The input units for our contrastive learning framework consist of textual indicator descriptions processed into 768-dimensional dense vector embeddings.

Each indicator description is tokenized and encoded using the BERT-base-uncased model, with a maximum sequence length of 512 tokens to capture comprehensive semantic information.

The encoder f_θ in our contrastive learning framework is implemented using BERT-base-uncased (Bidirectional Encoder Representations from Transformers), a pre-trained language model with 12 layers, 12 attention heads, and a hidden dimension of 768. We specifically chose BERT-base over alternatives like RoBERTa or DistilBERT due to its proven effectiveness in capturing semantic relationships in scientific literature and its balanced performance-efficiency trade-off for our corpus size. Additionally, BERT-base demonstrates superior performance in domain-specific fine-tuning tasks with limited data, which aligns with our corpus of 230 articles (31).

The BERT model was fine-tuned on our domain-specific literature corpus of 230 articles for 3 epochs with a learning rate of 2e-5, batch size of 16, and maximum sequence length of 512 tokens. It is important to note that all 230 articles in our corpus were published in English, which represents a limitation we address in our discussion of linguistic bias.

This fine-tuning process adapts the pre-trained representations to the specific vocabulary and semantic patterns present in community resilience literature, improving the quality of extracted embeddings for subsequent contrastive learning. The fine-tuning objective combines the original masked language modeling loss with our contrastive learning objective, ensuring domain adaptation while preserving the model's general language understanding capabilities.

To ensure reproducibility of our machine learning pipeline, we provide comprehensive technical specifications in Table 1. These specifications detail all critical hyperparameters, training configurations, and validation strategies employed in our contrastive learning framework.

The positive pairs were generated through data augmentation techniques that preserve semantic meaning while introducing lexical diversity. For each anchor document d_i, we applied random masking (masking 15% of tokens with [MASK] tokens), sentence reordering (randomly permuting sentence order within abstracts), and synonym replacement using WordNet to create the positive sample di+. These augmentations ensure that the model learns robust semantic representations invariant to surface-level textual variations.

Negative samples were drawn from in-batch negatives, where all other documents in the same training batch served as negative examples. With a batch size of 16, each anchor had 15 negative samples, providing a challenging contrastive learning signal. This in-batch negative sampling strategy is computationally efficient and has been shown to produce high-quality embeddings in similar text representation tasks.

Model validation was performed every 50 training steps using a held-out validation set of 35 articles (15% of the corpus). We monitored three key metrics: (1) contrastive accuracy (percentage of cases where positive pairs ranked higher than all negatives), (2) mean reciprocal rank (MRR) of positive pairs, and (3) embedding coherence score (average cosine similarity of embeddings from semantically similar indicator descriptions). Early stopping was triggered if MRR showed no improvement for 5 consecutive validation checks, though this criterion was not met during our training as the model converged stably within 3 epochs.

Given a corpus of documents D={d1,d2,...,dN}, the contrastive learning model aims to learn an encoder f_θ that maps each document to a representation vector. For each document d_i, we generate a positive pair by applying data augmentation techniques to create di+, which is a semantically equivalent version of d_i. The contrastive loss function used in this study is the InfoNCE loss, which is defined as:

where sim(u, v) represents the cosine similarity between vectors u and v, calculated as:

and τ is the temperature parameter controlling the concentration level of the distribution, set to 0.07 in our implementation. Through this optimization process, the model learns to encapsulate semantic information in the document representations, enabling the identification of important indicators based on their embedding patterns.

The research team adopted the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) method for literature screening, ultimately identifying 230 high-quality articles related to community resilience in public health emergencies from multiple databases for analysis (32).

The systematic literature search was conducted across four major databases: Web of Science (Core Collection, accessed January 2024), Scopus (accessed January 2024), PubMed (accessed January 2024), and CNKI (China National Knowledge Infrastructure, accessed January 2024). The search covered publications from January 2010 to December 2024.

The search string employed Boolean operators combining concept clusters: (“community resilience” OR “community preparedness” OR “community adaptation”) AND (“public health emergency” OR “epidemic” OR “pandemic” OR “health crisis” OR “disease outbreak”) AND (“assessment” OR “evaluation” OR “framework” OR “indicator” OR “measure”). This search strategy was adapted to each database's specific syntax requirements while maintaining conceptual consistency.

An important methodological constraint arose from our BERT-based contrastive learning pipeline, which requires full-text availability in English for computational text analysis. While CNKI was initially included to capture potentially relevant Chinese-language literature, articles available only in Chinese without English full-text versions were excluded during the screening process due to incompatibility with our natural language processing framework. This language filtering criterion was applied consistently across all databases, resulting in the retention of only English full-text articles in the final corpus. We acknowledge this as a limitation and discuss its implications for global representativeness in the Discussion section.

