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CAT-LDP: Cloud-edge Adaptive Taxonomy under Local Differential Privacy

Junzhe Yang, Chang Xia, Xiyun Wang, Anren Sun, Wenbo Ding, Xinye Chen

arXiv:2609.05095v1cs.DB

TL;DR

CAT-LDP addresses the privacy–utility challenge of recommendation under sparse implicit feedback, where local perturbation can obscure useful preferences. It combines category-tree modeling with adaptive privacy budgets and cloud-local task separation, and outperforms fixed-budget and representative baselines on Amazon Video Games HR@K and NDCG@K metrics.

  • Problem

    Privacy-preserving recommendation must limit server-side inference while retaining useful signals, but perturbation weakens accuracy and sparse implicit feedback makes this trade-off more severe.

  • Method

    CAT-LDP uses a hierarchical category tree, adaptive budgets favoring active categories, privacy-preserving cloud coarse ranking, and local fine-grained reranking.

  • Results

    On the Amazon Video Games dataset, CAT-LDP outperforms its fixed-budget ablation and comparative baselines across reported HR@K and NDCG@K metrics at ε = 1.0.

  • Takeaways & Limitations

    Category-space modeling and cloud-local collaboration help alleviate noise amplification in long-tail sparse scenarios while balancing privacy protection and ranking performance.

Abstract

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Recommender systems are widely used in daily life, but their direct collection and use of user preference data can also lead to privacy leakage. Existing privacy-preserving recommendation methods often find it hard to balance user privacy and recommendation performance. This problem is more serious in implicit-feedback settings, where data sparsity further increases the loss of useful signals caused by privacy perturbation. To solve this problem, we propose CAT-LDP, a cloud-local collaborative recommendation framework under local differential privacy constraints. CAT-LDP combines a hierarchical taxonomy tree with an adaptive privacy budget allocation strategy to keep more useful signals in users' active categories while protecting user privacy. Specifically, users upload perturbed category profiles that satisfy LDP. Based on these profiles, the cloud performs coarse-grained candidate generation, and the local device then carries out fine-grained reranking by using unperturbed local history. Experiments on the Amazon Video Games dataset show that CAT-LDP consistently outperforms its fixed-budget ablation variant and representative baselines on HR@K and NDCG@K under different privacy budgets. The results show that combining category-space modeling with cloud-local task decoupling can effectively reduce noise amplification in long-tail sparse settings and provide a better balance between privacy and utility for implicit-feedback recommendation.

I. INTRODUCTION

Privacy-preserving recommendation must protect users from inference by untrusted servers without erasing useful preference signals, a challenge intensified by sparse implicit feedback. CAT-LDP addresses these issues with taxonomy-aware, adaptive cloud-local recommendation.

  • Recommender systems expose sensitive user attributes because providers commonly access raw behavioral data.
  • LDP recommendation faces server-side inference risks and a privacy–utility trade-off as perturbation weakens preference signals, especially with sparse implicit feedback.
  • CAT-LDP combines a hierarchical category tree, adaptive budget allocation, cloud coarse ranking, and local metadata-assisted fine reranking under LDP.
  • Existing methods are vulnerable in long-tail settings because flat, high-dimensional perturbation reduces signal density and limits aggregation across related items.
  • Fixed privacy budgets overlook that items and categories expose different degrees of user privacy, while current pipelines underuse reliable local histories during ranking.
  • Experiments on Amazon Video Games report that CAT-LDP outperforms its fixed-budget ablation and representative LDP baselines on HR@K and NDCG@K.

II. PRELIMINARIES

CAT-LDP represents implicit-feedback history in category space and separates privacy-preserving cloud retrieval from local reranking. LDP perturbation protects the profile before upload, while category structure targets sparsity.

  • Items are organized in a category tree with coarse-grained Level-2 and fine-grained Level-3 hierarchies.
  • A user’s category profile is a binary vector in which each feature records positive implicit feedback for a category.
  • The device perturbs the profile before upload; the cloud clusters noisy profiles and ranks candidates, then the device reranks the returned Top-M items.
  • ε-LDP requires randomized outputs to remain similarly probable for any two input feature vectors under the privacy budget ε.
  • Binary Randomized Response is used for binary features, with the false-positive probability defined as q = 1/(1 + e^ε).
  • Uniform budgets can waste privacy resources on irrelevant dimensions in sparse category spaces, reducing effective signal use.

C. Adaptive Budget Policy

CAT-LDP replaces uniform dimensional budgets with bounded, mean-equivalent allocations that favor active categories. Its local-cloud-local workflow uses adaptive perturbation, cloud clustering, and subsequent local ranking to preserve useful signals.

