arXiv subjects

Kenichi Satoh

Publications and source records attributed to Kenichi Satoh.

7 recordsLinked to original sources

arXiv2026

Co-clustering of Response and Covariate Variables by Tri-Factorizing Their Non-negative Regression Coefficient Matrix

Two-block data---two sets of variables measured on the same individuals, such as microbial taxa and metabolites---raise the question of how \emph{groups} of covariate variables relate to \emph{groups} of response variables. Co-clustering answers this for a single matrix, not for two variable blocks; existing two-block methods either cluster only one side or return signed factors rather than clusters. Starting from the multivariate linear regression $Y_1\approx M Y_2$, we give its non-negative coefficient matrix a tri-factorization $M=X_1\Theta X_2$ (a tri-NMF), so that $X_1$ softly clusters the response variables, $X_2$ the covariate variables, and $\Theta$ is a tested matrix of block correspondences. This makes the method the non-negative member of the reduced-rank regression (RRR) family, expressing RRR's low-rank class in a parts-based basis as NMF relates to PCA; the constraint can only restrict the fit, so predictive accuracy is not the aim; the co-clustering and tested correspondences are. We give multiplicative update rules, choose the two ranks by cross-validation, and develop a conditional Wald test for $\Theta$ applied after basis selection; its size is nominal with fixed bases, conservative after re-estimation, and slightly above nominal under correlated responses, while a non-zero path's \emph{magnitude} stays conditional on the estimated bases. We illustrate the method---a tri-factorized non-negative RRR (NMF-RRR)---on four data sets spanning a permutation structure (Doubs, community ecology), a weak cross-structure under $p>n$ (nutrimouse, nutrigenomics), a pronounced one in a screened microbiome--metabolome study (FRANZOSA, where two microbial groups are jointly associated with each metabolite module), and a classification special case (Wine).

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arXiv2026

Wild Bootstrap Inference for Non-Negative Matrix Factorization with Random Effects

Non-negative matrix factorization (NMF) is widely used for parts-based representations, yet formal inference for covariate effects is rarely available when the basis is learned under non-negativity. We introduce non-negative matrix factorization with random effects (NMF-RE), a mean-structure latent-variable model $Y=X(\Theta A+U)+\mathcal{E}$ that combines covariate-driven scores with unit-specific deviations. Random effects act as a working device for modeling heterogeneity and controlling complexity; we monitor their effective degrees of freedom and enforce a df-based cap to prevent near-saturated fits. Estimation alternates closed-form ridge (BLUP-like) updates for $U$ with multiplicative non-negative updates for $X$ and $\Theta$. For inference on $\Theta$, we condition on $(\widehat X,\widehat U)$ and obtain fast uncertainty quantification via asymptotic linearization, a one-step Newton update, and a multiplier (wild) bootstrap; this avoids repeated constrained re-optimization. Simulations include a targeted stress test showing that, without df control, the random-effects penalty can collapse and inference for $\Theta$ becomes degenerate, whereas the df-cap prevents this failure mode. The non-negativity constraint induces sparse, parts-based loadings -- a measurement-side variable selection -- while inference on $\Theta$ identifies which covariates affect which components, providing covariate-side selection. Longitudinal, psychometric, spatial-flow, and text examples further illustrate stable, interpretable covariate-effect inference.

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arXiv2025

NMF-FFB: Non-negative matrix factorization with feedforward-feedback structure

Non-negative matrix factorization (NMF) approximates a non-negative endogenous data matrix as $Y_1 \approx XB$, with non-negative latent components $X$ and coefficients $B$. Standard covariate-aware NMF is feedforward: $B$ depends only on exogenous variables $Y_2$, with no latent feedback among endogenous variables. We propose NMF-FFB (NMF with feedforward-feedback structure), an exploratory data-fitting framework that embeds the simultaneous equation $B = \Theta_1 Y_1 + \Theta_2 Y_2$ in NMF, where $\Theta_1$ is non-negative latent feedback and $\Theta_2$ non-negative exogenous pathways. NMF-FFB is positioned within data-fitting structural equation modeling (SEM): it fits $Y_1$ directly rather than a model-implied covariance, and is not a confirmatory measurement model or a replacement for maximum-likelihood SEM under standard confirmatory factor analysis assumptions. When $\rho(X\Theta_1)<1$, the reduced form $Y_1 \approx (I-X\Theta_1)^{-1} X\Theta_2 Y_2$ defines a latent Leontief inverse separating direct from cumulative feedback-amplified effects. Estimation uses regularized multiplicative updates with orthogonality and sparsity penalties; an $X$-fixed bootstrap summarizes uncertainty for the feedback spectral radius, the amplification ratio, and path coefficients. Unlike conventional SEM, NMF-FFB requires only the latent rank $Q$ and lets $X$ group endogenous indicators into latent factors. This suits non-negative additive data, automatic loading discovery, Leontief-type cumulative effects, and small samples where covariance-based maximum-likelihood fitting is ill-conditioned. Applications to Holzinger-Swineford, Los Angeles pollution-mortality, and Mississippi county-level health data demonstrate interpretable parts-based representations across distinct latent-feedback regimes.

