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VG-TIE: An interpretable tabular-to-image encoding method based on visibility graphs

David Chushig-Muzo, Luis M. López-Ramos, Ángeles Rodríguez de Cara, Eva Milara, Luis Zhinin-Vera, Diego H. Peluffo-Ordóñez

arXiv:2609.29650v1cs.CVcs.LG

TL;DR

Tabular-to-image methods offer a way to apply CNNs and vision transformers to tabular data, but their spatial layouts do not inherently express feature relationships or provide interpretability. VG-TIE combines visibility graphs with PCA-based image encoding and feature-importance explanations. Across six datasets, it is competitive with other tabular-to-image methods while providing interpretability.

  • Problem

    Existing tabular-to-image methods assign features to pixels, but their spatial layouts are not inherently interpretable and explicit interpretability work remains limited.

    Source: §1 · p. 1

  • Method

    VG-TIE orders features using PCA loadings, constructs visibility graphs from ordered feature values, and renders the results as images with degree-based and Grad-CAM explanations.

    Source: §3.1 · p. 2, §1 · p. 2, §3.1.2 · p. 3

  • Results

    Across six tabular datasets, VG-TIE is competitive with other tabular-to-image methods while providing interpretability, mainly for feature importance.

    Source: §1 · p. 2

  • Takeaways & Limitations

    VG-TIE combines predictive modeling and explainability in one framework, with structural rankings and global Grad-CAM rankings offering complementary feature views.

    Source: §6 · p. 6

Abstract

from arXiv · show

Tabular-to-image encoding methods enable the application of models based on both convolutional neural networks and vision transformers to tabular data, transforming feature vectors into images. Existing methods employ linear and nonlinear dimensionality reduction techniques (e.g., Principal Component Analysis (PCA), t-SNE, and UMAP) to determine pixel positions, resulting in images whose spatial layout do not inherently reflect feature relationships. This paper introduces Visibility Graphs for Tabular-to-Image Encoding (VG-TIE), a novel method that encodes the structure of feature values using Natural Visibility Graph (NVG) and Horizontal Visibility Graph (HVG) into a two-dimensional space obtained through PCA. The resulting images are model-agnostic and intrinsically interpretable. Each pixel corresponds to an input feature, its intensity reflects the magnitude and direction of deviation from the population mean, and edges represent formally defined visibility relationships between features. VG-TIE provides two interpretability methods: (i) feature ranking from node degree distributions; and (ii) local and global feature importance from pixel intensity combined with Grad-CAM. Experiments on six public tabular datasets show that VG-TIE is competitive with other tabular-to-image methods while providing interpretability on feature importance and ranking similar to intrinsic interpretable methods. The results highlight the potential of the proposed image-based transformation to provide an effective framework that expands the use of deep learning across tabular data domains.

1 INTRODUCTION

VG-TIE uses visibility graphs to make tabular-to-image representations interpretable, addressing layouts that do not inherently communicate feature relationships. Across six datasets, it is reported as competitive with other methods while providing feature-importance interpretability.

  • Existing tabular-to-image layouts are not inherently interpretable, and visibility graphs had not been systematically investigated for this encoding task.In critical domains such as healthcare, interpretability is paramount.Source: §1 · p. 1
  • VG-TIE uses PCA to project feature values into two dimensions and visibility graphs to encode structural relationships among features.The method employs Horizontal and Natural Visibility Graphs.Source: §1 · pp. 1–2
  • Its interpretability framework combines node-degree feature ranking with local and global feature importance from pixel intensity and Grad-CAM.Source: §1 · p. 2
  • The benchmark compares VG-TIE with TINTO, IGTD, DeepInsight, BarGraph, DistanceMatrix, Combination, BIE, and Fotomics.Source: §1 · p. 2
  • Across six tabular datasets, VG-TIE is competitive with other state-of-the-art methods while providing interpretability mainly related to feature importance.Source: §1 · p. 2

2 RELATED WORK

Related methods assign features to image positions or encode them through other representations, using dimensionality reduction, distance-preservation optimization, or feature-specific transformations.

  • BarGraph maps each feature to a fixed column with value-determined bar height, while BIE and correlated BIE stack binary-digit sequences into images.Source: §2 · p. 2
  • DeepInsight uses t-SNE or kernel PCA with convex-hull analysis; MRep-DeepInsight creates multiple representations, and DeepInsight-3D converts data into tensors.Source: §2 · p. 2
  • Fotomics maps Fourier coefficients to image-plane coordinates, whereas FC-Viz clusters correlated features and uses ant colony optimization for their spatial arrangement.Source: §2 · p. 2
  • IGTD and LM-IGTD iteratively swap feature assignments to reduce disagreement between feature-distance and sample-distance rankings.LM-IGTD extends IGTD to low-dimensional and mixed-type data using unsupervised stochastic noise generation.Source: §2 · p. 2
  • REFINED uses t-SNE, kernel PCA, and multidimensional scaling for feature coordinates; TINTO uses PCA or t-SNE and adds image blurring.Source: §2 · p. 2

3 METHODS

VG-TIE turns each tabular sample into an RGB image through PCA-based feature ordering, visibility-graph construction, and rendering. Its graph structure and image intensities support feature ranking and local and global importance estimates.