  • The adaptive policy assigns each user a dimensionalized budget vector instead of one identical budget across categories.
  • Boundary and mean-equivalency constraints limit each dimension while keeping the user’s average budget approximately equal to the global baseline.
  • Initial budgets are built from activity in Level-2 categories, with higher budgets assigned to highly active categories.
  • A scaling factor is approximately solved by binary search to reallocate privacy resources under a fixed average overhead.
  • The system follows a local-cloud-local workflow: local profiles are adaptively perturbed, the cloud clusters noisy data for coarse ranking, and local information supports later processing.

C. Local Lightweight Reranking

CAT-LDP separates cloud-side coarse recommendation from local reranking: the cloud narrows candidates, while the device uses unperturbed history and metadata for lightweight personalization.

  • C. Local Lightweight Reranking: After receiving the cloud’s top M candidates, the local module retrieves each item’s public metadata and the user’s unperturbed interaction history.The local device performs this step without uploading the true history.
  • C. Local Lightweight Reranking: The framework divides processing into local preprocessing and perturbation, cloud collaborative clustering and coarse ranking, and local metadata-driven reranking.This three-module organization defines the cloud-local recommendation workflow.
  • C. Local Lightweight Reranking: The local device constructs a high-dimensional binary profile from users’ fine-grained Level-3 historical categories before privacy perturbation.Each active category corresponds to a one-valued profile dimension.
  • C. Local Lightweight Reranking: Adaptive budgets are allocated across profile dimensions according to activity in coarse Level-2 categories.The most active Level-2 categories are selected and used to organize the hierarchical allocation.

3) Symmetric Flipping Perturbation Logic:

The perturbation pipeline applies dimension-specific randomized response to the category profile, then uses noisy profiles for privacy-preserving cloud clustering and candidate screening.

  • 3) Symmetric Flipping Perturbation Logic:: The system assigns per-dimension budgets before applying symmetric randomized-response flipping to the binary category vector.The flipping probabilities depend on the allocated budget for each dimension.
  • 3) Symmetric Flipping Perturbation Logic:: The noisy indicator preserves or flips each binary input according to a sampled uniform random number and the corresponding probabilities.The piecewise mechanism handles both input values, xu,j = 1 and xu,j = 0.
  • 3) Symmetric Flipping Perturbation Logic:: The resulting noisy vector satisfies LDP and is transmitted to the cloud server.The cloud therefore receives perturbed rather than true category profiles.
  • 3) Symmetric Flipping Perturbation Logic:: Mean-equivalency normalization clips each dimension’s scaled initial budget between ϵmin and ϵmax.The scaling factor αu is selected by binary search after initial allocation.
  • 3) Symmetric Flipping Perturbation Logic:: The cloud uses noisy user profiles to extract collaborative signals and screen the candidate pool.Direct similarity calculations on noisy profiles can create ranking bias, motivating ensemble clustering.
  • 3) Symmetric Flipping Perturbation Logic:: Multiple K-Means configurations produce base clusters whose centers and relationships are combined before spectral clustering forms final clusters.Final cluster centers reduce variance from random perturbation, and users are assigned using cosine similarity.

2) Multiplicative Gated Coarse Ranking:

Cloud ranking combines cluster-level preference with the user’s visible category signal through a gated score, producing candidates for subsequent local processing.

  • 2) Multiplicative Gated Coarse Ranking:: For each candidate item, the cloud computes a multiplicative gated score from cluster preference and the user’s visible category value.The score combines global collaborative information with individual intent.
  • 2) Multiplicative Gated Coarse Ranking:: The scoring rule filters negative preferences and down-weights cluster preference for items lacking a positive category indicator.The parameter λ lies in [0, 1].
  • 2) Multiplicative Gated Coarse Ranking:: The cloud sends the candidate set to the local device, which reranks it using true local history and public item metadata.This creates a coarse-to-fine division between cloud retrieval and local personalization.

1) Metadata Feature Extraction:

Local reranking extracts metadata-token overlap with historical items, while the overall cloud-local pipeline is designed for feasible local and online computation.

  • 1) Metadata Feature Extraction:: The local device represents candidate and historical item metadata as token sets and computes their Jaccard similarity.Metadata includes fields such as title, brand, and category.
  • 1) Metadata Feature Extraction:: Max aggregation selects the strongest metadata match as the local reranking score.The score is computed between each candidate and the user’s historical items.
  • 1) Metadata Feature Extraction:: Only the top M cloud candidates are locally reranked, with local score prioritized and coarse score breaking ties.Unreranked tail items retain their cloud-side order before the final Top-K truncation.
  • 1) Metadata Feature Extraction:: Local profile extraction, adaptive budget allocation, and perturbation are dominated by O(|C|) time and require O(|C|) space.The coarse-category count is much smaller than the fine-category count, |G| ≪|C|.
  • 1) Metadata Feature Extraction:: Server clustering is decoupled into offline processing, while online coarse ranking sorts the retrieval candidate set in O(|Icand| log |Icand|).The offline stage includes K-Means, graph construction, and spectral clustering.
  • 1) Metadata Feature Extraction:: Server storage includes the noisy user matrix, final cluster centers, and the inter-cluster similarity matrix.These structures determine the stated server-side space requirements.