The PRISMA screening process was as follows:

Beyond methodological quality assessment, specific exclusion criteria were applied during the full-text review stage following established systematic review guidelines (32). Table 2 presents the seven categories of exclusion criteria systematically applied to ensure only high-quality, community-focused resilience studies were retained for analysis.

These exclusion criteria ensured that only studies with robust empirical foundations and community-focused resilience frameworks were included in our analysis, maintaining the scientific rigor necessary for reliable indicator extraction.

Figure 2 shows the PRISMA literature screening flow chart used in this study, visually presenting the screening process from initial retrieval to final inclusion in the analysis.

Contrastive learning algorithms were applied to these articles for theme extraction. First, the literature was preprocessed, including PDF-to-text conversion, word segmentation, and removal of stop words and punctuation (33). Then, the contrastive learning model analyzed the text, using data augmentation techniques such as random masking to generate positive sample pairs and negative samples from other documents in the batch (34). By minimizing the contrastive loss function, the model learned distributed representations of concepts in the literature and identified frequently occurring and representative indicators (35).

Figure 3 details the contrastive learning framework adopted in this study, including key components such as input literature, data augmentation, Transformer encoding, and InfoNCE loss function, as well as the four stages of indicator extraction.

The key phrase extraction process employed a multi-stage approach combining computational and manual validation methods:

Stage 1: TF-IDF and contrastive embeddings Initial candidate phrases were identified using a hybrid approach combining Term Frequency-Inverse Document Frequency (TF-IDF) scoring with contrastive embedding similarity measures. TF-IDF scores identified statistically significant terms, while contrastive embeddings captured semantic relationships and contextual relevance within the resilience domain.

Stage 2: manual validation Three independent researchers with expertise in public health, urban planning, and disaster management conducted manual validation of extracted phrases. Each researcher evaluated phrase relevance, clarity, and actionability using structured evaluation criteria.

Stage 3: inter-rater reliability assessment Cohen's kappa coefficient was calculated to assess inter-rater reliability among the three researchers, achieving κ = 0.82, indicating substantial agreement and validating the consistency of our extraction methodology.

Stage 4: quality assessment criteria and thresholds Quality assessment employed multiple criteria with specific thresholds to ensure methodological rigor. First, each phrase required a semantic coherence score of at least 0.65, measured by cosine similarity in embedding space, to confirm contextual relevance. Second, phrases needed to achieve a TF-IDF relevance score of 0.45 or higher when normalized across the corpus, indicating statistical significance within the literature. Third, manual reviewer consensus required agreement from at least 67% of evaluators (minimum 2 out of 3 researchers), ensuring human validation of computational results. Finally, phrases were required to meet a specificity index threshold of 0.50, effectively excluding overly generic terms that would compromise indicator precision.

Only phrases meeting all quality thresholds progressed to the subsequent clustering and expert validation stages, ensuring high-quality indicator extraction throughout the process.

To ensure the representativeness and reliability of the extracted indicators, strict candidate indicator screening rules and processes were established (36). The screening methodology incorporated three complementary criteria designed to maximize indicator quality and cross-study validity. Frequency thresholding required each candidate phrase to occur with a total frequency of at least 7 times across all literature, a threshold determined by calculating the quartiles of the frequency distribution of all extracted phrases and selecting the upper quartile (Q3) as the minimum frequency requirement. Source breadth validation ensured that each candidate phrase appeared in at least 10 different articles, guaranteeing that selected indicators demonstrate cross-study consistency rather than being emphasized only in individual studies. Finally, semantic relevance filtering required phrases to achieve a minimum score of 0.65 (out of 1.0) as calculated by the contrastive learning model, a threshold established through discussions with domain experts to ensure indicators maintained high relevance to the community resilience theme.

To validate the robustness of our screening criteria, we conducted a comprehensive sensitivity analysis by varying the semantic relevance threshold across a range of values (0.55, 0.60, 0.65, 0.70, 0.75). Table 3 presents the detailed results, demonstrating that our final indicator set demonstrates remarkable stability across different threshold values.

The high overlap rates (>85%) across reasonable threshold ranges demonstrate that our indicator selection is robust and not overly dependent on the specific threshold value. The threshold of 0.65 was selected as it provides the optimal balance between comprehensiveness and selectivity, capturing indicators that are both statistically significant and semantically coherent. This threshold corresponds to the point where the marginal utility of additional indicators begins to diminish while maintaining high expert validation scores (average 4.35/5.0).

