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Beyond Similarity: Heterogeneous Graph Learning for Multi-Objective Food Substitution in Charitable Food Agencies

Naimur Rahman Chowdhury, Limon Bin Hossain

arXiv:2608.21979v1cs.AI

TL;DR

Charitable food agencies need substitutes that balance household preferences, nutritional needs, and item similarity despite limited consumption records. The paper develops HeteroGNN over a unified public-data relational graph and evaluates multi-objective ranking under sparse and cold-start conditions. Results show added value from relational information, robustness to sparsity, and weak correlations among objectives that support keeping them separate.

  • Problem

    Food substitution decisions lack systematic, household-conditioned evidence for jointly matching behavior affinity, health suitability, and substitution similarity.

  • Method

    HeteroGNN integrates sparse public data into a unified relational graph and separately learns three objectives for ranking candidate substitutes.

  • Results

    The weighted multi-objective score is 0.9628 for HeteroGNN, exceeding MLP at 0.9164, BPR at 0.9211, and LightGCN at 0.9267; relational information adds predictive value beyond node features.

  • Takeaways & Limitations

    Weak correlations among the objectives support preserving separate targets so downstream decision-makers can inspect recommendation trade-offs.

  • Takeaways & Limitations

    The substitution similarity head is trained on only 56 mapped directional labels after 124 catalog-level pairs.

Abstract

from arXiv · show

Charitable food agencies play an important role in alleviating food insecurity by distributing donated food to people in need. However, they rely on ad hoc in-kind donations and often face shortages of specific foods, so they offer substitutes. A good food substitution requires matching household preferences, nutritional needs, and item similarity. Agencies have limited direct records of consumption behavior due to resource constraints, making it challenging to make an appropriate substitution decision that meets multiple criteria. In this study, we propose a heterogeneous graph neural network (HeteroGNN), a source-grounded recommendation framework for food substitution in charitable food agencies. We first build a unified relational graph from large-scale public data sources, combining household behavior on food consumption and food nutrient information in the United States (US) context. We treat the substitution recommendation as a multi-objective ranking problem with three targets, including behavior affinity, health suitability, and substitution similarity. We train and validate the proposed framework under standard graph relationship and adverse cold-start settings by removing relational edges from the graph. Our results show that the proposed framework leverages relational information beyond node features in predicting consumption behavior. Additionally, the proposed framework remains robust with sparsity when the model receives incomplete information about behavior and nutrient features. Finally, we show the weak correlation among different objectives, thereby justifying the multi-objective framing as a replacement for an aggregated decision. The proposed framework can help downstream charitable agency decision-makers make contextspecific substitution recommendations with limited information available.

I. INTRODUCTION

Food substitution in charitable agencies requires balancing household familiarity, nutritional suitability, and item similarity despite sparse, fragmented behavioral evidence. The proposed HeteroGNN unifies public relational data to rank substitutes across these distinct objectives.

  • Charitable agencies often substitute requested foods because donated inventories cannot reliably match household needs.
  • A suitable substitute must jointly reflect household behavior affinity, health suitability, and similarity to the requested item.
  • Existing food-assistance research emphasizes donation forecasting and inventory distribution, leaving household-conditioned substitution ranking largely unexplored.
  • Sparse, interdependent inputs from separate sources make analytical scoring difficult when behavioral or nutritional information is incomplete.
  • HeteroGNN integrates sparse public data into a relational graph and produces ranked substitutes while keeping the three objective scores distinct for trade-off evaluation.
  • The framework is evaluated for reliable recommendation performance under incomplete and sparse information.

A. Dataset and Graph Construction

The study combines public nutrition, demographic, dietary, and acquisition data into a unified heterogeneous graph. Separate construction streams produce a food catalog with substitution pairs and household-group behavioral relations.

  • USDA FoodData Central and FNDDS provide nutrient profiles and standardized food codes for the basic food catalog.
  • NHANES contributes demographic, dietary, and health information, while FoodAPS contributes household and individual food-acquisition records.
  • The pipeline builds food-catalog and substitution-pair data separately from person, household, and observed-behavior relations before merging them into one graph.
  • Directional substitution pairs use culinary-use overlap, food category, form, and nutrient closeness.
  • Household-context groups are formed using income band, household size, and SNAP participation, with consumption and acquisition aggregated as behavioral evidence.
  • The graph contains household groups, foods, nutrients, and categories connected by behavior, nutrient-content, category-membership, and substitution-similarity relations.

B. Objective Targets

The framework defines behavior affinity, health suitability, and substitution similarity as separate targets for candidate ranking. Health suitability uses profile-specific nutrient-density scores combined according to household health profiles.

