": "lol.project.lrcca",
      "title": "Low-rank Canonical Correlation Analysis (LR-CCA)",
      "topics": [
        "lol.project.lrcca"
      ]
    },
    {
      "page": "lol.project.lrlda",
      "title": "Low-Rank Linear Discriminant Analysis (LRLDA)",
      "topics": [
        "lol.project.lrlda"
      ]
    },
    {
      "page": "lol.project.pca",
      "title": "Principal Component Analysis (PCA)",
      "topics": [
        "lol.project.pca"
      ]
    },
    {
      "page": "lol.project.pls",
      "title": "Partial Least-Squares (PLS)",
      "topics": [
        "lol.project.pls"
      ]
    },
    {
      "page": "lol.project.rp",
      "title": "Random Projections (RP)",
      "topics": [
        "lol.project.rp"
      ]
    },
    {
      "page": "lol.sims.cigar",
      "title": "Stacked Cigar",
      "topics": [
        "lol.sims.cigar"
      ]
    },
    {
      "page": "lol.sims.cross",
      "title": "Cross",
      "topics": [
        "lol.sims.cross"
      ]
    },
    {
      "page": "lol.sims.fat_tails",
      "title": "Fat Tails Simulation",
      "topics": [
        "lol.sims.fat_tails"
      ]
    },
    {
      "page": "lol.sims.khump",
      "title": "Multiclass Trunk",
      "topics": [
        "lol.sims.khump"
      ]
    },
    {
      "page": "lol.sims.kident",
      "title": "Multiclass Trunk",
      "topics": [
        "lol.sims.kident"
      ]
    },
    {
      "page": "lol.sims.ktrunk",
      "title": "Multiclass Trunk",
      "topics": [
        "lol.sims.ktrunk"
      ]
    },
    {
      "page": "lol.sims.mean_diff",
      "title": "Mean Difference Simulation",
      "topics": [
        "lol.sims.mean_diff"
      ]
    },
    {
      "page": "lol.sims.qdtoep",
      "title": "Quadratic Discriminant Toeplitz Simulation",
      "topics": [
        "lol.sims.qdtoep"
      ]
    },
    {
      "page": "lol.sims.random_rotate",
      "title": "Random Rotation",
      "topics": [
        "lol.sims.random_rotate"
      ]
    },
    {
      "page": "lol.sims.rev_rtrunk",
      "title": "Reverse Random Trunk",
      "topics": [
        "lol.sims.rev_rtrunk"
      ]
    },
    {
      "page": "lol.sims.rotation",
      "title": "Sample Random Rotation",
      "topics": [
        "lol.sims.rotation"
      ]
    },
    {
      "page": "lol.sims.rtrunk",
      "title": "Random Trunk",
      "topics": [
        "lol.sims.rtrunk"
      ]
    },
    {
      "page": "lol.sims.sim_gmm",
      "title": "GMM Simulate",
      "topics": [
        "lol.sims.sim_gmm"
      ]
    },
    {
      "page": "lol.sims.toep",
      "title": "Toeplitz Simulation",
      "topics": [
        "lol.sims.toep"
      ]
    },
    {
      "page": "lol.sims.xor2",
      "title": "Xor Problem",
      "topics": [
        "lol.sims.xor2"
      ]
    },
    {
      "page": "lol.utils.decomp",
      "title": "A utility to use irlba when necessary",
      "topics": [
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    },
    {
      "page": "lol.utils.deltas",
      "title": "A function that performs a utility computation of information about the differences of the classes.",
      "topics": [
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    },
    {
      "page": "lol.utils.info",
      "title": "A function that performs basic utilities about the data.",
      "topics": [
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    },
    {
      "page": "lol.utils.ohe",
      "title": "A function for one-hot encoding categorical respose vectors.",
      "topics": [
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    },
    {
      "page": "lol.xval.eval",
      "title": "Embedding Cross Validation",
      "topics": [
        "lol.xval.eval"
      ]
    },
    {
      "page": "lol.xval.optimal_dimselect",
      "title": "Optimal Cross-Validated Number of Embedding Dimensions",
      "topics": [
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      ]
    },
    {
      "page": "lol.xval.split",
      "title": "Cross-Validation Data Splitter",
      "topics": [
        "lol.xval.split"
      ]
    },
    {
      "page": "predict.nearestCentroid",
      "title": "Nearest Centroid Classifier Prediction",
      "topics": [
        "predict.nearestCentroid"
      ]
    },
    {
      "page": "predict.randomChance",
      "title": "Randomly Chance Classifier Prediction",
      "topics": [
        "predict.randomChance"
      ]
    },
    {
      "page": "predict.randomGuess",
      "title": "Randomly Guessing Classifier Prediction",
      "topics": [
        "predict.randomGuess"
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      "filename": "nearestCentroid.html",
      "title": "Nearest Centroid Classifier",
      "author": "Eric Bridgeford",
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      "author": "Eric Bridgeford",
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        "DP",
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      "author": "Eric Bridgeford",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Writing New Classification Algorithms",
        "Writing a Classification Method",
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      "engine": "knitr::rmarkdown",
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        "Writing New Embedding Algorithms",
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      "title": "Linear Optimal Low-Rank Projection (LOL)",
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        "LOL",
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      "engine": "knitr::rmarkdown",
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        "LRLDA",
        "Stacked Cigar Simulation",
        "Trunk Simulation",
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      "filename": "pca.html",
      "title": "Principal Component Analysis (PCA)",
      "author": "Eric Bridgeford",
      "engine": "knitr::rmarkdown",
      "headings": [
        "PCA",
        "Stacked Cigar Simulation",
        "Trunk Simulation",
        "Rotated Trunk Simulation"
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      "modified": "2018-04-13 13:15:36",
      "commits": 15
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      "filename": "pls.html",
      "title": "Partial Least-Squares (PLS)",
      "author": "Eric Bridgeford",
      "engine": "knitr::rmarkdown",
      "headings": [
        "PLS",
        "Stacked Cigar Simulation",
        "Trunk Simulation",
        "Rotated Trunk Simulation"
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      "filename": "rp.html",
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      "engine": "knitr::rmarkdown",
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        "LR-CCA",
        "Stacked Cigar Simulation",
        "Trunk Simulation",
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      "modified": "2018-04-13 13:11:11",
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      "filename": "simulations.html",
      "title": "LOL Simulations",
      "author": "Eric Bridgeford",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Trunk, 2 Class",
        "Rotated Trunk, 2 Class, non-equal priors",
        "Trunk, 3 Class",
        "Mean Difference",
        "Toeplitz",
        "QD- Toeplitz",
        "XOR",
        "Cigar",
        "Fat Tails",
        "Cross"
      ],
      "created": "2017-12-14 11:16:30",
      "modified": "2018-06-01 18:57:42",
      "commits": 11
    },
    {
      "source": "xval.Rmd",
      "filename": "xval.html",
      "title": "LOL Cross-Validation",
      "author": "Eric Bridgeford",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Cross Validation to Determine Error of Embedding Alg composed with Classifier",
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