Context-Aware Interpretable Representations for Retrieval and Graph Convolutional Network Classification

# Context-Aware Interpretable Representations for Retrieval and Graph Convolutional Network Classification
Source: [https://arxiv.org/html/2608.29004](https://arxiv.org/html/2608.29004)
Conference:International Conference on Multimedia Retrieval; June 16–19, 2026; Amsterdam, NetherlandsInternational Conference on Multimedia Retrieval \(ICMR ’26\), June 16–19, 2026, Amsterdam, NetherlandsDOI:[10\.1145/3805622\.3810617](https://doi.org/10.1145/3805622.3810617)ISBN:979\-8\-4007\-2617\-0/2026/06CCS:Information systems Top\-k retrieval in databasesCCS:Computing methodologies Computer vision tasksCCS:Computing methodologies Image representationsThiago César Castilho Almeida[https://orcid.org/0000-0002-2167-0463](https://orcid.org/0000-0002-2167-0463)Affiliation:State University of São Paulo \(UNESP\),Rio Claro,São Paulo,Brazilemail:[tc\.almeida@unesp\.br](mailto:[email protected])Gustavo Rosseto Letício[https://orcid.org/0009-0008-3715-8991](https://orcid.org/0009-0008-3715-8991)Affiliation:State University of São Paulo \(UNESP\),Rio Claro,São Paulo,Brazilemail:[gustavo\.leticio@unesp\.br](mailto:[email protected]),Vinicius Atsushi Sato Kawai[https://orcid.org/0000-0003-0153-7910](https://orcid.org/0000-0003-0153-7910)Affiliation:State University of São Paulo \(UNESP\),Rio Claro,São Paulo,Brazilemail:[vinicius\.kawai@unesp\.br](mailto:[email protected])andDaniel Carlos Guimarães Pedronette[https://orcid.org/0000-0002-2867-4838](https://orcid.org/0000-0002-2867-4838)Affiliation:State University of São Paulo \(UNESP\),Rio Claro,São Paulo,Brazilemail:[daniel\.pedronette@unesp\.br](mailto:[email protected])

© cc

###### Abstract\.

The advances in visual information modeling and representation during the last decades are remarkable, mainly supported by Convolutional Neural Networks, Transformer\-based, and Foundation Models\. Despite this progress, critical challenges regarding the nature of similarity assessment and model transparency have been neglected\. A primary concern is theGeometric Gap, where traditional pairwise measures fail to capture the intrinsic geometry of the dataset manifold\. Furthermore, theInterpretability Gappersists, as representations often lack alignment with human cognition\. Therefore, how to provide interpretability to representations while maintaining low dimensionality and high effectiveness in downstream tasks remains an open challenge\. In this paper, we propose a novel unsupervised framework that integrates Manifold Learning strategies with Rank\-based Interpretable Graph Embeddings\. Our approach effectively bridges these gaps by first characterizing the contextual information of the dataset through manifold analysis and subsequently generating sparse, self\-explainable embeddings\. The proposed approach employs a flexible formulation, allowing different Manifold Learning and Representation Learning strategies\. Extensive experimental evaluation across diverse datasets and features demonstrates that our Context\-Aware representations not only provide intrinsic interpretability and dimensionality reduction but also maintain or enhance effectiveness in downstream tasks, specifically in image retrieval and semi\-supervised classification using Graph Convolutional Networks \(GCNs\)\.

###### Keywords:

Representation learning, Manifold learning, Unsupervised learning, Ranking

††cc\-license:byThe accepted version is published in the Proceedings of the 2026 International Conference on Multimedia Retrieval \(ICMR ’26\)\. DOI:[https://doi\.org/10\.1145/3805622\.3810617](https://doi.org/10.1145/3805622.3810617)\.

## 1\.Introduction

The fundamental pillars of Information Retrieval \(IR\) and Machine Learning \(ML\) reside in two interconnected components: data representation strategies and mechanisms for similarity assessment\. In recent decades, multimedia retrieval has undergone a profound transformation driven by Deep Learning\. The emergence of Convolutional Neural Networks \(CNNs\)\([He et al\., 2016](https://arxiv.org/html/2608.29004#bib.bib13);[Zheng et al\., 2018](https://arxiv.org/html/2608.29004#bib.bib52)\)and Vision Transformers \(ViTs\)\([Vaswani et al\., 2017](https://arxiv.org/html/2608.29004#bib.bib44);[Dosovitskiy et al\., 2021](https://arxiv.org/html/2608.29004#bib.bib8)\)has bridged the “semantic gap”, mapping raw data into dense latent spaces where complex patterns are encoded\. However, a critical asymmetry persists: while representation learning has advanced rapidly, the methods used to compare these representations have not evolved at the same pace\.

Despite the non\-linear nature of modern latent spaces, similarity assessment remains predominantly grounded in simple pairwise measures like Euclidean distance\. These metrics suffer from the “curse of dimensionality”\([Huang et al\., 2019](https://arxiv.org/html/2608.29004#bib.bib16)\)and fail to capture the intrinsic curvature of the data, leading to a mismatch known as theGeometric Gap\([Ermolov et al\., 2022](https://arxiv.org/html/2608.29004#bib.bib9);[Levada, 2022](https://arxiv.org/html/2608.29004#bib.bib19)\)\. Furthermore, the individual dimensions of these dense representations lack explicit semantic meaning\. This opacity creates a secondary barrier, theInterpretability Gap\([Anand et al\., 2025](https://arxiv.org/html/2608.29004#bib.bib3);[Zhao et al\., 2021](https://arxiv.org/html/2608.29004#bib.bib51)\), which prevents the adoption of retrieval systems in high\-stakes domains where trust and human understanding are paramount\([Rudin, 2019](https://arxiv.org/html/2608.29004#bib.bib38);[Marconato et al\., 2023](https://arxiv.org/html/2608.29004#bib.bib25)\)\. Consequently, the field faces a dual burden: optimizing for retrieval accuracy while ensuring the feature space remains semantically coherent to human observers\.

Existing approaches address these gaps in isolation: interpretability methods such as Disentangled Representation Learning\([Wang et al\., 2024](https://arxiv.org/html/2608.29004#bib.bib48);[Higgins et al\., 2017](https://arxiv.org/html/2608.29004#bib.bib14)\)and self\-explaining models\([Koh et al\., 2020](https://arxiv.org/html/2608.29004#bib.bib18);[Chen et al\., 2019](https://arxiv.org/html/2608.29004#bib.bib6)\)either impose restrictive assumptions or require expensive supervision, while graph\-based methods\([Kipf and Welling, 2017](https://arxiv.org/html/2608.29004#bib.bib17)\)that capture manifold structure depend critically on neighborhood quality, which Euclidean metrics may fail to guarantee in high dimensions\([Levada, 2022](https://arxiv.org/html/2608.29004#bib.bib19)\)\. Even recent rank\-based interpretable methods\([Alves de Fernando et al\., 2020](https://arxiv.org/html/2608.29004#bib.bib2);[Almeida et al\., 2025](https://arxiv.org/html/2608.29004#bib.bib1)\)that align embedding dimensions with semantic prototypes inherit this geometric flaw by relying on noisy initial neighborhoods\.