  • The objective formulation ranks each candidate substitute for a household context and requested food along three targets.
  • Behavior evidence records acquisition occasions for each household-group–food pair and treats observed pairs as positive implicit feedback.
  • The health database provides six profile-specific scores covering general, diabetes, hypertension, obesity, child nutrition, and senior nutrition.
  • Each food–profile health score is a nutrient-density score based on beneficial and limiting nutrients.
  • The profile-specific score follows the Nutrient-Rich Foods index on a per-reference-amount basis.
  • A household group’s health target combines profile-specific scores using its estimated health-profile mixture.

3) Substitution Similarity Target:

The framework constructs directional food-substitution candidates from catalog and graph information, then uses HeteroGNN message passing to represent them. Candidate pairs combine culinary-use, category, form, and nutrient-profile components, with similarity as a target in [0, 1].

  • Candidate construction: Candidate pairs are directional and combine culinary-use, category, form, and nutrient-profile components.Only pairs whose request and substitute foods map to nodes in the FNDDS graph are included.
  • HeteroGNN architecture: A type-specific encoder maps each node's input feature vector into a hidden representation.
  • HeteroGNN architecture: Relation-specific transformations aggregate information from neighboring nodes at each message-passing layer.Multiple layers support an inductive graph representation.
  • HeteroGNN architecture: The message-passing output is normalized and passed through a nonlinearity, using edge weights in the aggregation.

2) Heads and Training Objective:

After HeteroGNN encoding, three prediction heads estimate the behavior, health, and similarity objectives. The heads use sigmoid outputs and are trained jointly with objective-specific losses.

  • Prediction heads: Three prediction heads operate on node-pair embeddings after HeteroGNN encoding.
  • Prediction heads: Each prediction head is a small feed-forward network with a sigmoid output.
  • Training objective: The model is trained with a joint loss combining the three objectives.
  • Training objective: Behavior uses binary cross entropy, while health and similarity use mean-squared error.

D. Weighted Multi-Objective Score

The model combines predicted behavior, health, and similarity scores into a weighted composite ranking score. The weights expose trade-offs among objectives; this study uses uniform weighting.

  • Weighted multi-objective score: The model produces three predicted scores per candidate for composite scoring.
  • Weighted multi-objective score: The composite score is a weighted sum of the behavior, health, and similarity predictions.
  • Weighted multi-objective score: The objective weights let downstream decision-makers evaluate trade-offs among recommendations.
  • Weighted multi-objective score: This study uses a uniform weight across the three targets.

III. EXPERIMENTAL SETUP

The experiments compare HeteroGNN with feature-based, pairwise-ranking, and graph baselines across standard and cold-start settings. They evaluate behavior affinity, health suitability, substitution similarity, and a weighted multi-objective score.

  • Validation settings: The evaluation uses standard and two cold-start splits, withholding behavior supervision for 1,774 foods or 8 of 42 household groups.The standard split randomly partitions observed behavior edges; cold-start splits remove relevant behavior edges and, for foods, connected similarity edges.
  • Baselines: The comparison includes BPR, MLP, LightGCN, and HeteroGNN under identical splits, information, features, and supervision.The baselines span heuristics, feature-based nonlinear modeling, and graph-based approaches.
  • Standard results: 0.9480 ROC-AUC and 0.9027 PR-AUC give HeteroGNN the best standard behavior-affinity performance, surpassing LightGCN and MLP.HeteroGNN’s relation-specific message passing and heterogeneous representation learning distinguish it from the compared models.
  • Standard results: 0.0128 MAE and 0.982 Spearman correlation make MLP best for health suitability, outperforming HeteroGNN’s 0.0182 MAE and 0.962 correlation.The passage attributes this pattern to explicit nutrient and demographic attributes being sufficiently represented in node features.
  • Standard results: For substitution similarity, HeteroGNN and MLP remain competitive with MAE values of 0.0222 and 0.0344, respectively, while BPR and LightGCN perform worse.The limited similarity supervision provides insufficient relational signal for graph-based advantage.
  • Multi-objective results: 0.9628 is HeteroGNN’s weighted multi-objective score, compared with 0.9164 for MLP, 0.9211 for BPR, and 0.9267 for LightGCN.The results support treating the three objectives jointly rather than relying on a single ranking mechanism.

B. Cold-Start Generalization

Cold-start evaluation shows that HeteroGNN’s behavior-affinity prediction degrades substantially when foods or household groups lack behavioral supervision. Health and similarity predictions remain more stable because they rely on relatively stable feature or food-food relational information.

