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  "Title": "Non-Negative Matrix Factorization with Kernel Covariates",
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  "Date": "2026-10-29",
  "Authors@R": "person(\"Kenichi\", \"Satoh\",\nemail = \"kenichi-satoh@biwako.shiga-u.ac.jp\",\nrole = c(\"aut\", \"cre\"),\ncomment = c(ORCID = \"0000-0003-4436-9347\"))",
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  "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 with feed-forward and feedback structure\n(NMF-FFB) via nmf.ffb(), which fits a two-block input-output\nmodel for blind source separation and path analysis.\nReferences: Satoh (2025) <doi:10.48550/arXiv.2403.05359>; Satoh\n(2026) <doi:10.1007/s42081-026-00349-x>; Satoh (2025)\n<doi:10.48550/arXiv.2512.18250>; Satoh (2026)\n<doi:10.48550/arXiv.2603.01468>; Satoh and Tokuda (2026)\n<doi:10.48550/arXiv.2607.27474>; Satoh (2026)\n<doi:10.1007/s42081-025-00314-0>.",
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    "nmf.cluster.flow",
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    "nmf.ffb.cv",
    "nmf.ffb.diagnostics",
    "nmf.ffb.DOT",
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    "nmf.gmm",
    "nmf.gmm.inference",
    "nmf.gmm.select",
    "nmf.gmm.twostage",
    "nmf.rrr",
    "nmf.rrr.cv",
    "nmf.rrr.DOT",
    "nmf.rrr.ecv",
    "nmf.rrr.heatmap",
    "nmf.rrr.inference",
    "nmf.rrr.kernel.beta.cv",
    "nmf.rrr.rank",
    "nmf.rrr.rename",
    "nmf.rrr.signed",
    "nmf.rrr.signed.ecv",
    "nmf.rrr.signed.heatmap",
    "nmf.rrr.signed.inference",
    "nmf.rrr.signed.rank",
    "nmf.rrr.signed.rename",
    "nmfkc",
    "nmfkc.ar",
    "nmfkc.ar.degree.cv",
    "nmfkc.ar.DOT",
    "nmfkc.ar.latent",
    "nmfkc.ar.latent.inference",
    "nmfkc.ar.predict",
    "nmfkc.ar.stationarity",
    "nmfkc.ard",
    "nmfkc.bicv",
    "nmfkc.class",
    "nmfkc.consensus",
    "nmfkc.criterion",
    "nmfkc.cv",
    "nmfkc.denormalize",
    "nmfkc.DOT",
    "nmfkc.ecv",
    "nmfkc.inference",
    "nmfkc.kernel",
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    "nmfkc.kernel.beta.nearest.med",
    "nmfkc.kernel.gaussian",
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    "nmfkc.net",
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    "nmfkc.net.inference",
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    "nmfkc.normalize",
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    "nmfkc.signed.cv",
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    "nmfkc.signed.rank",
    "nmfkc.signed.rff",
    "nmfkc.signed.rff.gram",
    "nmfre",
    "nmfre.ecv",
    "nmfre.inference"
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  "_help": [
    {
      "page": "coef.nmf",
      "title": "Extract coefficients from NMF models",
      "topics": [
        "coef.nmf",
        "coef.nmf.ffb"
      ]
    },
    {
      "page": "coef.nmf.gmm",
      "title": "Extract the covariate-coefficient matrix from an NMF-GMM fit",
      "topics": [
        "coef.nmf.gmm"
      ]
    },
    {
      "page": "fitted.nmf",
      "title": "Extract fitted values from NMF models",
      "topics": [
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        "fitted.nmf.ffb",
        "fitted.nmfae",
        "fitted.nmfre"
      ]
    },
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      "page": "fitted.nmf.gmm",
      "title": "Fitted (responsibility-averaged) reconstruction of an NMF-GMM fit",
      "topics": [
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    {
      "page": "nmf.cluster.criteria",
      "title": "Sample-clustering quality across ranks",
      "topics": [
        "nmf.cluster.criteria"
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    },
    {