In this paper, we propose a novel approach that integrates the robustness of manifold learning with the transparency of rank\-based embeddings\. We argue that ranking structures provide the optimal framework for encoding topology, as they are inherently resilient to the scale variances of raw feature spaces\. By leveraging manifold learning to “unfold” the data geometry before graph construction, we ensure that the subsequent prototype selection is topologically accurate\. This generates vector representations where each dimension corresponds to a highly effective prototype, simultaneously bridging theGeometric Gapvia context\-aware processing and theInterpretability Gapvia self\-explanatory dimensions\.

The main contributions of this work are summarized as follows:

- •Context\-Aware and Interpretable Rank\-based Framework:We introduce a modular unsupervised formulation that exploits contextual ranking information through manifold learning to correct data geometry before embedding, allowing for the integration of different manifold learning algorithms and different rank\-based representation learning strategies\.
- •Low\-Dimensional and Effective Representation:We demonstrate that our approach maintains or surpasses the effectiveness of high\-dimensional features while significantly reducing dimensionality and providing semantic interpretability to each dimension\.
- •Representational Robustness:The proposed approach is evaluated across multiple tasks, including content\-based image retrieval and semi\-supervised classification, proving its robustness as a general\-purpose representation\.

Experimental evaluations on diverse public datasets, using state\-of\-the\-art CNN and Transformer backbones, indicate that the proposed method outperforms original features while offering qualitative insights\.

## 2\.Related Work

This section reviews existing literature across three key areas: Network Representation Learning \(NRL\), which focuses on embedding graph structures; Disentangled Representation Learning \(DRL\), which attempts to isolate independent factors of variation; and Interpretable\-by\-Design Models, specifically those employing prototype\-based reasoning\.

### 2\.1\.Network Representation Learning

Network Representation Learning \(NRL\) maps nodes from a high\-dimensional graph structure into a low\-dimensional vector space while preserving topological properties\([Chen et al\., 2020](https://arxiv.org/html/2608.29004#bib.bib7)\)\. Early “shallow embedding” approaches, inspired by Natural Language Processing, such asDeepWalk\([Perozzi et al\., 2014](https://arxiv.org/html/2608.29004#bib.bib35)\)andNode2vec\([Grover and Leskovec, 2016](https://arxiv.org/html/2608.29004#bib.bib12)\), treat random walks on graphs as sentences, optimizing for node co\-occurrence\. Concurrently, methods likeLINE\([Tang et al\., 2015](https://arxiv.org/html/2608.29004#bib.bib40)\)focused on preserving explicit first\- and second\-order proximities\.

The field subsequently shifted towardGraph Neural Networks \(GNNs\), which integrate node attributes with structural information\. Architectures likeGCNs\([Kipf and Welling, 2017](https://arxiv.org/html/2608.29004#bib.bib17)\)andGATs\([Salehi and Davulcu, 2020](https://arxiv.org/html/2608.29004#bib.bib39)\)utilize message\-passing mechanisms to aggregate neighbor information\. To handle unlabeled data, unsupervised frameworks such asGraphMAE\([Hou et al\., 2022](https://arxiv.org/html/2608.29004#bib.bib15)\)andDGI\([Veličković et al\., 2019](https://arxiv.org/html/2608.29004#bib.bib45)\)have been developed to maximize mutual information or reconstruct masked features\.

However, a major limitation of standard GNNs is that they produce “black\-box” representations where dimensions are semantically opaque\. To address this,Interpretable Graph Embeddingmethods have emerged\. Post\-hoc approaches likeDINE\([Piaggesi et al\., 2024](https://arxiv.org/html/2608.29004#bib.bib36)\)decompose existing embeddings into sparse, interpretable vectors\. More recently, rank\-based methods likeRaDE\([Alves de Fernando et al\., 2020](https://arxiv.org/html/2608.29004#bib.bib2);[Fernando et al\., 2022](https://arxiv.org/html/2608.29004#bib.bib10)\)andGRaCE\([Almeida et al\., 2025](https://arxiv.org/html/2608.29004#bib.bib1)\)generate interpretable embeddings directly from the graph structure\. Unlike traditional GNNs, these approaches construct dimensions that explicitly encode similarity to specific prototype nodes, ensuring semantic alignment\. While effective, these methods typically rely on input graphs constructed via standard distance metrics, leaving them vulnerable to theGeometric Gapif the initial topology is not sufficiently refined\.

### 2\.2\.Disentangled Representation Learning

A primary goal of representation learning is to separate the underlying explanatory factors of data, a concept known as Disentangled Representation Learning \(DRL\)\([Bengio et al\., 2013](https://arxiv.org/html/2608.29004#bib.bib5)\)\. In Computer Vision, Variational Autoencoders \(VAEs\) like𝜷\\boldsymbol\{\\beta\}\-VAE\([Higgins et al\., 2017](https://arxiv.org/html/2608.29004#bib.bib14)\)enforce statistical independence among latent dimensions\. These principles have been adapted to graphs by methods likeDisenGCN\([Ma et al\., 2019](https://arxiv.org/html/2608.29004#bib.bib24)\)andDiSeNE\([Piaggesi et al\., 2025](https://arxiv.org/html/2608.29004#bib.bib37)\), which decompose input graphs into independent factor graphs\.

However, applying strict disentanglement to general\-purpose retrieval is problematic\. As noted in\([Locatello et al\., 2019](https://arxiv.org/html/2608.29004#bib.bib23)\), unsupervised disentanglement is theoretically impossible without strong inductive biases\. Furthermore, DRL relies on the assumption that semantic factors are statistically independent\. In complex multimedia manifolds, concepts are naturally correlated \(e\.g\., “ocean” and “blue”\)\. Forcing independence can distort the intrinsic geometry of the data\.

In contrast, rank\-based strategies adopt a philosophy ofrepresentational coveragerather than statistical orthogonality\. Instead of forcing latent dimensions to be independent factors, methods like RaDE and GRaCE selectcomplementaryprototypes that maximize the coverage of the data manifold\. This approach respects natural correlations, offering a more geometrically faithful form of interpretability where dimensions represent tangible exemplars rather than abstract, independent factors\.