Table 4 outlines the specific criteria applied during the phrase quality filtering stage to ensure only high-quality, semantically meaningful indicators were retained.

The systematic indicator screening process was implemented through four distinct phases, as detailed in Table 5. This multi-stage approach ensures comprehensive evaluation while maintaining methodological rigor.

Figure 4 shows the detailed process of candidate indicator screening, clearly presenting the screening criteria and results from the initial 582 phrases to the final 39 indicators.

Expert validation: Five domain experts (including two public health experts, two urban planning experts, and one disaster management expert) conducted independent assessments to validate the suitability of each indicator (37). Only indicators that received approval from at least four experts (using a 5-point Likert scale, with an average score of ≥ 4) were retained.

The entire screening process employed a combination of quantitative criteria and qualitative expert judgment, ensuring that the final 39 indicators not only have statistical representativeness but also effectiveness and operability in practical applications (38). The screening process particularly emphasized complementarity and coverage between indicators to construct a comprehensive and non-redundant assessment framework (39).

The hyperbolic space can be defined using the Poincaré ball model of dimension n:

with the distance between two points x and y in the Poincaré ball given by:

A notable characteristic of hyperbolic space is its exponential expansion with increasing radius. The volume of a ball with radius r in hyperbolic space grows exponentially with r:

In contrast, the volume of a ball in Euclidean space grows only polynomially: VolE(Br)~rn. This exponential growth property makes hyperbolic space particularly suitable for embedding hierarchical structures, as the number of nodes in tree-like hierarchies typically grows exponentially with depth.

To quantify the effectiveness of hyperbolic embedding in preserving hierarchical structures, we introduced the Hierarchical Fidelity Score (HFS):

where H is the set of hierarchical relationships with i being a parent of j, x₀ is the origin (root) of the hierarchy, and 𝕀[·] is the indicator function. A higher HFS indicates better preservation of hierarchical relationships.

The ground truth hierarchical relationships H were established through a systematic three-stage process to avoid circular reasoning:

Stage 1: literature-based hierarchy construction: We first analyzed the co-occurrence patterns and citation relationships within our 230-article corpus to identify naturally emerging hierarchical structures. Indicators that consistently appeared as prerequisites or foundational concepts for other indicators were identified as potential parent nodes.

Stage 2: domain knowledge integration: Independent from our embedding model, we consulted established community resilience frameworks (Cutter et al.'s Community Resilience Index, PEOPLES framework, and Sendai Framework indicators) to identify theoretically grounded hierarchical relationships. This stage ensures our hierarchy reflects established domain knowledge rather than model-specific patterns.

Stage 3: expert consensus validation: A panel of 8 domain experts (distinct from those involved in indicator validation) independently ranked indicators by their foundational importance through structured expert review. Only hierarchical relationships with >75% expert agreement were included in H.

This multi-stage approach ensures that our HFS evaluation is based on independently established ground truth rather than model-generated hierarchies, thereby avoiding the risk of circular validation. The resulting H contains 156 validated hierarchical relationships among our 39 indicators.

Hyperbolic embeddings are particularly well-suited for capturing hierarchical relationships in resilience indicators for several theoretical reasons:

Figure 5 intuitively compares the characteristic differences between Euclidean space and hyperbolic space, and shows the performance comparison of the two embedding methods in terms of hierarchical fidelity and distortion rate.

The MHSA mechanism operates on the hyperbolic embeddings of our 39 indicators to generate a relationship matrix C ∈ ℝ^{39 × 39}. Each indicator's hyperbolic embedding hi∈ℝ768 is first projected into Query (Q), Key (K), and Value (V) spaces:

where WQ,WK,WV∈ℝ768×64 are learned projection matrices. The attention weight matrix is calculated as:

where d_k = 64 is the dimension of the key vectors. We employ 8 attention heads (h = 8), each capturing different types of relationships between indicators. The outputs from all heads are concatenated and linearly transformed to produce the final relationship matrix C.

The relationship matrix C is subject to a Directed Acyclic Graph (DAG) constraint to ensure hierarchical consistency: h(C) = tr(e^C°C) − 39 = 0, where ° is the Hadamard product. This constraint prevents circular dependencies in the indicator relationships.

Tangent space projection for clustering Acritical methodological consideration is that k-means clustering assumes Euclidean distance metrics and centroids, which are not directly compatible with hyperbolic embeddings in the Poincaré ball. To address this, we employ tangent space projection to map hyperbolic embeddings into Euclidean space before clustering, preserving local geometric relationships while enabling the use of standard clustering algorithms.

