\section{Introduction}
\label{sec:intro}
Since the advent of deep learning (DL) in medical image analysis~\cite{garbin2020deep,sarraf2020recent,rasool2023unveiling}, numerous studies have introduced customized convolutional neural network (CNN) architectures~\cite{li2014medical} and conducted large-scale predictive modeling using clinical datasets for computer-aided diagnosis~\cite{he2024open,ju2024universal,huang2024adapting}. Recent advances have demonstrated the applicability of DL to a wide range of clinical tasks. For instance, Lee~\textit{et al.} proposed CSS-Net~\cite{lee2022css} for rotator cuff tear (RCT) classification by modeling correlations between supraspinatus tendons and pathological regions. In breast cancer detection, Islam~\textit{et al.} introduced an ensemble CNN (EDCNN)~\cite{islam2024enhancing} combining MobileNet~\cite{howard2017mobilenetsefficientconvolutionalneural} and Xception~\cite{chollet2017xceptiondeeplearningdepthwise} via depthwise separable convolutions. For obstructive sleep apnea (OSA), Kim~\textit{et al.} presented a CNN-based framework surpassing traditional classification baselines~\cite{kim2024predicting,al2012automated}. Recent research has increasingly turned toward multi-modal learning to better exploit the rich, heterogeneous information embedded in DICOM data. This includes preprocessing pipelines and modality-bridging frameworks~\cite{anklesaria2022multi}, as well as methods for extracting complementary radiographic and pathological features~\cite{zhou2024multimodal}. With the rise of multi-modal image fusion~\cite{tang2022matr,team2024chameleon,zhou2024transfusion}, advanced architectures such as FusionM4Net~\cite{tang2022fusionm4net} and TFormer~\cite{zhang2023tformer} have been proposed for multi-scale lesion detection (MSLD). Concurrently, radiology-focused studies have underscored the value of integrating imaging with clinical metadata to construct more comprehensive and generalizable predictive models~\cite{cai2024multimodal,lu2024deep}.


However, significant challenges in medical imaging are the integration of patient-specific factors into predictive modeling~\cite{hodgetts2021shoulder}. Numerous studies have shown that demographic and physiological variables significantly influence disease manifestation. For instance, rotator cuff tears (RCT) exhibit distinct injury patterns between younger active individuals and elderly patients~\cite{reinholz2023advances}; breast cancer risk is modulated by occupational exposure~\cite{sari2020association}; and the severity of obstructive sleep apnea (OSA) is strongly correlated with anthropometric features such as BMI and neck circumference~\cite{ryu2013characteristics}. Caffo~\textit{et al.}~\cite{caffo2010novel} empirically demonstrated that stratifying patients based on attributes like age, gender, and race prior to feature selection significantly improves diagnostic performance. These findings underscore the importance of analytical frameworks that explicitly model patient heterogeneity. However, despite advances in deep learning for medical image analysis, most current approaches remain limited to isolated imaging modalities and fail to account for the multifactorial nature of clinical data.

To address these limitations, we propose the Statistically Coherent Network (SCN), a novel deep learning framework jointly integrating images and radiomics from DICOM and patient-specific attributes into a unified multi-space latent representation. SCN bridges heterogeneous modalities by enforcing statistical alignment among patient groups through a T-stochastic loss, which encourages samples with similar clinical profiles to exhibit coherent latent distributions. By aligning feature representations across diverse cohorts and imaging and linguistic modalities, SCN improves both predictive performance and model interpretability. Unlike conventional single-vector embeddings, our multi-space representation preserves fine-grained, group-specific variations, enabling the model to better capture clinically relevant heterogeneity. The key contributions of this work are summarized as follows:
\begin{itemize}
    \item We introduce a unified architecture integrating images, radiomics, and metadata to enable patient-aware representation learning.
    \item We design a matrix-based latent representation that encodes structured information across multiple subspaces.
    \item We propose a novel T-stochastic loss function to enforce distributional similarity among clinically similar subpopulations, extending beyond traditional distance-based objectives.
\end{itemize}