### 2\.3\.Interpretable\-by\-Design Models

To avoid the unreliability of post\-hoc explainers, recent research favors models that are interpretable by design\.Concept Bottleneck Models \(CBMs\)\([Koh et al\., 2020](https://arxiv.org/html/2608.29004#bib.bib18)\)map inputs to a set of human\-understandable attributes \(e\.g\., “wing color”\) before making a prediction\. While recent works leverage Large Language Models \(LLMs\) to automate concept discovery\([Oikarinen et al\., 2023](https://arxiv.org/html/2608.29004#bib.bib28);[Yang et al\., 2023](https://arxiv.org/html/2608.29004#bib.bib50)\), these methods suffer from theLinguistic Gap, assuming all discriminative visual features can be verbally described, limiting their utility in specialized or abstract domains\.

To bypass the linguistic bottleneck,Prototype\-based Modelsadopt athis looks like thatparadigm\. Architectures likeProtoPNet\([Chen et al\., 2019](https://arxiv.org/html/2608.29004#bib.bib6)\)andTesNet\([Wang et al\., 2021](https://arxiv.org/html/2608.29004#bib.bib47)\)learn prototypes as specific image patches\. While transparent, they require specialized training pipelines and are difficult to adapt to pre\-trained backbones\([Gautam et al\., 2024](https://arxiv.org/html/2608.29004#bib.bib11)\)\.

Recent “training\-free” approaches, such asKMEx\([Gautam et al\., 2024](https://arxiv.org/html/2608.29004#bib.bib11)\)andIDEAL\([Angelov et al\., 2025](https://arxiv.org/html/2608.29004#bib.bib4)\), attempt to identify prototypes in the frozen latent space of pre\-trained models using clustering or density peaks\. However, a critical limitation persists: these methods rely on the assumption that the latent space is Euclidean\. As established, high\-dimensional spaces often exhibit non\-Euclidean manifold structures\([Levada, 2022](https://arxiv.org/html/2608.29004#bib.bib19)\)\. Relying on simple distances in such distorted spaces leads to theGeometric Gap, where selected prototypes may not be truly representative\. This motivates our proposed approach, which integrates manifold learning to unfold the data geometry before prototype selection, ensuring that explanations are topologically accurate\.

## 3\.Proposed Approach

![Refer to caption](https://arxiv.org/html/2608.29004v1/proposed-approach.png)Figure 1\.Overview of the proposedContext\-Aware and Interpretable Rank\-based Framework\.We propose a fully unsupervised, modular framework that integrates manifold learning with rank\-based interpretable embeddings to simultaneously address theGeometricandInterpretabilitygaps\. We postulate that a ranked list serves as a robust regional discretization of the feature space\. By leveraging this perspective, our framework transforms raw features into a sparse, interpretable embedding where context is encoded directly into the vector dimensions\. The overall pipeline, illustrated in Figure[1](https://arxiv.org/html/2608.29004#S3.F1), proceeds in three sequential stages: \(1\) Manifold Refinement, \(2\) Prototype Discovery, and \(3\) Interpretable Embedding Generation\.

### 3\.1\.Problem Formulation

Let𝒞=\{e1,e2,…,eN\}\\mathcal\{C\}=\\\{e\_\{1\},e\_\{2\},\\dots,e\_\{N\}\\\}be a multimedia collection\. A standard encoderfθf\_\{\\theta\}maps each objecteie\_\{i\}to a feature vector𝐱i∈ℝD\\mathbf\{x\}\_\{i\}\\in\\mathbb\{R\}^\{D\}\. Conventionally, similarity is estimated via a pairwise distance functionρ⁡\(⋅,⋅\)\\rho\(\\cdot,\\cdot\)\(e\.g\., Euclidean distance\), inducing a ranked listτq\\tau\_\{q\}for each queryeqe\_\{q\}, such that:

\(1\)τq​\(i\)<τq​\(j\)⟺ρ⁡\(eq,ei\)≤ρ⁡\(eq,ej\)\.\\tau\_\{q\}\(i\)<\\tau\_\{q\}\(j\)\\Longleftrightarrow\\rho\(e\_\{q\},e\_\{i\}\)\\leq\\rho\(e\_\{q\},e\_\{j\}\)\.
However, due to the non\-isotropic nature of deep feature spaces,ρ\\rhooften fails to reflect true semantic affinity, introducing false positives in the neighborhood𝒩⁡\(q,k\)\\mathcal\{N\}\(q,k\)\. Our objective is to learn a transformationΦ:𝒳→ℝd\\Phi:\\mathcal\{X\}\\to\\mathbb\{R\}^\{d\},d≪Dd\\ll D, mapping𝐱i\\mathbf\{x\}\_\{i\}to a new embeddingviv\_\{i\}that satisfies two conditions:

1. \(1\)Topological Fidelity:The similarity in the new space must reflect geodesic distances on the true data manifoldℳ\\mathcal\{M\}, correcting theGeometric Gap\.
2. \(2\)Intrinsic Interpretability:The target space must be defined by a set of prototypesℛ=\{r1,…,rd\}⊂𝒞\\mathcal\{R\}=\\\{r\_\{1\},\\dots,r\_\{d\}\\\}\\subset\\mathcal\{C\}, such that theii\-th dimension ofvev\_\{e\}explicitly quantifies the similarity to theii\-th prototype: \(2\)ve,i=s⁡\(τe,τri\)\.v\_\{e,i\}=s\(\\tau\_\{e\},\\tau\_\{r\_\{i\}\}\)\.

### 3\.2\.The Framework

The proposed methodology, detailed below, is modular, integrating Manifold Learning with Rank\-based Graph Embeddings\.

#### Stage 1: Contextual Manifold Refinement

The first stage aims to “unfold” the data geometry to correct theGeometric Gap\. Raw feature spaces often suffer from the “curse of dimensionality”\([Huang et al\., 2019](https://arxiv.org/html/2608.29004#bib.bib16)\), creating short\-circuit edges between semantically unrelated points\. To mitigate this, we employ Manifold Learning strategies that exploit local neighborhood structures\. We considered both Neighbor Embedding Projection and Context\-Aware Similarity Learning\([Pereira\-Ferrero et al\., 2024](https://arxiv.org/html/2608.29004#bib.bib34)\)methods\. Specifically, we adopt the following methods:

∙\\bulletUniform Manifold Approximation and Projection \(UMAP\)\([McInnes et al\., 2018](https://arxiv.org/html/2608.29004#bib.bib26)\)operates as a neighbor embedding projection technique, constructing a weighted neighborhood graph in the original feature space and optimizing a low\-dimensional representation that preserves local topological structures\. This new representation is then used to compute the similarity relationships that better reflect the manifold information\.

∙\\bulletRank\-Based Diffusion Process for Assured Convergence \(RDPAC\)\([Pedronette et al\., 2021a](https://arxiv.org/html/2608.29004#bib.bib30)\)follows a rank\-based diffusion strategy, propagating affinity scores over a mutual neighborhood graph to smooth similarity estimates, attenuate noise, and ensure convergence, thereby producing refined ranked lists that exploit the manifold geometry\.

