{
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  "Package": "nmfkc",
  "Type": "Package",
  "Title": "Non-Negative Matrix Factorization with Kernel Covariates",
  "Version": "0.7.3",
  "Date": "2026-05-14",
  "Authors@R": "person(\"Kenichi\", \"Satoh\",\nemail = \"kenichi-satoh@biwako.shiga-u.ac.jp\",\nrole = c(\"aut\", \"cre\"),\ncomment = c(ORCID = \"0000-0003-4436-9347\"))",
  "Maintainer": "Kenichi Satoh <kenichi-satoh@biwako.shiga-u.ac.jp>",
  "URL": "https://github.com/ksatohds/nmfkc,\nhttps://ksatohds.github.io/nmfkc/",
  "BugReports": "https://github.com/ksatohds/nmfkc/issues",
  "Description": "Performs Non-negative Matrix Factorization (NMF) with\nKernel Covariates. Given an observation matrix and kernel\ncovariates, it optimizes both a basis matrix and a parameter\nmatrix. Notably, if the kernel matrix is an identity matrix,\nthe method simplifies to standard NMF. Also provides NMF with\nRandom Effects (NMF-RE) via nmfre(), which estimates a\nmixed-effects model combining covariate-driven scores with\nunit-specific random effects together with wild bootstrap\ninference, and NMF-based Structural Equation Modeling (NMF-SEM)\nvia nmf.sem(), which fits a two-block input-output model for\nblind source separation and path analysis. References: Satoh\n(2025) <doi:10.48550/arXiv.2403.05359>; Satoh (2025)\n<doi:10.48550/arXiv.2510.10375>; Satoh (2025)\n<doi:10.48550/arXiv.2512.18250>; Satoh (2026)\n<doi:10.48550/arXiv.2603.01468>; Satoh (2026)\n<doi:10.1007/s42081-025-00314-0>.",
  "License": "MIT + file LICENSE",
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  "Repository": "https://ksatohds.r-universe.dev",
  "Date/Publication": "2026-05-13 22:54:06 UTC",
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  "Author": "Kenichi Satoh [aut, cre] (ORCID:\n<https://orcid.org/0000-0003-4436-9347>)",
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  "_exports": [
    "nmf.ffb",
    "nmf.ffb.cv",
    "nmf.ffb.DOT",
    "nmf.ffb.inference",
    "nmf.ffb.split",
    "nmf.sem",
    "nmf.sem.cv",
    "nmf.sem.DOT",
    "nmf.sem.inference",
    "nmf.sem.split",
    "nmfae",
    "nmfae.cv",
    "nmfae.DOT",
    "nmfae.ecv",
    "nmfae.heatmap",
    "nmfae.inference",
    "nmfae.kernel.beta.cv",
    "nmfae.rename",
    "nmfae.signed",
    "nmfae.signed.ecv",
    "nmfae.signed.heatmap",
    "nmfae.signed.inference",
    "nmfae.signed.rename",
    "nmfkc",
    "nmfkc.ar",
    "nmfkc.ar.degree.cv",
    "nmfkc.ar.DOT",
    "nmfkc.ar.predict",
    "nmfkc.ar.stationarity",
    "nmfkc.class",
    "nmfkc.criterion",
    "nmfkc.cv",
    "nmfkc.denormalize",
    "nmfkc.DOT",
    "nmfkc.ecv",
    "nmfkc.inference",
    "nmfkc.kernel",
    "nmfkc.kernel.beta.cv",
    "nmfkc.kernel.beta.nearest.med",
    "nmfkc.kernel.gaussian",
    "nmfkc.net",
    "nmfkc.net.DOT",
    "nmfkc.net.ecv",
    "nmfkc.net.inference",
    "nmfkc.normalize",
    "nmfkc.rank",
    "nmfkc.residual.plot",
    "nmfkc.signed",
    "nmfkc.signed.cv",
    "nmfkc.signed.ecv",
    "nmfre",
    "nmfre.dfU.scan",
    "nmfre.inference"
  ],
  "_help": [
    {
      "page": "coef.nmf",
      "title": "Extract coefficients from NMF models",
      "topics": [
        "coef.nmf",
        "coef.nmf.sem"
      ]
    },
    {
      "page": "fitted.nmf",
      "title": "Extract fitted values from NMF models",
      "topics": [
        "fitted.nmf",
        "fitted.nmf.sem",
        "fitted.nmfae"
      ]
    },
    {
      "page": "nmf.sem",
      "title": "NMF-FFB Main Estimation Algorithm (formerly NMF-SEM)",
      "topics": [
        "nmf.ffb",
        "nmf.sem"
      ]
    },
    {
      "page": "nmf.sem.cv",
      "title": "Cross-Validation for NMF-FFB",
      "topics": [
        "nmf.ffb.cv",
        "nmf.sem.cv"
      ]
    },
    {
      "page": "nmf.sem.DOT",
      "title": "Generate a Graphviz DOT Diagram for an NMF-FFB Model",
      "topics": [
        "nmf.ffb.DOT",
        "nmf.sem.DOT"
      ]
    },
