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Tensor-based Fusion of Multi-modal Data for Predicting Cancer Risk Levels

Ali Anaissi, Yuanzhe Jia, Qishun Peng, Weidong Huang, Ali Braytee, Junaid Akram

arXiv:2610.13221v1cs.LGq-bio.QM

TL;DR

High-dimensional multi-modal cancer data are difficult to interpret and conventional approaches may not capture cross-modal features for risk stratification. The paper combines feature extraction, tensor decomposition, and clustering, and reports that tSVD+GMM performs best across clinical indicators.

  • Problem

    High-dimensional multi-modal data challenge interpretation and dimensionality reduction, while conventional methods may not extract cross-modal features for cancer risk stratification.

    Source: §1 · p. 2

  • Method

    The framework reduces feature matrices, builds a third-order tensor from genomic and clinical data, applies CP decomposition, and clusters the resulting representations.

    Source: §4 · p. 8, §6 · p. 11

  • Results

    tSVD+GMM consistently showed superior accuracy, robustness, and alignment with clinical risk indicators including pathologic stages and tumor purity.

    Source: §6 · pp. 11–12, Overview and Future Perspectives · p. 11

  • Takeaways & Limitations

    The authors conclude that tensor-based fusion with feature extraction and clustering provides a reliable unsupervised approach to cancer risk prediction.

    Source: §6 · p. 12

    Future work will extend evaluation to additional cancer types and incorporate survival modeling and external validation.

    Source: §6 · p. 12

Abstract

from arXiv · show

Cancer diagnosis and treatment increasingly rely on multi-modal diagnostic technologies that generate high-dimensional datasets. Although these datasets are rich in pathological information, they pose considerable challenges in interpretation, dimensionality reduction, and clinical applicability. Conventional machine learning approaches often fail to extract meaningful cross-modal features, thereby limiting predictive accuracy in patient risk stratification. To address these limitations, this paper proposes an unsupervised machine learning framework that integrates feature extraction, tensor decomposition, and clustering to improve cancer risk prediction. The framework employs tensor decomposition to fuse heterogeneous genomic and clinical data, enabling the extraction of latent, biologically meaningful features that outperform unimodal feature sets. Multiple feature extraction strategies are investigated, and the resulting features are subsequently clustered using a range of clustering algorithms. Comparative evaluations based on internal and external metrics are then used to identify the most effective configurations. The framework is validated on LinkedOmics data comprising 11,158 patients across 32 cancer types. For patient risk stratification, clinically relevant attributes such as tumor purity, pathological stage, and survival outcomes serve as ground-truth indicators. Experimental results demonstrate the superiority of tSVD+GMM, which consistently outperforms other configurations across clinical benchmarks.

1 Introduction

The paper proposes an unsupervised approach that integrates genomic and clinical patient data to distinguish high- and low-risk cancer groups.

1 Introduction

  • The paper frames cancer’s genetic heterogeneity and AI models’ narrow gene focus as challenges for diagnosis and risk analysis.The introduction cites diagnostic error rates of 15–45% in U.S. clinical settings.Source: §1 · p. 2
  • The proposed unsupervised framework integrates micro-level genomic and macro-level clinical data to analyze cancer and distinguish high- from low-risk patients.Source: §1 · p. 2
  • The paper presents multi-faceted cancer data integration as a basis for risk detection, prognostic assessment, and support for personalized therapeutic interventions.Source: §1 · p. 2

2 Related Work

Prior work applies machine learning, network analysis, and tensor methods to genome–disease prediction, while the review identifies a need to integrate genomic and clinical information.

2 Related Work

  • Semi-supervised methods address limitations involving unlabeled samples and similarity measures, while KATZ and CATAPULT combine machine learning with network analysis.KATZ uses known genome–disease associations and similarity information; CATAPULT uses clustering to construct an SVM classifier.Source: §2 · p. 3
  • Tensor research includes joint SVD and CMF for multi-domain integration, CORCONDIA for selecting PARAFAC components, and models combining genetic or environmental data.Examples include KBMF-MDI and MGDFMDE.Source: §2 · p. 3
  • The review argues that genomic or clinical data alone are insufficient for cancer analysis and that both genetic and demographic factors matter for subtype models.Source: §2 · p. 3

3 Preliminary

The preliminary section introduces dimensionality reduction and algebraic operations used to prepare and relate feature representations for tensor analysis.