∙\\bulletLog\-based Hypergraph of Ranking References \(LHRR\)\([Pedronette et al\., 2019](https://arxiv.org/html/2608.29004#bib.bib32)\)models contextual similarity using a hypergraph structure, where relationships are derived from shared ranking references, with logarithmic weighting emphasizing top\-kkneighbors\.

∙\\bulletBreadth\-First Search Tree \(BFSTREE\)\([Pedronette et al\., 2021b](https://arxiv.org/html/2608.29004#bib.bib33)\)computes a new similarity measure by exploiting the manifold information provided by the ranking references in a breadth\-first tree, thus computing refined similarity rankings\.

Formally, this stage transforms the initial noisy rankings into a set ofrefined ranked lists𝒯′=\{τ1′,…,τN′\}\\mathcal\{T\}^\{\\prime\}=\\\{\\tau^\{\\prime\}\_\{1\},\\dots,\\tau^\{\\prime\}\_\{N\}\\\}\. In𝒯′\\mathcal\{T\}^\{\\prime\}, the rank positionτi′​\(j\)\\tau^\{\\prime\}\_\{i\}\(j\)approximates the geodesic distance on the manifoldℳ\\mathcal\{M\}rather than the linear Euclidean distance\. These refined lists serve as the input for the subsequent graph construction, ensuring that the topology is corrected before any embedding learning begins\.

#### Stage 2: Rank\-based Graph Construction and Prototype Selection

In the second stage, we model the collection as a graphG=\(V,E,𝐖\)G=\(V,E,\\mathbf\{W\}\)to discover the most effective reference points \(representative samples/prototypes\)\. The graph is constructed using the refined neighborhoods from Stage 1\. Unlike standard GNNs that use opaque message passing, we employ rank\-based similarity measures, exemplified by RaDE\([Alves de Fernando et al\., 2020](https://arxiv.org/html/2608.29004#bib.bib2);[Fernando et al\., 2022](https://arxiv.org/html/2608.29004#bib.bib10)\)and GRaCE\([Almeida et al\., 2025](https://arxiv.org/html/2608.29004#bib.bib1)\), to define edge weights𝐖i​j\\mathbf\{W\}\_\{ij\}\. RaDE uses logarithmic decay \(wi​j=1−logk⁡\(τi′​\(j\)\)w\_\{ij\}=1\-\\log\_\{k\}\(\\tau^\{\\prime\}\_\{i\}\(j\)\)\), while GRaCE uses rank correlation measures \(e\.g\., JaccardMax\([Valem et al\., 2022](https://arxiv.org/html/2608.29004#bib.bib41)\)\)\.

From this graph, we select a subset of prototypesℛ=\{r1,…,rd\}⊂𝒞\\mathcal\{R\}=\\\{r\_\{1\},\\dots,r\_\{d\}\\\}\\subset\\mathcal\{C\}\. The selection follows a greedy optimization scheme designed to maximizeRepresentational Coveragewhile minimizing redundancy\. Letℛi−1\\mathcal\{R\}\_\{i\-1\}be the set of prototypes selected up to stepi−1i\-1\. The next prototyperir\_\{i\}is chosen to maximize a marginal gain function:

\(3\)ri=arg⁡maxc∈𝒞∖ℛi−1​η⁡\(c\)1\+∑r∈ℛi−1s⁡\(τc′,τr′\),r\_\{i\}=\\underset\{c\\in\\mathcal\{C\}\\setminus\\mathcal\{R\}\_\{i\-1\}\}\{\\arg\\max\}\\;\\frac\{\\eta\(c\)\}\{1\+\\sum\_\{r\\in\\mathcal\{R\}\_\{i\-1\}\}s\(\\tau^\{\\prime\}\_\{c\},\\tau^\{\\prime\}\_\{r\}\)\},
whereη⁡\(c\)\\eta\(c\)estimates the node’s effectiveness \(e\.g\., via Reciprocal Affinities in RaDE and QPP measures, like Reciprocal Density\([Pedronette and Torres, 2015](https://arxiv.org/html/2608.29004#bib.bib31)\), in GRaCE\) and the denominator penalizes candidates similar to existing prototypes\. This ensures the setℛ\\mathcal\{R\}spans the diverse semantic concepts of the manifold\.

#### Stage 3: Interpretable Embedding Generation

The final stage generates the interpretable vectorvev\_\{e\}for every objectee\. By projecting the object onto the selected prototypes, we obtain:

\(4\)ve=\[s⁡\(τe′,τr1′\),…,s⁡\(τe′,τrd′\)\],v\_\{e\}=\[s\(\\tau^\{\\prime\}\_\{e\},\\tau^\{\\prime\}\_\{r\_\{1\}\}\),\\dots,s\(\\tau^\{\\prime\}\_\{e\},\\tau^\{\\prime\}\_\{r\_\{d\}\}\)\],wheres⁡\(⋅\)s\(\\cdot\)represents the rank\-based similarity \(e\.g\., diffusion affinity or rank correlation\)\.

This transformation solves theInterpretability Gap\. Unlike “black\-box” dense layers, every dimensioniiofvev\_\{e\}has a transparent semantic definition: it represents the degree of similarity to the specific prototyperir\_\{i\}\. Furthermore, because the input rankingsτ′\\tau^\{\\prime\}were refined in Stage 1, this similarity assessment respects the non\-linear manifold structure, simultaneously bridging theGeometric Gap\.

## 4\.Experimental Setup

The following subsections describe the datasets and features, evaluation protocol, and implementation details required for reproducibility\.

### 4\.1\.Datasets and Representations

We evaluate our approach on four diverse datasets covering both general object categories and fine\-grained domains: Oxford17Flowers \(Flowers\)\([Nilsback and Zisserman, 2006](https://arxiv.org/html/2608.29004#bib.bib27)\)\(17 classes, 1,360 images\), Corel5k\([Liu and Yang, 2013](https://arxiv.org/html/2608.29004#bib.bib20)\)\(50 classes, 5,000 images\), Oxford\-IIIT Pet \(Pets\)\([Parkhi et al\., 2012](https://arxiv.org/html/2608.29004#bib.bib29)\)\(37 breeds, 7,390 images\), and CUB\-200\([Wah et al\., 2011](https://arxiv.org/html/2608.29004#bib.bib46)\)\(200 species, 11,788 images\)\.

For feature extraction, we employ three state\-of\-the\-art architectures pre\-trained on ImageNet\-1K: Vision Transformer \(ViT\-B/16\)\([Dosovitskiy et al\., 2021](https://arxiv.org/html/2608.29004#bib.bib8)\)\(d=768d=768\); Swin Transformer \(Swin\-Tf\)\([Liu et al\., 2021](https://arxiv.org/html/2608.29004#bib.bib21)\)\(d=1024d=1024\); and ConvNeXt\-Base\([Liu et al\., 2022](https://arxiv.org/html/2608.29004#bib.bib22)\)\(d=1024d=1024\)\. These high\-dimensional vectors serve as the input for our manifold learning pipeline\.