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      "title": "Cluster-flow (alluvial) diagram across a sequence of fits",
      "topics": [
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      ]
    },
    {
      "page": "nmf.ffb",
      "title": "NMF-FFB: non-negative matrix factorization with latent feedback",
      "topics": [
        "nmf.ffb"
      ]
    },
    {
      "page": "nmf.ffb.cv",
      "title": "Cross-Validation for NMF-FFB",
      "topics": [
        "nmf.ffb.cv"
      ]
    },
    {
      "page": "nmf.ffb.diagnostics",
      "title": "Structural Diagnostics of a Fitted NMF-FFB Feedback Matrix",
      "topics": [
        "nmf.ffb.diagnostics"
      ]
    },
    {
      "page": "nmf.ffb.DOT",
      "title": "Generate a Graphviz DOT Diagram for an NMF-FFB Model",
      "topics": [
        "nmf.ffb.DOT"
      ]
    },
    {
      "page": "nmf.ffb.ecv",
      "title": "Choose the number of factors for NMF-FFB by element-wise cross-validation",
      "topics": [
        "nmf.ffb.ecv"
      ]
    },
    {
      "page": "nmf.ffb.inference",
      "title": "Bootstrap inference for NMF-FFB (X held fixed)",
      "topics": [
        "nmf.ffb.inference"
      ]
    },
    {
      "page": "nmf.ffb.split",
      "title": "Heuristic Variable Splitting for NMF-FFB",
      "topics": [
        "nmf.ffb.split"
      ]
    },
    {
      "page": "nmf.ffb.test",
      "title": "Test the feed-forward null of an NMF-FFB fit",
      "topics": [
        "nmf.ffb.test"
      ]
    },
    {
      "page": "nmf.gmm",
      "title": "Fit NMF-GMM: a Gaussian-mixture latent-class extension of NMF with covariates",
      "topics": [
        "nmf.gmm"
      ]
    },
    {
      "page": "nmf.gmm.inference",
      "title": "Statistical inference for an NMF-GMM fit (given basis)",
      "topics": [
        "nmf.gmm.inference"
      ]
    },
    {
      "page": "nmf.gmm.select",
      "title": "Choose the number of mixture components K for NMF-GMM",
      "topics": [
        "nmf.gmm.select"
      ]
    },
    {
      "page": "nmf.gmm.twostage",
      "title": "Two-stage (adjust-then-cluster) baseline for NMF-GMM",
      "topics": [
        "nmf.gmm.twostage"
      ]
    },
    {
      "page": "nmf.rrr",
      "title": "Three-Layer Non-negative Matrix Factorization (NMF-AE)",
      "topics": [
        "nmf.rrr"
      ]
    },
    {
      "page": "nmf.rrr.cv",
      "title": "Sample-wise k-fold Cross-Validation for nmfae",
      "topics": [
        "nmf.rrr.cv"
      ]
    },
    {
      "page": "nmf.rrr.DOT",
      "title": "DOT graph visualization for nmfae objects",
      "topics": [
        "nmf.rrr.DOT"
      ]
    },
    {
      "page": "nmf.rrr.ecv",
      "title": "Element-wise Cross-Validation for nmfae (Wold's CV)",
      "topics": [
        "nmf.rrr.ecv"
      ]
    },
    {
      "page": "nmf.rrr.heatmap",
      "title": "Heatmap visualization of nmfae factor matrices",
      "topics": [
        "nmf.rrr.heatmap"
      ]
    },
    {
      "page": "nmf.rrr.inference",
      "title": "Statistical Inference for NMF-AE Parameter Matrix",
      "topics": [
        "nmf.rrr.inference"
      ]
    },
    {
      "page": "nmf.rrr.kernel.beta.cv",
      "title": "Optimize kernel beta for nmfae by cross-validation",
      "topics": [
        "nmf.rrr.kernel.beta.cv"
      ]
    },
    {
      "page": "nmf.rrr.rank",
      "title": "Rank selection for nmfae (paired rank, concise diagnostics)",
      "topics": [
        "nmf.rrr.rank"
      ]
    },
    {
      "page": "nmf.rrr.rename",
      "title": "Rename decoder and encoder bases",
      "topics": [
        "nmf.rrr.rename"
      ]
    },
    {
      "page": "nmf.rrr.signed",
      "title": "Signed-Bottleneck NMF-AE: Three-Layer NMF-AE with Signed Bottleneck",