3) User Side 2: •

The Video Games dataset provides implicit-feedback histories, hierarchical category features, and metadata for local reranking. Evaluation uses HR@K and NDCG@K under a one-ground-truth-item test protocol.

  • Dataset: The experiments use the Amazon Video Games 5-core subset and corresponding item metadata.
  • Dataset: Explicit ratings are binarized into implicit interaction histories for each active user.
  • Dataset: Hierarchical categories form binary feature profiles, while titles and brands provide tokens for local Jaccard reranking.
  • Evaluation metrics: HR@K measures whether the held-out target item appears within the top-K recommendation list.
  • Evaluation metrics: NDCG@K additionally rewards higher-ranked hits through position-based score decay.

3) Baselines:

The evaluation compares CAT-LDP with a fixed-budget ablation and representative locally perturbed recommendation baselines under a unified sampled-candidate protocol. Shared random seeds and common reranking settings support comparability across methods.

  • Evaluation protocol: Each test user is evaluated on one positive item paired with 99 randomly sampled negative items.
  • Evaluation protocol: All methods rank items within the same 100-item candidate set when computing HR@K and NDCG@K.
  • Baselines: CT-LDP isolates adaptive-budget effects by retaining CAT-LDP’s tree, clustering, and reranking while using fixed-budget perturbation.
  • Baselines: LCF-SP and LCF-AP directly compute cloud similarities from perturbed data without unbiased noise correction.
  • Baselines: DPLCF-SP and DPLCF-AP apply cloud-side unbiased or inverse estimation to correct symmetric or asymmetric perturbation bias.
  • Implementation settings: Random sampling is fixed with a common seed, while baseline reranking uses depth 20 and shared Jaccard computation where applicable.

B. Performance Comparison

At ε = 1.0 on Amazon Video Games, CAT-LDP achieves the strongest reported recommendation performance in both cloud-only coarse ranking and hybrid local reranking. Its adaptive budget allocation remains advantageous over fixed allocation across privacy budgets and ranking settings.

  • CAT-LDP achieves the best performance across all reported metrics for K = 2 ∼10 at ε = 1.0 on the Video Games dataset.
  • CoarseOnly: At K = 10 in CoarseOnly, CAT-LDP reaches HR@10 0.2050 and NDCG@10 0.0990.
  • CoarseOnly: CAT-LDP improves HR@10 by approximately 17.5% and NDCG@10 by 16.0% over the fixed-budget CT-LDP variant in CoarseOnly.
  • CoarseOnly: Compared with LCF-AP, CAT-LDP improves HR@10 by approximately 42.7% and NDCG@10 by 40.0%.
  • HybridLocalRerank: Local metadata reranking substantially improves recommendation metrics for all algorithms by using unperturbed local history for Jaccard similarity.
  • HybridLocalRerank: Under HybridLocalRerank, CAT-LDP remains approximately 13.0% higher in HR@10 and 12.7% higher in NDCG@10 than CT-LDP.
  • Privacy-budget sensitivity: As ε increases from 0.1 to 1.0, all models improve steadily across the evaluated HR and NDCG metrics.
  • Ablation trends: CAT-LDP outperforms CT-LDP across all tested ε values and truncation lengths in both coarse ranking and hybrid reranking.

VI. CONCLUSION

CAT-LDP addresses high-dimensional sparsity and signal degradation in implicit-feedback recommendation under LDP by combining category-space modeling, adaptive budget allocation, cloud clustering, and local metadata reranking. On the Video Games dataset at ε = 1.0, it outperforms the fixed-budget ablation and comparative baselines across reported HR@K and NDCG@K metrics, while broader generalizability remains future work.

  • CAT-LDP combines a category tree, adaptive privacy budgets, cloud coarse ranking, and local metadata reranking for implicit-feedback recommendation under LDP.
  • At ε = 1.0 on the Video Games dataset, CAT-LDP outperforms the fixed-budget ablation and comparative baselines across all reported HR@K and NDCG@K metrics.
  • The authors identify future validation across multiple datasets and evaluation protocols as necessary to assess generalizability.
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