Formally, for a hyperbolic embedding x ∈ 𝔹ⁿ (Poincaré ball), the tangent space projection at the origin o is given by the logarithmic map:

This projection maps points from the Poincaré ball to the tangent space To𝔹n≅ℝn at the origin, which is isomorphic to Euclidean space. The scaling factor 21-∥x∥2 ensures that hyperbolic distances are approximately preserved for points near the origin, making this projection particularly suitable for our indicator embeddings which are relatively concentrated near the center of the Poincaré ball due to their semantic coherence.

The MHSA output serves as input to our clustering algorithm through the following workflow:

Selection of optimal cluster number The choice of k = 4 clusters was determined through comprehensive evaluation using multiple clustering quality metrics. We systematically tested cluster numbers from k = 3 to k = 7 and evaluated each configuration using three complementary metrics: (1) Silhouette Coefficient, which measures how similar an object is to its own cluster compared to other clusters (higher is better), (2) Davies-Bouldin Index, which evaluates the average similarity ratio of each cluster with its most similar cluster (lower is better), and (3) Topic Coherence Score, which assesses the semantic interpretability of resulting clusters.

As detailed in Figure 8, the k = 4 configuration achieved the highest Silhouette Coefficient (0.68), lowest Davies-Bouldin Index (0.52), and highest Topic Coherence Score (0.74) among all tested values. This convergence across multiple independent metrics provides strong evidence for the robustness of the four-cluster solution. Additionally, k = 4 yielded clusters with meaningful semantic interpretability corresponding to established community resilience domains: Medical and Safety Measures, Spatial Design and Infrastructure, Community Services and Support, and Landscape and Ecology.

This integration ensures that our clustering reflects both the hyperbolic geometric relationships and the attention-based semantic relationships between indicators.

Figure 6 presents the complete hierarchical relationship matrix for all 39 indicators, visualizing the strength of relationships both within and across the four identified categories.

Our validation methodology employs three distinct but interconnected stages, each serving specific validation objectives:

Stage 1: methodological validation (lines 243–255): three independent researchers with expertise in public health, urban planning, and disaster management conducted manual validation of the key phrase extraction methodology. This stage focused on assessing extraction quality, consistency, and methodological rigor, achieving Cohen's kappa coefficient of 0.82, indicating substantial inter-rater agreement.

Stage 2: indicator applicability validation (line 338): five domain experts (two public health experts, two urban planning experts, and one disaster management expert) evaluated the practical applicability and relevance of candidate indicators using a structured 5-point Likert scale assessment. Only indicators receiving approval from at least four experts (average score ≥4) were retained for the final framework.

Stage 3: framework comprehensive validation (lines 470–505): Fifteen international experts conducted holistic evaluation of the complete framework, assessing both individual indicator validity and overall framework coherence. This stage achieved a mean importance score of 4.35/5.0, demonstrating high professional consensus on the framework's content validity.

Table 6 summarizes the validation process design and outcomes.

The expert selection process followed rigorous criteria to ensure both expertise and geographical diversity:

Selection criteria: All experts were required to hold doctoral degrees, possess minimum 5 years of relevant field experience, and have published at least 3 peer-reviewed articles in community resilience, public health emergency management, or related fields.

Recruitment process: Experts were identified through a combination of professional society recommendations and snowball sampling, ensuring representation across different geographical regions and disciplinary backgrounds.

To mitigate potential bias arising from heterogeneous national pandemic responses, we classified the 15 experts by country/region and by the stringency of non-pharmaceutical interventions (NPIs) in their jurisdictions.

The panel comprised four experts from China, three from Malaysia, two from India, two from Nigeria, two from Algeria, one from Australia and one from Jordan.

Table 7 provides detailed information about the disciplinary composition of our expert panel.

Table 8 summarizes the regional distribution.

This stratification revealed three indicators–related to public trust and behavioral compliance—exhibiting variance greater than 20% between NPI groups; these indicators were retained but flagged for contextual interpretation in downstream applications.

Notwithstanding these precautions, expert validation remains constrained by evolving pandemic knowledge and the limited size of the panel.

Future iterations will broaden geographical coverage, include additional low-income settings and update indicator weightings as empirical evidence accumulates.

All expert participants provided written informed consent after receiving detailed information about the research objectives, methodology, and their expected contributions. The validation process adhered to ethical guidelines established by our institutional review boards, ensuring:

The validation process was designed to minimize participant burden while maximizing the quality and reliability of expert input, contributing to the overall scientific rigor of our assessment framework.