    {
      "page": "nmf.sem.inference",
      "title": "Statistical inference for NMF-FFB via X-fixed full pair bootstrap",
      "topics": [
        "nmf.ffb.inference",
        "nmf.sem.inference"
      ]
    },
    {
      "page": "nmf.sem.split",
      "title": "Heuristic Variable Splitting for NMF-FFB",
      "topics": [
        "nmf.ffb.split",
        "nmf.sem.split"
      ]
    },
    {
      "page": "nmfae",
      "title": "Three-Layer Non-negative Matrix Factorization (NMF-AE)",
      "topics": [
        "nmfae"
      ]
    },
    {
      "page": "nmfae.cv",
      "title": "Sample-wise k-fold Cross-Validation for nmfae",
      "topics": [
        "nmfae.cv"
      ]
    },
    {
      "page": "nmfae.DOT",
      "title": "DOT graph visualization for nmfae objects",
      "topics": [
        "nmfae.DOT"
      ]
    },
    {
      "page": "nmfae.ecv",
      "title": "Element-wise Cross-Validation for nmfae (Wold's CV)",
      "topics": [
        "nmfae.ecv"
      ]
    },
    {
      "page": "nmfae.heatmap",
      "title": "Heatmap visualization of nmfae factor matrices",
      "topics": [
        "nmfae.heatmap"
      ]
    },
    {
      "page": "nmfae.inference",
      "title": "Statistical Inference for NMF-AE Parameter Matrix",
      "topics": [
        "nmfae.inference"
      ]
    },
    {
      "page": "nmfae.kernel.beta.cv",
      "title": "Optimize kernel beta for nmfae by cross-validation",
      "topics": [
        "nmfae.kernel.beta.cv"
      ]
    },
    {
      "page": "nmfae.rename",
      "title": "Rename decoder and encoder bases",
      "topics": [
        "nmfae.rename"
      ]
    },
    {
      "page": "nmfae.signed",
      "title": "Signed-Bottleneck NMF-AE: Three-Layer NMF-AE with Signed Bottleneck",
      "topics": [
        "nmfae.signed"
      ]
    },
    {
      "page": "nmfae.signed.ecv",
      "title": "Element-wise Cross-Validation for Signed-Bottleneck NMF-AE",
      "topics": [
        "nmfae.signed.ecv"
      ]
    },
    {
      "page": "nmfae.signed.heatmap",
      "title": "Heatmap visualization of nmfae.signed factor matrices",
      "topics": [
        "nmfae.signed.heatmap"
      ]
    },
    {
      "page": "nmfae.signed.inference",
      "title": "Statistical Inference for Signed-Bottleneck NMF-AE Signed Bottleneck",
      "topics": [
        "nmfae.signed.inference"
      ]
    },
    {
      "page": "nmfae.signed.rename",
      "title": "Rename Dec/Enc labels on nmfae.signed objects",
      "topics": [
        "nmfae.signed.rename"
      ]
    },
    {
      "page": "nmfkc",
      "title": "Optimize NMF with kernel covariates (Full Support for Missing Values)",
      "topics": [
        "nmfkc"
      ]
    },
    {
      "page": "nmfkc.ar",
      "title": "Construct observation and covariate matrices for a vector autoregressive model",
      "topics": [
        "nmfkc.ar"
      ]
    },
    {
      "page": "nmfkc.ar.degree.cv",
      "title": "Optimize lag order for the autoregressive model",
      "topics": [
        "nmfkc.ar.degree.cv"
      ]
    },
    {
      "page": "nmfkc.ar.DOT",
      "title": "Generate a Graphviz DOT Diagram for NMF-AR / NMF-VAR Models",
      "topics": [
        "nmfkc.ar.DOT"
      ]
    },
    {
      "page": "nmfkc.ar.predict",
      "title": "Forecast future values for NMF-VAR model",
      "topics": [
        "nmfkc.ar.predict"
      ]
    },
    {
      "page": "nmfkc.ar.stationarity",
      "title": "Check stationarity of an NMF-VAR model",
      "topics": [
        "nmfkc.ar.stationarity"
      ]
    },
    {
      "page": "nmfkc.class",
      "title": "Create a class (one-hot) matrix from a categorical vector",
      "topics": [
        "nmfkc.class"
      ]
    },
    {
      "page": "nmfkc.criterion",
      "title": "Compute model selection criteria for a fitted nmfkc model",
      "topics": [
        "nmfkc.criterion"
      ]
    },
    {
      "page": "nmfkc.cv",
