\begin{algorithm}
\caption{sPCA}
\begin{algorithmic}[1]
\State \textbf{Input}: matrix observations $\{\mathbf{X}_t\}_{t=1}^T$, factor numbers $k_1$ and $k_2$.
\State Estimate loading matrices by equations \eqref{estimator_R} and \eqref{estimator_C}.
\State Estimate factor matrices and the signal part by equations \eqref{factormatrix_RaDFaM} and \eqref{signal_RaDFaM} for $t\in[T]$.
\State \textbf{Output}: $\widehat{\mathbf{R}}$, $\widehat{\mathbf{C}}$, $\{\widehat{\mathbf{Z}}_t\}_{t=1}^T$,
$\{\widehat{\mathbf{F}}_t\}_{t=1}^T$, $\{\widehat{\mathbf{E}}_t\}_{t=1}^T$, and $\{\widehat{\mathbf{S}}_t\}_{t=1}^T$.
\end{algorithmic}
\label{algorithm}
\end{algorithm}

\begin{algorithm}
\caption{sPCA}
\begin{algorithmic}
[1]
\State \textbf{Input}: matrix observations $\{\mathbf{X}_t\}_{t=1}^T$, factor numbers $k_1$ and $k_2$.
\State Estimate loading matrices by equations \eqref{estimator_R} and \eqref{estimator_C}.
\State Estimate factor matrices and the signal part by equations \eqref{factormatrix_RaDFaM} and \eqref{signal_RaDFaM} for $t\in[T]$.
\State \textbf{Output}: $\widehat{\mathbf{R}}$, $\widehat{\mathbf{C}}$, $\{\widehat{\mathbf{Z}}_t\}_{t=1}^T$,
$\{\widehat{\mathbf{F}}_t\}_{t=1}^T$, $\{\widehat{\mathbf{E}}_t\}_{t=1}^T$, and $\{\widehat{\mathbf{S}}_t\}_{t=1}^T$.
\end{algorithmic}
\end{algorithm}
{
    "title": "modeling and learning on high-dimensional matrix-variate sequences",
    "id": "2209.14846",
    "abstract": "we propose a new matrix factor model, named radfam, which is strictly derived based on the general rank decomposition and assumes a structure of a high-dimensional vector factor model for each basis vector. radfam contributes a novel class of low-rank latent structure that makes tradeoff between signal intensity and dimension reduction from the perspective of tensor subspace. based on the intrinsic separable covariance structure of radfam, for a collection of matrix-valued observations, we derive a new class of pca variants for estimating loading matrices, and sequentially the latent factor matrices. the peak signal-to-noise ratio of radfam is proved to be superior in the category of pca-type estimations. we also establish the asymptotic theory including the consistency, convergence rates, and asymptotic distributions for components in the signal part. numerically, we demonstrate the performance of radfam in applications such as matrix reconstruction, supervised learning, and clustering, on uncorrelated and correlated data, respectively.",
    "categories": "stat.me",
    "doi": "",
    "created": "2022-09-29",
    "updated": "2024-02-12",
    "authors": [
        "xu zhang",
        "catherine c. liu",
        "jianhua guo",
        "k. c. yuen",
        "a. h. welsh"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2209.14846"
}
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