### 4\.2\.Experimental Protocol

We assess the effectiveness and robustness of the proposed framework across two primary tasks: Content\-Based Image Retrieval \(CBIR\) and Semi\-supervised Classification using GCNs\.

#### Image Retrieval\.

In the retrieval task, we evaluate the quality of the learned representations by using every image in the dataset as a query, while the remaining images constitute the retrieval gallery\. The retrieval effectiveness is reported using the Mean Average Precision at depth 1000 \(MAP@1000\)\. This metric provides a comprehensive assessment of ranking quality, penalizing relevant items that appear low in the retrieved list\. The depth of 1000 was adopted to align with prior works\([Almeida et al\., 2025](https://arxiv.org/html/2608.29004#bib.bib1)\), ensuring comparability from the same evaluation protocol\.

#### Semi\-supervised Classification\.

To evaluate the discriminative power of the representations in label\-scarce scenarios, we employ a Graph Convolutional Network \(GCN\) classification protocol\. Following the methodology established in\([Valem et al\., 2023](https://arxiv.org/html/2608.29004#bib.bib42)\), we utilize a stratified cross\-validation scheme designed to simulate semi\-supervised conditions\. The evaluation consists of five rounds of 10\-fold cross\-validation\. In each fold, only10%10\\%of the data is used as the training set, while the remaining90%90\\%serves as the test set\. The classification performance is reported as the average Accuracy across these runs\.

### 4\.3\.Implementation Details and Parameters

#### Manifold Learning\.

For the manifold learning stage, we evaluated both neighbor embedding and context\-aware similarity methods\. For UMAP, we utilized the standard implementation with default parameters\. For the Context\-Aware Similarity methods, we employed three methods from the Unsupervised Distance Learning Framework \(UDLF\)\([Valem and Pedronette, 2017](https://arxiv.org/html/2608.29004#bib.bib43)\): RDPAC\([Pedronette et al\., 2021a](https://arxiv.org/html/2608.29004#bib.bib30)\), LHRR\([Pedronette et al\., 2019](https://arxiv.org/html/2608.29004#bib.bib32)\), and BFSTREE\([Pedronette et al\., 2021b](https://arxiv.org/html/2608.29004#bib.bib33)\)\. For LHRR and BFSTREE, the size of the initial ranked lists was fixed atL=1000L=1000, and the neighborhood set sizekkwas tuned according to the specific characteristics of each dataset:k=80k=80for Oxford17Flowers,k=100k=100for Corel5k,k=200k=200for Oxford\-IIIT Pet, andk=60k=60for CUB\-200\. Specifically, for RDPAC, the parameters were set toL=500L=500, andkkto the default method configuration\.

#### Rank\-based Graph Embedding\.

The construction of the rank\-based graph and the subsequent prototype selection relied on the RaDE\([Alves de Fernando et al\., 2020](https://arxiv.org/html/2608.29004#bib.bib2)\)and GRaCE\([Almeida et al\., 2025](https://arxiv.org/html/2608.29004#bib.bib1)\)\. For graph construction, the neighborhood size parameter \(denoted asLLin RaDE andkkin GRaCE\) was set identically to the manifold learning stage \(k∈\{60,80,100,200\}k\\in\\\{60,80,100,200\\\}depending on the dataset\)\. For RaDE, the scaling parameter was set tot=2t=2\. In prototype selection, we employedReciprocal Density\([Pedronette and Torres, 2015](https://arxiv.org/html/2608.29004#bib.bib31)\)for the node effectiveness estimation andJaccardMax\([Valem et al\., 2022](https://arxiv.org/html/2608.29004#bib.bib41)\)for the rank correlation measure within GRaCE\. Concerning the embedding dimensions, the target dimensionality of the interpretable embedding was set tod=128d=128for the Flowers, Corel5k, and Pets datasets, following the value adopted in the foundational works of RaDE\([Alves de Fernando et al\., 2020](https://arxiv.org/html/2608.29004#bib.bib2);[Fernando et al\., 2022](https://arxiv.org/html/2608.29004#bib.bib10)\)and GRaCE\([Almeida et al\., 2025](https://arxiv.org/html/2608.29004#bib.bib1)\), neither of which evaluated on datasets with a large number of classes\. For the CUB\-200 dataset \(200 classes\), the dimension was increased tod=256d=256to better accommodate the higher semantic diversity of this fine\-grained benchmark\.

#### GCN Configuration\.

For the semi\-supervised classification task, the input graph topology was constructed using akk\-Nearest Neighbor \(kk\-NN\) or Reciprocalkk\-NN strategy withk=40k=40\. The GCN model, specifically the Simple Graph Convolution Network\([Wu et al\., 2019](https://arxiv.org/html/2608.29004#bib.bib49)\), was optimized using the Adam optimizer for200200epochs\. The learning rate was set to10−310^\{\-3\}for the Flowers, Corel5k, and Pets datasets, while for CUB\-200, it was set to10−210^\{\-2\}\.

#### Software and Availability\.

## 5\.Results and Discussion

The following subsections present quantitative and qualitative analyses covering image retrieval, comparison with state\-of\-the\-art graph embedding methods, semi\-supervised classification, and interpretability\.

### 5\.1\.Retrieval

Results are compared against the original features and interpretable representations \(RaDE, GRaCE\) without manifold learning, across all dataset and backbone combinations\.

Table[2](https://arxiv.org/html/2608.29004#S5.T2)reports the results on theFlowersdataset\. The best results for each feature are highlighted in bold, while the overall best results are shown in blue\. We observe that, in addition to interpretability aspects, the retrieval effectiveness of the proposed approaches surpasses that of the original features and of interpretable representations in isolation\. GRaCE, combined with rank\-based manifold learning approaches, achieved the best performance\.

Table 1\.Retrieval results on theFlowersdataset, considering MAP \(%\)\. The best result per feature is highlighted inbold; the best overall result is highlighted inbold blue\.Table 2\.Retrieval results on theCorel5kdataset, considering MAP \(%\)\. The best result per feature is highlighted inbold; the best overall result is highlighted inbold blue\.Tables[2](https://arxiv.org/html/2608.29004#S5.T2),[4](https://arxiv.org/html/2608.29004#S5.T4), and[4](https://arxiv.org/html/2608.29004#S5.T4)present the retrieval results for theCorel5k,Pets, andCUB\-200datasets, respectively\. The results are highly consistent across different datasets and features\. Except for Swin\-Tf on the Pets dataset, the best results for each feature were achieved by GRaCE combined with manifold learning methods, predominantly BFSTREE and RDPAC\. It is worth noting the substantial effectiveness gains over the original features observed in several scenarios\. On the Corel5k dataset, for instance, the best performance was achieved byGRaCE\+BFSTREE, reaching a MAP score of 96\.90%, whereas the original feature \(Swin\-Tf\) achieved 73\.27%\.