      "title": "Perform k-fold cross-validation for NMF with kernel covariates",
      "topics": [
        "nmfkc.cv"
      ]
    },
    {
      "page": "nmfkc.denormalize",
      "title": "Denormalize a matrix from [0,1] back to its original scale",
      "topics": [
        "nmfkc.denormalize"
      ]
    },
    {
      "page": "nmfkc.DOT",
      "title": "Generate Graphviz DOT Scripts for NMF or NMF-with-Covariates Models",
      "topics": [
        "nmfkc.DOT"
      ]
    },
    {
      "page": "nmfkc.ecv",
      "title": "Perform Element-wise Cross-Validation (Wold's CV)",
      "topics": [
        "nmfkc.ecv"
      ]
    },
    {
      "page": "nmfkc.inference",
      "title": "Statistical inference for the parameter matrix C (Theta)",
      "topics": [
        "nmfkc.inference"
      ]
    },
    {
      "page": "nmfkc.kernel",
      "title": "Create a kernel matrix from covariates",
      "topics": [
        "nmfkc.kernel"
      ]
    },
    {
      "page": "nmfkc.kernel.beta.cv",
      "title": "Optimize beta of the Gaussian kernel function by cross-validation",
      "topics": [
        "nmfkc.kernel.beta.cv"
      ]
    },
    {
      "page": "nmfkc.kernel.beta.nearest.med",
      "title": "Estimate Gaussian/RBF kernel parameter beta from covariates (supports landmarks)",
      "topics": [
        "nmfkc.kernel.beta.nearest.med"
      ]
    },
    {
      "page": "nmfkc.kernel.gaussian",
      "title": "Create a Gaussian kernel matrix from covariates",
      "topics": [
        "nmfkc.kernel.gaussian"
      ]
    },
    {
      "page": "nmfkc.net",
      "title": "Symmetric NMF for networks (tri / bi / signed)",
      "topics": [
        "nmfkc.net"
      ]
    },
    {
      "page": "nmfkc.net.DOT",
      "title": "Generate a Graphviz DOT Diagram for a Symmetric NMF Network",
      "topics": [
        "nmfkc.net.DOT"
      ]
    },
    {
      "page": "nmfkc.net.ecv",
      "title": "Element-wise cross-validation for nmfkc.net (upper-triangle folds)",
      "topics": [
        "nmfkc.net.ecv"
      ]
    },
    {
      "page": "nmfkc.net.inference",
      "title": "Statistical Inference for Symmetric NMF Parameters",
      "topics": [
        "nmfkc.net.inference"
      ]
    },
    {
      "page": "nmfkc.normalize",
      "title": "Normalize a matrix to the range [0,1]",
      "topics": [
        "nmfkc.normalize"
      ]
    },
    {
      "page": "nmfkc.rank",
      "title": "Rank selection diagnostics with graphical output",
      "topics": [
        "nmfkc.rank"
      ]
    },
    {
      "page": "nmfkc.residual.plot",
      "title": "Plot Diagnostics: Original, Fitted, and Residual Matrices as Heatmaps",
      "topics": [
        "nmfkc.residual.plot"
      ]
    },
    {
      "page": "nmfkc.signed",
      "title": "NMF-KC with signed covariate matrix",
      "topics": [
        "nmfkc.signed"
      ]
    },
    {
      "page": "nmfkc.signed.cv",
      "title": "Column-wise k-fold cross-validation for nmfkc.signed",
      "topics": [
        "nmfkc.signed.cv"
      ]
    },
    {
      "page": "nmfkc.signed.ecv",
      "title": "Element-wise cross-validation for nmfkc.signed",
      "topics": [
        "nmfkc.signed.ecv"
      ]
    },
    {
      "page": "nmfre",
      "title": "Non-negative Matrix Factorization with Random Effects",
      "topics": [
        "nmfre"
      ]
    },
    {
      "page": "nmfre.dfU.scan",
      "title": "Scan dfU cap rates for NMF-RE",
      "topics": [
        "nmfre.dfU.scan"
      ]
    },
    {
      "page": "nmfre.inference",
      "title": "Statistical inference for the coefficient matrix C from NMF-RE",
      "topics": [
        "nmfre.inference"
      ]
    },
    {
      "page": "plot.nmfae",
      "title": "'plot.nmfae' displays the convergence trajectory of the objective function across iterations. The title shows the achieved R^2.",
      "topics": [
        "plot.nmfae"
      ]
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