To demonstrate the methodological advantages of our chosen approach, we conducted systematic comparative analysis between hyperbolic and Euclidean embedding methods. The application of hyperbolic embedding enables more accurate capture of hierarchical structural relationships between indicators. Compared to traditional Euclidean space embedding, hyperbolic embedding demonstrates substantial advantages in preserving indicator hierarchical structures, as evidenced by improved Hierarchical Fidelity Scores across our evaluation metrics.

Figure 10 demonstrates the superior performance of hyperbolic embedding over traditional Euclidean embedding in terms of both hierarchical fidelity preservation and distortion reduction. Quantitatively, hyperbolic embedding achieved an HFS of 0.847 compared to 0.623 for Euclidean embedding (35.9% improvement), while simultaneously reducing embedding distortion by 42.3% (distortion rate: 0.184 vs. 0.319). These improvements are statistically significant and demonstrate that hyperbolic geometry provides genuine advantages for representing hierarchical indicator relationships.

The detailed clustering performance analysis across different k values is presented in Figure 11, which validates our selection of k = 4 as the optimal number of clusters based on multiple evaluation metrics. This comparative analysis demonstrates that k = 4 outperforms alternative configurations: achieving a Silhouette Coefficient of 0.68 (vs. 0.61 for k = 3 and 0.59 for k = 5), a Davies-Bouldin Index of 0.52 (vs 0.67 for k = 3 and 0.71 for k = 5, where lower is better), and a Topic Coherence Score of 0.74 (vs 0.65 for k = 3 and 0.68 for k = 5). The convergence of optimal performance across three independent metrics provides strong evidence that our configuration choice is not arbitrary but methodologically justified.

Figure 12 shows the detailed results of the cluster analysis, including the number of indicators in each category, representative indicators, category characteristics, and silhouette coefficients.

To substantiate the novelty claims, Table 9 provides a comprehensive mapping of all 39 indicators against existing frameworks (CRI, PEOPLES, Sendai), indicating presence (✓) or absence (–) in each framework and identifying novel contributions.

The detailed mapping reveals that 23 indicators (59%) are novel contributions specifically tailored for public health emergency preparedness. These novel indicators predominantly address capabilities proven critical during COVID-19: digital infrastructure for remote activities, telemedicine systems, flexible space utilization, physical distancing-compatible design, contact tracing capabilities, and emergency mental health support. The 16 indicators present in existing frameworks provide theoretical grounding while the 23 novel indicators reflect evidence-based lessons from recent health crises, positioning our framework as both theoretically robust and practically responsive to contemporary public health challenges.

To demonstrate the framework's practical application, we provide a brief illustrative example of how a hypothetical mid-sized community might use the assessment process. Consider a community of approximately 50,000 residents seeking to evaluate its public health emergency preparedness following lessons learned from the COVID-19 pandemic.

Assessment process: the community would begin by assembling an interdisciplinary assessment team including public health officials, urban planners, and community representatives. For each of the 39 indicators, the team would collect relevant data from existing administrative records, spatial databases, and community surveys. For instance, indicators under Medical and Safety Measures might include counting the number of isolation facilities per 10,000 residents, measuring average distance to emergency medical services, and assessing telemedicine infrastructure capacity. Spatial Design indicators could evaluate the availability of outdoor spaces accessible during lockdowns and the flexibility of community facilities for emergency conversion. Each indicator would be scored on a standardized scale (e.g., 0-5) based on predefined criteria aligned with evidence-based benchmarks from the literature.

Results interpretation: hypothetically, the assessment might reveal that the community scores highly (average 4.2/5.0) on Medical and Safety Measures due to well-distributed healthcare facilities and strong emergency protocols, but scores lower (average 2.8/5.0) on Spatial Design and Infrastructure, particularly regarding flexible space utilization and outdoor accessibility during restrictions. Community Services and Support might show moderate scores (3.5/5.0), with strengths in social cohesion but gaps in mental health support systems. The hierarchical relationship matrix would help identify interdependencies–for example, showing how deficits in digital infrastructure (Spatial Design dimension) limit the effectiveness of telemedicine services (Medical Measures dimension).

Actionable outcomes: based on these findings, the community could prioritize investments in retrofitting public facilities for multi-purpose emergency use, enhancing digital connectivity in underserved neighborhoods, and establishing integrated mental health support networks. The assessment results would provide evidence-based justification for funding applications and policy development, with the framework enabling periodic re-assessment to track improvement over time.

This illustrative example demonstrates the framework's potential for translating abstract indicators into concrete assessment practices and actionable resilience-building strategies. However, we acknowledge that comprehensive field validation with real-world data collection remains as essential future work to fully establish the framework's operational validity and practical utility across diverse community contexts.