Table 3\.Retrieval results on thePetsdataset, considering MAP \(%\)\. The best result per feature is highlighted inbold; the best overall result is highlighted inbold blue\.Table 4\.Retrieval results on theCUB\-200dataset, considering MAP \(%\)\. The best result per feature is highlighted inbold; the best overall result is highlighted inbold blue\.Despite the overall positive trend, certain backbone–manifold combinations yield degraded performance relative to their baselines, most notably RaDE paired with RDPAC on the Pets and CUB\-200 datasets\. GRaCE proves more resilient to this effect, consistently benefiting from manifold refinement across all datasets\.

### 5\.2\.Comparison with State\-of\-the\-Art

Beyond the isolated evaluation of retrieval effectiveness, we position the proposed framework against representative graph embedding strategies\. We compare our method withDeepWalk \(DW\)\([Perozzi et al\., 2014](https://arxiv.org/html/2608.29004#bib.bib35)\), a classical topological embedding method;DINE\([Piaggesi et al\., 2024](https://arxiv.org/html/2608.29004#bib.bib36)\), a state\-of\-the\-artpost\-hocinterpretable method; and the rank\-based interpretable models,RaDE\([Alves de Fernando et al\., 2020](https://arxiv.org/html/2608.29004#bib.bib2)\)andGRaCE\([Almeida et al\., 2025](https://arxiv.org/html/2608.29004#bib.bib1)\)\.

Both DeepWalk and DINE were evaluated using the implementations provided in the official DINE repository555[https://github\.com/simonepiaggesi/dine](https://github.com/simonepiaggesi/dine)\. To ensure a fair comparison, the embedding dimensionalityddand the neighborhood sizekkused for graph construction follow the configurations detailed in Section[4\.3](https://arxiv.org/html/2608.29004#S4.SS3)\.

Table[5](https://arxiv.org/html/2608.29004#S5.T5)summarizes the comparative results using ViT\-B/16 features\. While classical DeepWalk generally improves over the original features, it produces opaque dimensions\. Conversely, applying DINE to DeepWalk results in a huge loss of effectiveness, suggesting that its sparse decomposition destroys the fine\-grained manifold structure necessary for retrieval\. In sharp contrast, the proposed framework systematically elevates performance beyond all baselines, achieving the highest MAP across all datasets\. This confirms that, unlike DINE, our framework successfully resolves the trade\-off between transparency and accuracy\.

Table 5\.Comparison of Graph Embedding approaches in retrieval effectiveness \(MAP %\) across all datasets with ViT\-B/16 features\. The best results are highlighted inbold\.
### 5\.3\.Classification

Table 6\.Accuracy \(%\) of GCN semi\-supervised classification on Flowers dataset\.Input FeatureGraph TypeInput GraphOriginalProposed ApproachManifold: NoneManifold: LHRRManifold: UMAPGRaCERaDEGRaCERaDEGRaCERaDEConvNeXtkk\-NNConvNeXt96\.75±\\pm0\.0298\.77±\\pm0\.0199\.19±\\pm0\.0199\.28±\\pm0\.0599\.84±\\pm0\.0199\.10±\\pm0\.0299\.03±\\pm0\.00Swin\-Tf97\.04±\\pm0\.0499\.26±\\pm0\.0099\.47±\\pm0\.0198\.66±\\pm0\.0799\.57±\\pm0\.0299\.38±\\pm0\.0299\.39±\\pm0\.00ViT\-B/1695\.50±\\pm0\.0295\.44±\\pm0\.0395\.37±\\pm0\.0294\.72±\\pm0\.0296\.44±\\pm0\.0896\.60±\\pm0\.0497\.52±\\pm0\.01RECConvNeXt99\.48±\\pm0\.0299\.33±\\pm0\.0299\.42±\\pm0\.0299\.77±\\pm0\.0199\.87±\\pm0\.0399\.21±\\pm0\.0199\.01±\\pm0\.01Swin\-Tf99\.70±\\pm0\.0199\.38±\\pm0\.0199\.48±\\pm0\.0399\.77±\\pm0\.0199\.76±\\pm0\.0199\.43±\\pm0\.0199\.39±\\pm0\.00ViT\-B/1697\.66±\\pm0\.0295\.97±\\pm0\.0396\.13±\\pm0\.0397\.29±\\pm0\.0297\.76±\\pm0\.0297\.11±\\pm0\.0397\.61±\\pm0\.01Swin\-Tfkk\-NNConvNeXt96\.87±\\pm0\.0598\.87±\\pm0\.0199\.26±\\pm0\.0198\.87±\\pm0\.1099\.89±\\pm0\.0099\.03±\\pm0\.0199\.04±\\pm0\.00Swin\-Tf97\.06±\\pm0\.0199\.32±\\pm0\.0199\.51±\\pm0\.0198\.70±\\pm0\.0499\.58±\\pm0\.0199\.42±\\pm0\.0199\.39±\\pm0\.00ViT\-B/1695\.48±\\pm0\.0395\.65±\\pm0\.0295\.60±\\pm0\.0494\.80±\\pm0\.0396\.53±\\pm0\.0796\.81±\\pm0\.0597\.68±\\pm0\.00RECConvNeXt99\.64±\\pm0\.0299\.47±\\pm0\.0199\.48±\\pm0\.0199\.83±\\pm0\.0199\.92±\\pm0\.0199\.22±\\pm0\.0199\.04±\\pm0\.00Swin\-Tf99\.80±\\pm0\.0199\.48±\\pm0\.0099\.50±\\pm0\.0199\.88±\\pm0\.0399\.78±\\pm0\.0199\.48±\\pm0\.0099\.40±\\pm0\.00ViT\-B/1697\.79±\\pm0\.0296\.13±\\pm0\.0296\.31±\\pm0\.0297\.57±\\pm0\.0297\.83±\\pm0\.0197\.36±\\pm0\.0197\.71±\\pm0\.01ViT\-B/16kk\-NNConvNeXt96\.31±\\pm0\.0698\.89±\\pm0\.0099\.20±\\pm0\.0196\.23±\\pm0\.1899\.82±\\pm0\.0298\.30±\\pm0\.0899\.01±\\pm0\.01Swin\-Tf96\.22±\\pm0\.0599\.25±\\pm0\.0299\.44±\\pm0\.0396\.48±\\pm0\.1499\.42±\\pm0\.0398\.85±\\pm0\.0699\.39±\\pm0\.00ViT\-B/1694\.08±\\pm0\.0395\.00±\\pm0\.0295\.00±\\pm0\.0793\.39±\\pm0\.1596\.06±\\pm0\.0895\.62±\\pm0\.0797\.11±\\pm0\.03RECConvNeXt98\.84±\\pm0\.0299\.37±\\pm0\.0299\.39±\\pm0\.0198\.68±\\pm0\.0699\.46±\\pm0\.0198\.98±\\pm0\.0298\.98±\\pm0\.02Swin\-Tf98\.85±\\pm0\.0499\.11±\\pm0\.0099\.39±\\pm0\.0198\.82±\\pm0\.0599\.29±\\pm0\.0399\.19±\\pm0\.0399\.40±\\pm0\.00ViT\-B/1696\.50±\\pm0\.0395\.25±\\pm0\.0395\.47±\\pm0\.0296\.54±\\pm0\.0696\.96±\\pm0\.0496\.81±\\pm0\.0397\.50±\\pm0\.02