  • Cold-start results: Cold-start behavior-affinity ROC-AUC falls from 0.9480 to 0.8381 for unseen foods and 0.6070 for unseen household groups.The group cold-start setting also reduces PR-AUC to 0.4367.
  • Cold-start results: The behavior decline indicates that HeteroGNN relies strongly on observed group–food behavioral structure and struggles when those behavioral edges are absent.The model does not fail across all objectives under group cold start; it specifically struggles to recover unseen household preferences.
  • Cold-start results: MLP outperforms HeteroGNN on cold-start behavior affinity because static node attributes remain available after relational behavioral supervision is removed.This makes MLP unusually competitive in the deliberately sparse relational setting.
  • Cold-start results: Similarity MAE rises from 0.0222 to 0.1260 for HeteroGNN in cold-start food, while reaching only 0.0333 in cold-start household groups.Removing food-similarity edges eliminates the primary relational signal for similarity, whereas food-food relations remain available when household groups are withheld.

1) Fairness Across Demographic Segments:

Cold-start household-group performance varies substantially across demographic segments, while sparsity analysis indicates that relational modeling remains useful when behavioral or nutritional information is incomplete.

  • Fairness Across Demographic Segments: 0.324 ROC-AUC for small households was the worst cold-start household-group result, below the random-ranker level.Performance was 0.781 below the poverty line and 0.640 for large households.
  • Fairness Across Demographic Segments: 0.781 ROC-AUC for households below the poverty line was the best reported cold-start household-group result.The aggregate ROC-AUC was 0.607, but the demographic breakdown ranged from 0.324 to 0.781.
  • Sparsity Analysis: Removing behavior relations affects both behavior affinity and health scoring, whereas removing nutrient features affects health scoring and can also affect behavioral affinity.The analyses report ROC-AUC for behavioral affinity and MAE for health suitability across both sparsity types.
  • Sparsity Analysis: HeteroGNN’s ROC-AUC dropped only 0.7%, from 0.9444 to 0.9378, when behavior edges were removed from 0% to 50%.MLP remained steady at 0.889 across these removal levels.
  • Sparsity Analysis: Under nutrient sparsity, HeteroGNN achieved better health-suitability MAE at 50% removal than MLP, 0.0379 versus 0.0481.The results state that graph relations can compensate when behavioral or nutritional information is incomplete.

D. Multi-Objective Trade-offs

The three substitution objectives are only weakly correlated, so the paper treats them as separate targets rather than as reliable proxies or a single aggregated objective. This preserves trade-offs for downstream ranking decisions.

  • Multi-Objective Trade-offs: Behavior affinity and health suitability are weakly negatively correlated at −0.067.The correlation is reported among the three predicted objectives.
  • Multi-Objective Trade-offs: Behavior affinity and similarity are weakly positively correlated at 0.090, while health suitability and similarity correlate at 0.070.None of the reported correlations is strong enough to treat one objective as a reliable proxy for another.
  • Multi-Objective Trade-offs: Because the objectives are weakly related, changing the weights αb, αh, and αs can change which candidate ranks first.The paper recommends condition-driven weights, such as increasing αh for a person with health conditions.
  • Food Assistance Operations and the Substitution Decision Gap: Food substitution is framed as ranking a candidate set conditioned on a household request, rather than forecasting donated supply alone.Prior food-assistance research focuses on inventory allocation and donation timing, while the substitution decision remains distinct.

C. Multi-Objective Recommendation

The paper presents heterogeneous graph learning as a way to combine relational evidence for multi-objective food substitution while retaining separate decision criteria. It also identifies scope limits from sparse similarity labels, limited cold-start groups, and fixed architecture reuse.

  • Multi-Objective Recommendation: Classic recommenders collapse relevance into one score, whereas food substitution requires preserving trade-offs among familiarity, nutrition, and similarity.The paper notes that familiarity-only ranking can reinforce nutritional gaps, while health-only ranking can suggest unfamiliar foods.
  • Graph Neural Networks for Heterogeneous Recommendation: Heterogeneous graph models propagate information across relations and support inductive representations for nodes unseen during training when features are available.The paper uses this relational-learning perspective to address gaps in food-bank substitution modeling.
  • Multi-Objective Recommendation: The framework integrates public data into a unified relational structure and predicts behavior affinity, health suitability, and substitution similarity as separate objectives.The conclusion describes four disparate public data sources and reports predictive value beyond node features alone.
  • Limitations: The substitution similarity head is trained on only 56 mapped directional labels, limiting the evidence available for that objective.The small label count is identified as the main reason similarity MAE degrades most under cold-start food.
  • Limitations: Cold-start household-group performance is estimated from only 8 held-out groups out of 42, making the aggregate ROC-AUC of 0.607 noisy.The segment results range from 0.324 to 0.781, showing substantial variation beneath the aggregate.
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