Aggregating Neighbor Embedding Projection and Rank-Based Manifold Learning for Image Retrieval

Content-based image retrieval (CBIR) has advanced significantly with deep learning, yet effectively ranking similar images remains challenging, particularly in high-dimensional feature spaces, where pairwise distances often fail to capture contextual relationships and the semantic gap between visual features and high-level concepts persists. Manifold learning and rank-based refinement methods have emerged as complementary strategies, respectively improving feature representations and exploiting contextual information embedded in ranked lists, such as neighborhood relationships among images. However, combining these projection-based and rank-based strategies to exploit their complementary properties remains a challenging research problem. To address this, we propose a framework that combines neighbor embedding projections with rank-based manifold learning through rank aggregation. Uniform Manifold Approximation and Projection (UMAP) generates alternative low-dimensional feature representations, and ranked lists obtained from UMAP projections and rank-based re-ranking methods are combined using the Borda Count aggregation strategy. Experiments were conducted on several public datasets using deep learning features extracted from ResNet152, Swin Transformer, and DINOv2 models. Results show that the proposed approach improves retrieval effectiveness in several scenarios, particularly when the baseline representation struggles to achieve high precision. The aggregation strategy also often improves the quality of top-ranked positions, leading to competitive Mean Average Precision (MAP) and Precision values across different datasets and feature extractors. These findings suggest that combining projection-based and rank-based manifold learning strategies through rank aggregation can provide complementary contextual information for image retrieval tasks.

Aggregate-then-Calibrate for Human-centered Assessment with Theoretical Guarantees

Human-centered assessment tasks, which are essential for systematic decision-making, rely heavily on human judgment and typically lack verifiable ground truth. Existing approaches face a dilemma: methods using only human judgments suffer from heterogeneous expertise and inconsistent rating scales, while methods using only model-generated scores must learn from imperfect proxies or incomplete features. We propose Aggregate-then-Calibrate (AtC), a two-stage framework that combines these complementary sources. Stage-1 aggregates heterogeneous comparative judgments into a consensus ranking using a rank-aggregation model that accounts for annotator reliability. Stage-2 calibrates any predictive model's scores by an isotonic projection onto the order, enforcing ordinal consistency while preserving as much of the model's quantitative information as possible. Theoretically, we show: (1) modeling annotator heterogeneity yields strictly more efficient consensus estimation than homogeneity; (2) isotonic calibration enjoys risk bounds even when the consensus ranking is misspecified; and (3) AtC asymptotically outperforms model-only assessment. Across semi-synthetic and real-world datasets, AtC consistently improves accuracy and robustness over human-only or model-only assessments. Our results bridge judgment aggregation with model-free calibration, providing a principled recipe for human-centered assessment when ground truth is costly, scarce, or unverifiable.

Hierarchical Partial-Order Models for Ranking

Rank aggregation combines information from ordered lists ranking items by preference. Classical parametric models for such data, including the Mallows and Plackett-Luce models, assume the orders concentrate around one or more complete consensus rankings. Recent work relaxes the total-order assumption by allowing the consensus structure to be a partial order (poset), allowing for incomparabilities in preferences. However, in many applications preference data exhibit group structure. We introduce hierarchical partial order (HPO) models, which extend poset-based models to accommodate grouped data through a hierarchy of latent posets. This framework, which parallels mixture model extensions of the Mallows and Plackett-Luce models, enables principled sharing of information across groups while preserving partial-order structure. We show that the Plackett-Luce model and its hierarchical variants are special cases of HPO-models. We develop a hierarchical clustering extension (HCPO) for unsupervised clustering in settings where group labels are unknown. Bayesian inference for the latent poset hierarchy is performed using Markov chain Monte Carlo methods. Experiments on synthetic and real-world datasets, including pairwise acoustic preference data and LLM agent traces, demonstrate that the proposed HPO and HCPO models outperform existing approaches in both predictive performance and structural interpretability.

Generalized Rank-based Evaluation for Knowledge Graph Completion: Perspectives, Framework, and Analyses

Knowledge graph completion (KGC) aims to predict missing facts from an observed knowledge graph (KG), playing a crucial role in a wide range of real-world applications such as drug discovery, recommender systems, and retrieval-augmented generation (RAG). Although numerous KGC models have been proposed, the evaluation of KGC remains underexplored, despite its critical role in reliably assessing model performance and selecting appropriate models for real-world applications. In this paper, we introduce two important perspectives for KGC evaluation that are overlooked by existing evaluation metrics, (P1) predictive sharpness and (P2) popularity-bias robustness. To address both perspectives, we propose a generalized evaluation framework, PROBE, which consists of a rank transformer (RT) that estimates the score of each prediction based on a desired level of predictive sharpness and a rank aggregator (RA) that determines the final evaluation score by aggregating all prediction scores according to a desired level of popularity-bias robustness. We theoretically analyze PROBE by defining six key properties for reliable KGC evaluation and prove that PROBE satisfies all the properties, while existing metrics fail to satisfy some. In particular, due to the open-world nature of KGs, an evaluation metric should preserve the relative performance of KGC models even when only incomplete facts are observed. We show that PROBE better maintains such consistency, providing a more reliable estimate of intrinsic model performance than existing metrics. Extensive experiments with six KGC models on six real-world KGs reveal that existing metrics may over- or under-estimate model performance depending on different evaluation perspectives, whereas PROBE enables a more comprehensive, flexible, and consistent evaluation of KGC models.