Table 7\.Accuracy \(%\) of GCN semi\-supervised classification on Corel5k dataset\.Input FeatureGraph TypeInput GraphOriginalProposed ApproachManifold: NoneManifold: LHRRManifold: UMAPGRaCERaDEGRaCERaDEGRaCERaDEConvNeXtkk\-NNConvNeXt94\.42±\\pm0\.0292\.69±\\pm0\.0192\.68±\\pm0\.0393\.61±\\pm0\.0495\.37±\\pm0\.0592\.86±\\pm0\.0794\.27±\\pm0\.08Swin\-Tf95\.99±\\pm0\.0392\.93±\\pm0\.0294\.45±\\pm0\.0295\.26±\\pm0\.0597\.18±\\pm0\.0294\.57±\\pm0\.1496\.31±\\pm0\.03ViT\-B/1695\.08±\\pm0\.0493\.74±\\pm0\.0193\.75±\\pm0\.0193\.63±\\pm0\.0395\.64±\\pm0\.0393\.37±\\pm0\.0594\.59±\\pm0\.02RECConvNeXt96\.30±\\pm0\.0893\.41±\\pm0\.0493\.40±\\pm0\.0996\.03±\\pm0\.0495\.96±\\pm0\.0694\.17±\\pm0\.0394\.46±\\pm0\.03Swin\-Tf97\.39±\\pm0\.0594\.06±\\pm0\.0295\.06±\\pm0\.0496\.98±\\pm0\.0397\.45±\\pm0\.0695\.95±\\pm0\.0696\.63±\\pm0\.06ViT\-B/1696\.47±\\pm0\.0194\.37±\\pm0\.0194\.60±\\pm0\.0295\.30±\\pm0\.0396\.10±\\pm0\.0995\.17±\\pm0\.0595\.02±\\pm0\.03Swin\-Tfkk\-NNConvNeXt94\.62±\\pm0\.0392\.89±\\pm0\.0193\.37±\\pm0\.0293\.75±\\pm0\.0595\.67±\\pm0\.0293\.35±\\pm0\.0594\.77±\\pm0\.06Swin\-Tf95\.75±\\pm0\.0493\.12±\\pm0\.0294\.47±\\pm0\.0595\.81±\\pm0\.0597\.22±\\pm0\.0195\.14±\\pm0\.0496\.46±\\pm0\.02ViT\-B/1695\.33±\\pm0\.0393\.87±\\pm0\.0194\.06±\\pm0\.0493\.69±\\pm0\.0595\.83±\\pm0\.0293\.71±\\pm0\.0694\.77±\\pm0\.02RECConvNeXt97\.09±\\pm0\.0593\.88±\\pm0\.0294\.27±\\pm0\.0796\.74±\\pm0\.0596\.49±\\pm0\.0394\.79±\\pm0\.0595\.01±\\pm0\.02Swin\-Tf97\.76±\\pm0\.0494\.20±\\pm0\.0195\.18±\\pm0\.1197\.56±\\pm0\.0297\.65±\\pm0\.0496\.43±\\pm0\.0396\.79±\\pm0\.01ViT\-B/1696\.84±\\pm0\.0194\.69±\\pm0\.0194\.88±\\pm0\.0396\.02±\\pm0\.0296\.41±\\pm0\.0695\.78±\\pm0\.0195\.20±\\pm0\.03ViT\-B/16kk\-NNConvNeXt94\.56±\\pm0\.0492\.75±\\pm0\.0192\.87±\\pm0\.0593\.44±\\pm0\.0795\.44±\\pm0\.0192\.95±\\pm0\.0794\.40±\\pm0\.12Swin\-Tf95\.81±\\pm0\.0392\.93±\\pm0\.0294\.48±\\pm0\.0695\.23±\\pm0\.0697\.16±\\pm0\.0294\.39±\\pm0\.0396\.43±\\pm0\.03ViT\-B/1694\.64±\\pm0\.0493\.60±\\pm0\.0193\.65±\\pm0\.0393\.23±\\pm0\.1095\.65±\\pm0\.0293\.29±\\pm0\.0894\.48±\\pm0\.05RECConvNeXt96\.61±\\pm0\.0993\.57±\\pm0\.0293\.72±\\pm0\.1795\.93±\\pm0\.0296\.10±\\pm0\.0694\.41±\\pm0\.0694\.56±\\pm0\.09Swin\-Tf97\.35±\\pm0\.0594\.01±\\pm0\.0395\.10±\\pm0\.0696\.72±\\pm0\.0297\.31±\\pm0\.1095\.71±\\pm0\.0796\.62±\\pm0\.06ViT\-B/1696\.24±\\pm0\.0294\.19±\\pm0\.0294\.30±\\pm0\.1094\.81±\\pm0\.0395\.81±\\pm0\.0694\.99±\\pm0\.0594\.87±\\pm0\.07

The proposed context\-aware representations were also evaluated for computingkk\-NN and Reciprocalkk\-NN \(REC\) graphs exploited for semi\-supervised classification using GCNs\([Kipf and Welling, 2017](https://arxiv.org/html/2608.29004#bib.bib17)\)\. The experiments compared graphs computed from the original high\-dimensional features with those derived from the interpretable embeddings, evaluating the impact of the manifold learning step\. The best results obtained with interpretable representations are highlighted in bold within each row and in blue for each feature\.

Table[6](https://arxiv.org/html/2608.29004#S5.T6)presents the results on theFlowersdataset\. The highest accuracy scores were achieved by RaDE interpretable representations combined with rank\-based manifold learning using LHRR\. Table[7](https://arxiv.org/html/2608.29004#S5.T7)reports the results for theCorel5kdataset, where similar trends were observed\. Tables[8](https://arxiv.org/html/2608.29004#S5.T8)and[9](https://arxiv.org/html/2608.29004#S5.T9)present the classification results for thePetsandCUB\-200datasets, respectively\. In these fine\-grained scenarios, RaDE representations also achieved the best performance, predominantly when combined with LHRR and UMAP manifold learning strategies\.

Overall, when comparing the interpretable representations with the original features, we observe that classification accuracy is robustly maintained in most scenarios\. This indicates that the proposed approach effectively compresses the feature space \(e\.g\., from 1024 to 128 dimensions\) and provides semantic interpretability without compromising the discriminative power required for downstream classification tasks\.