      "topics": [
        "nmf.rrr.signed"
      ]
    },
    {
      "page": "nmf.rrr.signed.ecv",
      "title": "Element-wise Cross-Validation for Signed-Bottleneck NMF-AE",
      "topics": [
        "nmf.rrr.signed.ecv"
      ]
    },
    {
      "page": "nmf.rrr.signed.heatmap",
      "title": "Heatmap visualization of nmfae.signed factor matrices",
      "topics": [
        "nmf.rrr.signed.heatmap"
      ]
    },
    {
      "page": "nmf.rrr.signed.inference",
      "title": "Statistical Inference for Signed-Bottleneck NMF-AE Signed Bottleneck",
      "topics": [
        "nmf.rrr.signed.inference"
      ]
    },
    {
      "page": "nmf.rrr.signed.rank",
      "title": "Rank selection for nmfae.signed (paired rank, concise diagnostics)",
      "topics": [
        "nmf.rrr.signed.rank"
      ]
    },
    {
      "page": "nmf.rrr.signed.rename",
      "title": "Rename Resp/Cov labels on nmfae.signed objects",
      "topics": [
        "nmf.rrr.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.latent",
      "title": "Latent transition matrices of an NMF-VAR model",
      "topics": [
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    },
    {
      "page": "nmfkc.ar.latent.inference",
      "title": "Bootstrap inference for the latent VAR of an NMF-VAR model",
      "topics": [
        "nmfkc.ar.latent.inference"
      ]
    },
    {
      "page": "nmfkc.ar.predict",
      "title": "Forecast future values for NMF-VAR model",
      "topics": [
        "nmfkc.ar.predict"
      ]
    },
    {
      "page": "nmfkc.ar.stationarity",
      "title": "Stationarity of an NMF-VAR model",
      "topics": [
        "nmfkc.ar.stationarity"
      ]
    },
    {
      "page": "nmfkc.ard",
      "title": "Automatic relevance determination for NMF rank (experimental)",
      "topics": [
        "nmfkc.ard"
      ]
    },
    {
      "page": "nmfkc.bicv",
      "title": "Bi-cross-validation for NMF rank selection",
      "topics": [
        "nmfkc.bicv"
      ]
    },
    {
      "page": "nmfkc.class",
      "title": "Create a class (one-hot) matrix from a categorical vector",
      "topics": [
        "nmfkc.class"
      ]
    },
    {
      "page": "nmfkc.consensus",
      "title": "Consensus-clustering rank selection for NMF (Brunet 2004)",
      "topics": [
        "nmfkc.consensus"
      ]
    },
    {
      "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.cv.methods",
      "title": "Print/plot methods for nmfkc cross-validation objects",
      "topics": [
        "nmfkc.cv.methods",
        "plot.nmfkc.bicv",
        "plot.nmfkc.cv",
        "plot.nmfkc.ecv",
        "print.nmfkc.bicv",
        "print.nmfkc.cv",
        "print.nmfkc.ecv"
      ]
    },
    {
      "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.kernel.gram",
      "title": "Block-wise Gram accumulation of Nystroem kernel covariates for large N",
      "topics": [
        "nmfkc.kernel.gram"
      ]
    },
    {
      "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.net.rank",
      "title": "Rank selection for nmfkc.net (concise diagnostics)",
      "topics": [
        "nmfkc.net.rank"
      ]
    },
    {
      "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.rff.beta.cv",
      "title": "Select the bandwidth of random-feature covariates by cross-validation",
      "topics": [
        "nmfkc.rff.beta.cv"
      ]
    },
    {
      "page": "nmfkc.rff.positive",
      "title": "Positive (non-negative) random features for the Gaussian kernel",
      "topics": [
        "nmfkc.rff.positive"
      ]
    },
    {
      "page": "nmfkc.rff.positive.gram",
      "title": "Block-wise Gram accumulation of positive random features for large N",
      "topics": [
        "nmfkc.rff.positive.gram"