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arXiv2025

Applying non-negative matrix factorization with covariates to label matrix for classification

Non-negative matrix factorization (NMF) is widely used for dimensionality reduction and interpretable analysis, but standard formulations are unsupervised and cannot directly exploit class labels. Existing supervised or semi-supervised extensions usually incorporate labels only via penalties or graph constraints, still requiring an external classifier. We propose \textit{NMF-LAB} (Non-negative Matrix Factorization for Label Matrix), which redefines classification as the inverse problem of non-negative matrix tri-factorization (tri-NMF). Unlike joint NMF methods, which reconstruct both features and labels, NMF-LAB directly factorizes the label matrix $Y$ as the observation, while covariates $A$ are treated as given explanatory variables. This yields a direct probabilistic mapping from covariates to labels, distinguishing our method from label-matrix factorization approaches that mainly model label correlations or impute missing labels. Our inversion offers two key advantages: (i) class-membership probabilities are obtained directly from the factorization without a separate classifier, and (ii) covariates, including kernel-based similarities, can be seamlessly integrated to generalize predictions to unseen samples. In addition, unlabeled data can be encoded as uniform distributions, supporting semi-supervised learning. Experiments on diverse datasets, from small-scale benchmarks to the large-scale MNIST dataset, demonstrate that NMF-LAB achieves competitive predictive accuracy, robustness to noisy or incomplete labels, and scalability to high-dimensional problems, while preserving interpretability. By unifying regression and classification within the tri-NMF framework, NMF-LAB provides a novel, probabilistic, and scalable approach to modern classification tasks.

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arXiv2025

Applying non-negative matrix factorization with covariates to multivariate time series data as a vector autoregression model

We propose a novel framework for analyzing multivariate time series (MTS) data by integrating non-negative matrix factorization (NMF) with vector autoregression (VAR). Termed NMF-VAR, this method models the coefficient matrix of NMF as a VAR process, enabling simultaneous extraction of latent components and temporal dependencies. Unlike standard VAR, which struggles with high dimensionality and lacks clarity, our method introduces a low-rank latent structure that reduces the number of parameters while retaining explanatory power. The proposed framework generalizes the standard VAR model to high-dimensional non-negative data, including the standard VAR as a special case. We formulate the estimation as a constrained optimization problem and present multiplicative update rules for NMF based on existing tri-factorization techniques. We evaluate the method on three real-world datasets: quarterly first-differenced macroeconomic indicators of Canada, monthly international airline passenger volumes, and daily COVID-19 infection counts across Japanese prefectures. The results demonstrate that NMF-VAR effectively captures meaningful patterns such as economic cycles, seasonal travel behavior, and regional epidemic trends. Moreover, the method yields a significant reduction in regression parameters, improving both scalability and model transparency. Overall, NMF-VAR provides an efficient and insightful tool for analyzing high-dimensional and large-scale time series data.

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arXiv2025

Transfer Learning Strategies for Pathological Foundation Models: A Systematic Evaluation in Brain Tumor Classification

Foundation models pretrained on large-scale pathology datasets have shown promising results across various diagnostic tasks. Here, we present a systematic evaluation of transfer learning strategies for brain tumor classification using these models. We analyzed 254 cases comprising five major tumor types: glioblastoma, astrocytoma, oligodendroglioma, primary central nervous system lymphoma, and metastatic tumors. Comparing state-of-the-art foundation models with conventional approaches, we found that foundation models demonstrated robust classification performance with as few as 10 patches per case, despite the traditional assumption that extensive per-case image sampling is necessary. Furthermore, our evaluation revealed that simple transfer learning strategies like linear probing were sufficient, while fine-tuning often degraded model performance. These findings suggest a paradigm shift from "training encoders on extensive pathological data" to "querying pre-trained encoders with labeled datasets", providing practical implications for implementing AI-assisted diagnosis in clinical pathology.

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arXiv2024

Applying Non-negative Matrix Factorization with Covariates to the Longitudinal Data as Growth Curve Model

Using Non-negative Matrix Factorization (NMF), an observed matrix is approximated by a basis matrix times a coefficient matrix. When each individual's coefficient vector is explained by covariates, the coefficient matrix factorizes into a parameter matrix and a covariate matrix -- a tri-factorization whose mean structure coincides with that of the Growth Curve Model (GCM) for longitudinal data. This correspondence has been noted but not examined. We make three contributions. First, we compare NMF with covariates and the GCM: the basis is prescribed in the GCM but optimized in NMF, and the NMF-optimized basis can be used within the GCM and may improve its fit, the two agreeing when covariate effects are non-negative. Second, the main contribution, we develop statistical inference for the parameter matrix linking covariates to basis components: conditional on the optimized basis we provide standard errors, Wald-type tests, and one-sided confidence intervals, with a simulation study confirming good calibration for covariate-effect contrasts. Third, we compare NMF with principal component analysis (PCA) and functional PCA (FPCA): its non-negative coefficients are membership probabilities giving a soft clustering directly, whereas signed PCA/FPCA scores require a downstream classifier. Illustrations use growth data and a kernel-based varying-coefficient model.

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