\begin{algorithm}
\caption{Algorithm to solve the optimisation problem \ref{met:merge}}\label{alg:cap}
\begin{algorithmic}
\Require Dataset $\mathbf{Y}$ and hyperparameter $\beta$
    \State $\mathbf{w}= \mathbf{1}$
    \For{$i \in$   $\{1,...,I\}$}
        \State Solve the regression problem equation \ref{met:reg2}
        \State $\mathbf{h} =  \mathbf{Y} \mathbf{w} $
        \State $\mathbf{z}=\mathbf{h}$
        \State $z_t=0$ for $t \in \{1,...,T_d\}$ if $z_t>0$
        \State $z_t=1$ for $t \in \{T_f,...,T\}$ if $z_t<1$
        \State Perform isotonic projection on $\mathbf{z}$ using the PAVA algorithm \cite{wang2021remaining}
    \EndFor
\end{algorithmic}
\end{algorithm}

\begin{algorithm}
\caption{Algorithm to solve the optimisation problem \ref{met:merge}}\begin{algorithmic}
\Require Dataset $\mathbf{Y}$ and hyperparameter $\beta$
\State $\mathbf{w}= \mathbf{1}$
\For{$i \in$ $\{1,...,I\}$}
\State Solve the regression problem equation \ref{met:reg2}
\State $\mathbf{h} = \mathbf{Y} \mathbf{w} $
\State $\mathbf{z}=\mathbf{h}$
\State $z_t=0$ for $t \in \{1,...,T_d\}$ if $z_t>0$
\State $z_t=1$ for $t \in \{T_f,...,T\}$ if $z_t<1$
\State Perform isotonic projection on $\mathbf{z}$ using the PAVA algorithm \cite{wang2021remaining}
\EndFor
\end{algorithmic}
\end{algorithm}
{
    "title": "semi-supervised health index monitoring with feature generation and   fusion",
    "id": "2312.02867",
    "abstract": "the health index (hi) is crucial for evaluating system health, aiding tasks like anomaly detection and predicting remaining useful life for systems demanding high safety and reliability. tight monitoring is crucial for achieving high precision at a lower cost. obtaining hi labels in real-world applications is often cost-prohibitive, requiring continuous, precise health measurements. therefore, it is more convenient to leverage run-to failure datasets that may provide potential indications of machine wear condition, making it necessary to apply semi-supervised tools for hi construction. in this study, we adapt the deep semi-supervised anomaly detection (deepsad) method for hi construction. we use the deepsad embedding as a condition indicators to address interpretability challenges and sensitivity to system-specific factors. then, we introduce a diversity loss to enrich condition indicators. we employ an alternating projection algorithm with isotonic constraints to transform the deepsad embedding into a normalized hi with an increasing trend. validation on the phme 2010 milling dataset, a recognized benchmark with ground truth his demonstrates meaningful his estimations. our contributions create opportunities for more accessible and reliable hi estimation, particularly in cases where obtaining ground truth hi labels is unfeasible.",
    "categories": "cs.lg stat.me",
    "doi": "",
    "created": "2023-12-05",
    "updated": "2024-02-16",
    "authors": [
        "ga\u00ebtan frusque",
        "ismail nejjar",
        "majid nabavi",
        "olga fink"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2312.02867"
}
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