      ]
    },
    {
      "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": "nmfkc.signed.rank",
      "title": "Rank selection for nmfkc.signed (concise diagnostics)",
      "topics": [
        "nmfkc.signed.rank"
      ]
    },
    {
      "page": "nmfkc.signed.rff",
      "title": "Random Fourier Features for nmfkc.signed()",
      "topics": [
        "nmfkc.signed.rff"
      ]
    },
    {
      "page": "nmfkc.signed.rff.gram",
      "title": "Block-wise Gram accumulation of Random Fourier Features for large N",
      "topics": [
        "nmfkc.signed.rff.gram"
      ]
    },
    {
      "page": "nmfre",
      "title": "Non-negative Matrix Factorization with Random Effects",
      "topics": [
        "nmfre"
      ]
    },
    {
      "page": "nmfre.ecv",
      "title": "NMF-RE element-wise cross-validation for rank selection",
      "topics": [
        "nmfre.ecv"
      ]
    },
    {
      "page": "nmfre.inference",
      "title": "Statistical inference for the coefficient matrix C from NMF-RE",
      "topics": [
        "nmfre.inference"
      ]
    },
    {
      "page": "plot.nmf.cluster.criteria",
      "title": "Plot clustering-quality criteria across a sequence of fits",
      "topics": [
        "plot.nmf.cluster.criteria"
      ]
    },
    {
      "page": "plot.nmf.cluster.flow",
      "title": "Plot a cluster-flow (alluvial) diagram",
      "topics": [
        "plot.nmf.cluster.flow"
      ]
    },
    {
      "page": "plot.nmf.gmm",
      "title": "Plot method for nmf.gmm objects",
      "topics": [
        "plot.nmf.gmm"
      ]
    },
    {
      "page": "plot.nmf.gmm.select",
      "title": "Plot method for nmf.gmm.select objects",
      "topics": [
        "plot.nmf.gmm.select"
      ]
    },
    {
      "page": "plot.nmf.rank",
      "title": "Plot a rank-selection (nmf.rank) object",
      "topics": [
        "plot.nmf.rank"
      ]
    },
    {
      "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"
      ]
    },
    {
      "page": "plot.nmfkc",
      "title": "Plot method for objects of class 'nmfkc'",
      "topics": [
        "plot.nmfkc"
      ]
    },
    {
      "page": "plot.nmfkc.ar.latent",
      "title": "Plot the latent dynamics of an NMF-VAR model",
      "topics": [
        "plot.nmfkc.ar.latent"
      ]
    },
    {
      "page": "plot.nmfkc.ar.stationarity",
      "title": "Plot the stationarity bracket of an NMF-VAR model",
      "topics": [
        "plot.nmfkc.ar.stationarity"
      ]
    },
    {
      "page": "plot.nmfkc.ard",
      "title": "Plot method for nmfkc.ard objects",
      "topics": [
        "plot.nmfkc.ard"
      ]
    },
    {
      "page": "plot.nmfkc.consensus",
      "title": "Plot a consensus rank-selection (nmfkc.consensus) object",
      "topics": [
        "plot.nmfkc.consensus"
      ]
    },
    {
      "page": "plot.nmfkc.DOT",
      "title": "Plot method for nmfkc.DOT objects",
      "topics": [
        "plot.nmfkc.DOT"
      ]
    },
    {
      "page": "plot.nmfkc.signed",
      "title": "Plot method for nmfkc.signed (convergence)",
      "topics": [
        "plot.nmfkc.signed"
      ]
    },
    {
      "page": "plot.nmfre",
      "title": "Plot convergence diagnostics for NMF models",
      "topics": [
        "plot.nmf.ffb",
        "plot.nmfre"
      ]
    },
    {
      "page": "plot.nmfre.ecv",
      "title": "Plot method for nmfre.ecv objects",
      "topics": [
        "plot.nmfre.ecv"
      ]
    },
    {
      "page": "predict.nmf.gmm",
      "title": "Class assignments / responsibilities from an NMF-GMM fit",
      "topics": [
        "predict.nmf.gmm"
      ]
    },
    {
      "page": "predict.nmfkc",
      "title": "Prediction method for objects of class 'nmfkc'",
      "topics": [