Principal Component Analysis (PCA)

  • PCA projects high-dimensional data into a lower-dimensional representation that retains dominant variance, using the top k eigenvectors of the covariance matrix.The transformed representation is Z = XVk.Source: Principal Component Analysis (PCA) · p. 3

Truncated Singular Value Decomposition (tSVD)

Multidimensional Scaling (MDS)

  • MDS embeds data in fewer dimensions while preserving pairwise dissimilarities; matrix products provide operations downstream for tensor construction and decomposition.The Kronecker product generates pairwise multiplicative matrix interactions, Khatri-Rao is column-wise Kronecker, and Hadamard is element-wise for identically sized matrices.Source: Multidimensional Scaling (MDS) · p. 4

3.2 Tensor Decomposition

CP decomposition represents a tensor as a sum of rank-one tensors, exposing multidimensional relationships in the data.

3.2 Tensor Decomposition

  • CP decomposition expresses a tensor as a sum of rank-one tensors and uses mode-n matricization to define its decomposition.Source: §3.2 · p. 5

CANDECOMP/PARAFAC (CP) decomposition

CP decomposition approximates a tensor using rank-one components combined into factor matrices. ALS iteratively updates these matrices, while CORCONDIA is used to tune the decomposition rank.

CANDECOMP/PARAFAC (CP) decomposition

K-means

The section describes three clustering approaches: K-means uses cluster means, K-medians uses component-wise medians, and GMM assigns points through Gaussian-component probabilities.

K-means

  • K-means assigns each point to its nearest centroid, then updates each centroid to the mean of its assigned points until convergence.It partitions data into a predefined number K of clusters by minimizing within-cluster squared distances.Source: K-means · p. 6

K-medians

  • K-medians minimizes Manhattan distances and updates cluster centers with component-wise medians, making it more robust to outliers and noise than K-means.Source: K-medians · p. 6

Gaussian Mixture Model (GMM)

  • GMM models data as a mixture of K multivariate Gaussian components and uses EM to estimate parameters and assign points to the most probable component.Its probabilistic framework supports soft assignments for downstream analysis.Source: Gaussian Mixture Model (GMM) · p. 6

DBSCAN

The section presents density-based DBSCAN, hierarchical clustering, and the high-dimensional subspace method CLIQUE, which combines grid- and density-based strategies.

DBSCAN

  • DBSCAN groups dense regions separated by lower-density regions, using ε and minPts to identify core points and treating neither-core-nor-border samples as noise.It can find arbitrarily shaped clusters without specifying their number in advance.Source: DBSCAN · p. 6

Hierarchical Clustering

  • Hierarchical clustering builds a nested tree through bottom-up agglomerative merging or top-down divisive splitting.Agglomerative clustering merges the closest clusters until the desired number is reached; divisive clustering recursively partitions the full dataset.Source: Hierarchical Clustering · p. 7

Clustering in Quest (CLIQUE)

  • CLIQUE grids each dimension, identifies dense units across subspaces, and merges adjacent units into connected cluster regions.It is designed for high-dimensional datasets and does not require the number of clusters in advance.Source: Clustering in Quest (CLIQUE) · p. 7

4 Methodology

The methodology preprocesses feature matrices, reduces their dimensionality, stacks them into a tensor for CP decomposition, and clusters the resulting patient factors against clinical labels.