3.1 VG-TIE

  • Each sample becomes a fixed-size RGB image through feature ordering by PCA loading magnitude, visibility-graph construction, and pixel rendering.The same pipeline is applied to each sample in the dataset.Source: §3.1 · p. 2

3.1.1 Feature ordering by principal component analysis loading

  • Features are ordered by descending absolute PC1 loading, with high-loading features placed early in the visibility sequence.PCA is fitted on the normalized training matrix, and its ordering is reused for validation and test samples.Source: §3.1.1 · pp. 2–3

3.1.2 Visibility graph construction

  • HVG connects features according to relative height, while NVG also permits sloped-line visibility, producing denser graphs at O(n^2) complexity.HVG node degree reflects local ordinal structure; NVG includes every HVG edge and may add long-range edges.Source: §3.1.2 · p. 3

3.1.3 Pixel layout and image rendering

  • The RGB rendering uses blue intensity for weighted graph edges, green for positive deviations, and red for negative deviations from the mean.Feature-node intensity scales with the absolute standardized deviation; a black pixel represents a feature at its mean.Source: §3.1.3 · p. 3

3.2 Interpretability via visibility graph structure and class activation mapping methods

  • Visibility-graph structure provides a basis for interpreting the encoded images directly from their graph relationships.The method presents this as an advantage over existing tabular-to-image approaches.Source: §3.2 · p. 3

3.2.1 Feature ranking based on node degree distribution of visibility graphs

  • Feature ranking combines mean degree, degree variability, and degree-distribution asymmetry across samples into an importance score.Local peaks tend to block neighboring features, yielding low mean degree, high variance, and negative skewness; features are ranked by descending score.Source: §3.2.1 · pp. 3–4

3.2.2 Local and global feature importance via Grad-CAM and pixel intensity

  • Grad-CAM relevance at each feature’s fixed pixel is weighted by pixel intensity to produce local attribution, then aggregated across samples for global importance.The class-discriminative score is positive when a feature attracts more attention in class 1 and negative when it favors class 0.Source: §3.2.2 · p. 4

4 RESULTS

Across six UCI datasets, VG-TIE variants were competitive with other tabular-to-image methods. Feature fingerprints and feature rankings also provide dataset- and sample-level interpretability.

4.1 Datasets

  • The study evaluated six UCI datasets: MUSK, PAR, PIMA, QSAR, SPA, and WDBC, with Table 1 summarizing sample and feature counts.Source: §4.1 · p. 4, Table 1 · p. 4

4.2 Experimental setup

  • Evaluation used 80/20 train/test splits, five-fold stratified cross-validation, training-only random undersampling, and a shared SmallCNN backbone to isolate image-generation quality.Source: §4.2 · p. 4

4.3 Classification results

  • VG-TIE variants were competitive across six datasets; HVG was second-highest in PIMA AUCROC, both variants exceeded 0.9 AUCROC on WDBC, and HVG tied Combination for best AUCROC on PAR.Source: §4.3 · p. 5

4.4 Feature maps and fingerprints

  • PIMA diabetic fingerprints show denser top-right edges associated with glucose and age; Parkinson’s fingerprints show negative MDVP values and denser central connectivity, while malignant WDBC fingerprints highlight elevated size features.Source: §4.4 · p. 5

4.5 Local interpretability using Grad-CAM

  • Local Grad-CAM maps vary across samples: PIMA’s sixth diabetic sample is dominated by glucose, while malignant WDBC samples focus on tumor-size features.PIMA samples also highlight pregnancies and diabetes pedigree or blood pressure and BMI; benign WDBC samples emphasize texture, symmetry, or smoothness.Source: §4.5 · p. 5

4.6 Global interpretability using visibility graph and Grad-CAM

  • For PIMA, all five methods rank glucose first; degree ranks insulin and skin thickness higher than tree models, while pregnancies has low degree and high Grad-CAM discriminative rank.Source: §4.6 · p. 5
  • For PIMA, all five methods rank worst-case size measurements above mean and standard-error measurements; texture3 ranks higher under Grad-CAM, while fractal dimension ranks last.Degree distribution shows the broadest spread across feature groups.Source: §4.6 · p. 5

5 DISCUSSION

VG-TIE achieved competitive classification performance, with deterministic position-preserving encodings performing similarly and stochastic dimensionality-reduction methods doing worse on smaller, low-feature datasets. Its graph rankings offer a complementary interpretability signal to model-based rankings.

5 DISCUSSION

  • VG-TIE achieved competitive classification performance; Table 2 benchmarks tabular-to-image methods by mean AUCROC and standard deviation.Source: §5 · p. 5, Table 2 · p. 6
  • Deterministic position-preserving methods performed similarly to VG-TIE, while stochastic dimensionality-reduction methods performed worse on smaller datasets with fewer features.Visibility graphs capture co-occurrence structure in datasets with complex feature interactions.Source: §5 · p. 6
  • Degree-based rankings agreed moderately with model-based rankings, most strongly for top features and least for mid-ranked features; WDBC size features ranked highest structurally.The graph rankings provide a complementary signal to tree-based importance and CNN gradient attributions.Source: §5 · p. 6

6 CONCLUSIONS

VG-TIE encodes tabular data as RGB images using PCA-based visibility graphs and combines prediction with explainability. Its HVG and NVG variants performed among the best, while graph and Grad-CAM rankings exposed differing feature signals.

6 CONCLUSIONS

  • VG-TIE encodes tabular data as RGB images using PCA-based HVG or NVG graphs; HVG produced sparser, more interpretable graphs and generally slightly higher AUCROC.Source: §6 · p. 6
  • Degree-based structural rankings and global Grad-CAM rankings showed moderate agreement, with divergences identifying features structurally prominent in the graph but less discriminative for the CNN.Source: §6 · p. 6
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