        "predict.nmfkc"
      ]
    },
    {
      "page": "predict.nmfkc.signed",
      "title": "Predict method for nmfkc.signed",
      "topics": [
        "predict.nmfkc.signed"
      ]
    },
    {
      "page": "predict.nmfre",
      "title": "Predict method for nmfre objects",
      "topics": [
        "predict.nmfre"
      ]
    },
    {
      "page": "print.nmf",
      "title": "Print method for fitted NMF models",
      "topics": [
        "print.nmf"
      ]
    },
    {
      "page": "print.nmf.cluster.criteria",
      "title": "Print method for nmf.cluster.criteria objects",
      "topics": [
        "print.nmf.cluster.criteria"
      ]
    },
    {
      "page": "print.nmf.cluster.flow",
      "title": "Print method for nmf.cluster.flow objects",
      "topics": [
        "print.nmf.cluster.flow"
      ]
    },
    {
      "page": "print.nmf.ffb.test",
      "title": "Print a calibrated test of the feed-forward null",
      "topics": [
        "print.nmf.ffb.test"
      ]
    },
    {
      "page": "print.nmf.gmm",
      "title": "Print an NMF-GMM fit",
      "topics": [
        "print.nmf.gmm"
      ]
    },
    {
      "page": "print.nmf.gmm.select",
      "title": "Print method for nmf.gmm.select objects",
      "topics": [
        "print.nmf.gmm.select"
      ]
    },
    {
      "page": "print.nmf.inference",
      "title": "Print method for NMF inference objects",
      "topics": [
        "print.nmf.inference"
      ]
    },
    {
      "page": "print.nmf.rank",
      "title": "Print method for rank-selection (nmf.rank) objects",
      "topics": [
        "print.nmf.rank"
      ]
    },
    {
      "page": "print.nmfae.ecv",
      "title": "Print method for nmf.rrr element-wise CV results",
      "topics": [
        "print.nmfae.ecv"
      ]
    },
    {
      "page": "print.nmfkc.ar.latent",
      "title": "Print method for nmfkc.ar.latent objects",
      "topics": [
        "print.nmfkc.ar.latent"
      ]
    },
    {
      "page": "print.nmfkc.ar.latent.inference",
      "title": "Print method for nmfkc.ar.latent.inference objects",
      "topics": [
        "print.nmfkc.ar.latent.inference"
      ]
    },
    {
      "page": "print.nmfkc.ar.stationarity",
      "title": "Print method for nmfkc.ar.stationarity objects",
      "topics": [
        "print.nmfkc.ar.stationarity"
      ]
    },
    {
      "page": "print.nmfkc.ard",
      "title": "Print method for nmfkc.ard objects",
      "topics": [
        "print.nmfkc.ard"
      ]
    },
    {
      "page": "print.nmfkc.consensus",
      "title": "Print method for nmfkc.consensus objects",
      "topics": [
        "print.nmfkc.consensus"
      ]
    },
    {
      "page": "print.nmfkc.DOT",
      "title": "Print method for nmfkc.DOT objects",
      "topics": [
        "print.nmfkc.DOT"
      ]
    },
    {
      "page": "print.nmfkc.gram",
      "title": "Print method for nmfkc.gram",
      "topics": [
        "print.nmfkc.gram"
      ]
    },
    {
      "page": "print.nmfre.ecv",
      "title": "Print method for nmfre.ecv objects",
      "topics": [
        "print.nmfre.ecv"
      ]
    },
    {
      "page": "print.summary.nmf.ffb",
      "title": "Print method for summary.nmf.ffb objects",
      "topics": [
        "print.summary.nmf.ffb"
      ]
    },
    {
      "page": "print.summary.nmf.gmm",
      "title": "Print method for summary.nmf.gmm objects",
      "topics": [
        "print.summary.nmf.gmm"
      ]
    },
    {
      "page": "print.summary.nmfkc",
      "title": "Print method for 'summary.nmfkc' objects",
      "topics": [
        "print.summary.nmfkc"
      ]
    },
    {
      "page": "print.summary.nmfkc.inference",
      "title": "Print method for summary.nmfkc.inference objects",
      "topics": [