4 Methodology

  • At least 95% of original variance is preserved when PCA, tSVD, and MDS project the feature matrices into a common low-dimensional space.Five hundred components were identified as optimal across the genomic datasets; preprocessing removes attributes with missing values.Source: §4 · pp. 7–8
  • The reduced patient-feature matrices are stacked into a third-order tensor, and CP decomposition uses rank 2 selected by CORCONDIA.The patient factor dimension is selected for downstream analysis; the stacking order has negligible impact on results.Source: §4 · p. 8
  • The patient factors are clustered with partition-, density-, model-, grid-, and hierarchical methods and evaluated against clinical labels using internal and external metrics.Labels include tumor purity, pathologic T stage, pathologic N stage, and pathologic stage; Figure 1 depicts the proposed model architecture.Source: §4 · pp. 7–8, Figure 1 · p. 7

5 Experiments

The experiments evaluate multimodal patient-risk clustering on LinkedOmics data, comparing feature-reduction and clustering configurations against clinical indicators. Across the reported evaluations, tSVD+GMM most consistently aligns with clinical risk labels, while other algorithms and metrics show configuration-specific strengths.

5.1 Dataset

  • LinkedOmics data covered 32 cancer types and 11,158 patients; the Breast Invasive Carcinoma analysis integrated clinical, methylation, miRNA, RNA-seq, and copy-number data.The breast-cancer subsets ranged from 755 to 1,097 patients and varied substantially in feature counts.Source: §5.1 · p. 8

5.2 Settings

  • PCA, tSVD, and MDS used 500 components to retain at least 95% variance, and CORCONDIA selected rank 2 for PARAFAC.The rank was chosen after evaluating ranks 1 through 10.Source: §5.2 · p. 9
  • The hierarchical-clustering comparison favored Manhattan distance with complete linkage, while K-means, K-medians, and GMM used two clusters.The table caption identifies the comparison as hierarchical-clustering configurations but provides no cell values.Source: Table 1 · p. 9, §5.2 · p. 10

Feature Selection

  • Tumor purity, pathologic T and N stages, and pathologic stage informed binary risk classification; overall survival was excluded from external evaluation because discretization was impractical.Tumor purity's Jaccard-based cutoff was 0.75.Source: Feature Selection · p. 10

Overview and Future Perspectives

Evaluation Metrics

  • The evaluation used pathology T stage as a baseline, with Silhouette and Calinski-Harabasz internal metrics and Fowlkes-Mallows and accuracy external metrics.The internal measures assess cohesion and separation, while external measures assess agreement with clinical labels.Source: Evaluation Metrics · p. 10

Comparative Analysis

  • For pathology N stage, every model combination exceeded 0.5 accuracy; tSVD+GMM reached 0.661, while pathologic-stage Silhouette scores ranged from 0.3 to 0.6.For pathologic stage, tSVD-enhanced K-means, K-medians, and GMM each achieved Calinski-Harabasz scores above 1000; tSVD+GMM also performed effectively for tumor purity, with slightly lower Fowlkes-Mallows and accuracy scores than for pathologic stage.Source: Comparative Analysis · p. 11

Clustering Algorithms

  • DBSCAN formed clusters inconsistently and struggled to meet the specified cluster count; hierarchical clustering peaked at 45% accuracy, and CLIQUE had difficulty extracting labels.Numerous hierarchical-clustering outcomes registered below 1% accuracy.Source: Clustering Algorithms · p. 11

6 Conclusion

The conclusion presents an unsupervised framework that combines feature extraction, tensor decomposition, and clustering for genomic and clinical data. It reports tSVD+GMM as the strongest pipeline in the LinkedOmics experiments and identifies broader cancer coverage, survival modeling, and external validation as future work.

6 Conclusion

  • The framework combines PCA, tSVD, and MDS, CP decomposition, and clustering to analyze patient genomic and clinical data.It constructs a third-order tensor and extracts latent patient, feature, and method components.Source: §6 · p. 11
  • On LinkedOmics data, tSVD+GMM achieved superior accuracy, robustness, and alignment with pathologic T and N stages and tumor purity, supporting high- and low-risk patient stratification.The conclusion characterizes the combined tensor-fusion and clustering approach as a reliable unsupervised method for cancer risk prediction.Source: §6 · pp. 11–12
  • Future work will extend the framework to additional cancer types and incorporate survival modeling and external validation.Source: §6 · p. 12
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