        "print.summary.nmfkc.inference"
      ]
    },
    {
      "page": "print.summary.nmfkc.net",
      "title": "Print method for summary.nmfkc.net objects",
      "topics": [
        "print.summary.nmfkc.net"
      ]
    },
    {
      "page": "print.summary.nmfkc.net.inference",
      "title": "Print method for summary.nmfkc.net.inference objects",
      "topics": [
        "print.summary.nmfkc.net.inference"
      ]
    },
    {
      "page": "print.summary.nmfkc.net.signed",
      "title": "Print method for summary.nmfkc.net.signed objects",
      "topics": [
        "print.summary.nmfkc.net.signed"
      ]
    },
    {
      "page": "print.summary.nmfkc.signed",
      "title": "Print method for summary.nmfkc.signed",
      "topics": [
        "print.summary.nmfkc.signed"
      ]
    },
    {
      "page": "residuals.nmf",
      "title": "Extract residuals from NMF models",
      "topics": [
        "residuals.nmf",
        "residuals.nmf.ffb",
        "residuals.nmfae",
        "residuals.nmfre"
      ]
    },
    {
      "page": "residuals.nmf.gmm",
      "title": "Residuals from an NMF-GMM fit",
      "topics": [
        "residuals.nmf.gmm"
      ]
    },
    {
      "page": "summary.nmf.ffb",
      "title": "Summary method for nmf.ffb objects",
      "topics": [
        "summary.nmf.ffb"
      ]
    },
    {
      "page": "summary.nmf.gmm",
      "title": "Summary of an NMF-GMM fit",
      "topics": [
        "summary.nmf.gmm"
      ]
    },
    {
      "page": "summary.nmfkc",
      "title": "Summary method for objects of class 'nmfkc'",
      "topics": [
        "summary.nmfkc"
      ]
    },
    {
      "page": "summary.nmfkc.inference",
      "title": "Summary method for nmfkc.inference objects",
      "topics": [
        "summary.nmfkc.inference"
      ]
    },
    {
      "page": "summary.nmfkc.net",
      "title": "Summary method for nmfkc.net objects",
      "topics": [
        "summary.nmfkc.net"
      ]
    },
    {
      "page": "summary.nmfkc.net.inference",
      "title": "Summary method for nmfkc.net.inference objects",
      "topics": [
        "summary.nmfkc.net.inference"
      ]
    },
    {
      "page": "summary.nmfkc.net.signed",
      "title": "Summary method for nmfkc.net.signed objects",
      "topics": [
        "summary.nmfkc.net.signed"
      ]
    },
    {
      "page": "summary.nmfkc.signed",
      "title": "Summary method for nmfkc.signed",
      "topics": [
        "summary.nmfkc.signed"
      ]
    },
    {
      "page": "summary.nmfre",
      "title": "Summary method for objects of class 'nmfre'",
      "topics": [
        "print.summary.nmfre",
        "summary.nmfre"
      ]
    }
  ],
  "_readme": "https://github.com/ksatohds/nmfkc/raw/HEAD/README.md",
  "_rundeps": [],
  "_vignettes": [
    {
      "source": "introduction-to-nmfkc.Rmd",
      "filename": "introduction-to-nmfkc.html",
      "title": "Introduction to nmfkc",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Introduction",
        "1. Basic Usage: Analyzing Movie Ratings",
        "Creating the Data",
        "Running NMF",
        "Interpretation",
        "1. Basis Matrix X: User Preferences",
        "2. Coefficient Matrix B: Movie Genres",
        "2. Visualization",
        "Convergence Plot",
        "Visualizing the Reconstruction",
        "3. Handling Missing Values (Imputation)",
        "Creating Data with Missing Values",
        "Running NMF with NAs",
        "Predicting the Unknown Rating",
        "Summary"
      ],
      "created": "2025-10-13 04:49:23",
      "modified": "2025-11-24 21:22:05",
      "commits": 3
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  "_score": 6.854548935812951,
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