Table 8\.Accuracy \(%\) of GCN semi\-supervised classification on Pets dataset\.Input FeatureGraph TypeInput GraphOriginalProposed ApproachManifold: NoneManifold: LHRRManifold: UMAPGRaCERaDEGRaCERaDEGRaCERaDEConvNeXtkk\-NNConvNeXt88\.52±\\pm0\.0391\.46±\\pm0\.0192\.12±\\pm0\.0291\.13±\\pm0\.0291\.59±\\pm0\.0190\.35±\\pm0\.0490\.73±\\pm0\.04Swin\-Tf85\.90±\\pm0\.0688\.69±\\pm0\.0289\.82±\\pm0\.0285\.62±\\pm0\.0285\.43±\\pm0\.0287\.88±\\pm0\.0787\.75±\\pm0\.02ViT\-B/1691\.16±\\pm0\.0192\.57±\\pm0\.0192\.56±\\pm0\.0291\.33±\\pm0\.0392\.63±\\pm0\.0193\.19±\\pm0\.0493\.34±\\pm0\.02RECConvNeXt92\.14±\\pm0\.0191\.81±\\pm0\.0192\.44±\\pm0\.0191\.66±\\pm0\.0291\.69±\\pm0\.0291\.10±\\pm0\.0391\.12±\\pm0\.04Swin\-Tf91\.02±\\pm0\.0389\.05±\\pm0\.0190\.05±\\pm0\.0286\.65±\\pm0\.0286\.87±\\pm0\.0188\.16±\\pm0\.0288\.18±\\pm0\.02ViT\-B/1693\.27±\\pm0\.0392\.72±\\pm0\.0192\.96±\\pm0\.0191\.90±\\pm0\.0192\.95±\\pm0\.0293\.34±\\pm0\.0193\.50±\\pm0\.02Swin\-Tfkk\-NNConvNeXt87\.84±\\pm0\.0591\.64±\\pm0\.0192\.21±\\pm0\.0190\.63±\\pm0\.0391\.67±\\pm0\.0189\.78±\\pm0\.0190\.85±\\pm0\.03Swin\-Tf83\.92±\\pm0\.0488\.62±\\pm0\.0089\.64±\\pm0\.0285\.65±\\pm0\.0285\.39±\\pm0\.0287\.57±\\pm0\.0687\.74±\\pm0\.01ViT\-B/1690\.90±\\pm0\.0292\.65±\\pm0\.0092\.61±\\pm0\.0190\.65±\\pm0\.0392\.68±\\pm0\.0192\.41±\\pm0\.0393\.22±\\pm0\.02RECConvNeXt91\.76±\\pm0\.0391\.88±\\pm0\.0292\.57±\\pm0\.0291\.48±\\pm0\.0392\.09±\\pm0\.0291\.06±\\pm0\.0391\.34±\\pm0\.02Swin\-Tf89\.61±\\pm0\.0488\.80±\\pm0\.0189\.79±\\pm0\.0086\.45±\\pm0\.0186\.60±\\pm0\.0187\.89±\\pm0\.0388\.11±\\pm0\.00ViT\-B/1692\.91±\\pm0\.0292\.84±\\pm0\.0193\.01±\\pm0\.0191\.44±\\pm0\.0292\.92±\\pm0\.0092\.89±\\pm0\.0293\.33±\\pm0\.03ViT\-B/16kk\-NNConvNeXt88\.81±\\pm0\.0491\.52±\\pm0\.0192\.20±\\pm0\.0191\.06±\\pm0\.0591\.51±\\pm0\.0390\.17±\\pm0\.0490\.51±\\pm0\.02Swin\-Tf86\.08±\\pm0\.0488\.56±\\pm0\.0289\.81±\\pm0\.0285\.58±\\pm0\.0285\.22±\\pm0\.0287\.56±\\pm0\.0887\.45±\\pm0\.04ViT\-B/1691\.09±\\pm0\.0492\.44±\\pm0\.0192\.25±\\pm0\.0691\.47±\\pm0\.0492\.50±\\pm0\.0193\.10±\\pm0\.0493\.02±\\pm0\.02RECConvNeXt92\.47±\\pm0\.0291\.92±\\pm0\.0292\.45±\\pm0\.0191\.66±\\pm0\.0491\.92±\\pm0\.0291\.03±\\pm0\.0490\.87±\\pm0\.04Swin\-Tf91\.08±\\pm0\.0589\.00±\\pm0\.0190\.09±\\pm0\.0186\.58±\\pm0\.0286\.76±\\pm0\.0287\.78±\\pm0\.0287\.90±\\pm0\.06ViT\-B/1692\.87±\\pm0\.0392\.57±\\pm0\.0192\.58±\\pm0\.0491\.84±\\pm0\.0192\.60±\\pm0\.0393\.15±\\pm0\.0293\.09±\\pm0\.08

Table 9\.Accuracy \(%\) of GCN semi\-supervised classification on CUB\-200 dataset\.Input FeatureGraph TypeInput GraphOriginalProposed ApproachManifold: NoneManifold: LHRRManifold: UMAPGRaCERaDEGRaCERaDEGRaCERaDEConvNeXtkk\-NNConvNeXt76\.96±\\pm0\.0373\.24±\\pm0\.0374\.85±\\pm0\.0275\.84±\\pm0\.0675\.98±\\pm0\.0475\.07±\\pm0\.0373\.99±\\pm0\.03Swin\-Tf77\.90±\\pm0\.0275\.97±\\pm0\.0277\.91±\\pm0\.0377\.37±\\pm0\.0477\.41±\\pm0\.0277\.98±\\pm0\.0977\.26±\\pm0\.03ViT\-B/1671\.33±\\pm0\.0363\.32±\\pm0\.0166\.60±\\pm0\.0268\.51±\\pm0\.0568\.78±\\pm0\.0365\.25±\\pm0\.0464\.55±\\pm0\.03RECConvNeXt80\.29±\\pm0\.0273\.64±\\pm0\.0475\.31±\\pm0\.0277\.08±\\pm0\.0977\.51±\\pm0\.0575\.99±\\pm0\.0575\.35±\\pm0\.06Swin\-Tf82\.17±\\pm0\.0276\.95±\\pm0\.0278\.72±\\pm0\.0478\.86±\\pm0\.0379\.39±\\pm0\.0378\.77±\\pm0\.0278\.50±\\pm0\.02ViT\-B/1676\.27±\\pm0\.0164\.83±\\pm0\.0167\.67±\\pm0\.0370\.63±\\pm0\.0370\.91±\\pm0\.0466\.52±\\pm0\.0265\.64±\\pm0\.02Swin\-Tfkk\-NNConvNeXt77\.67±\\pm0\.0073\.72±\\pm0\.0275\.52±\\pm0\.0376\.21±\\pm0\.0376\.52±\\pm0\.0575\.31±\\pm0\.0474\.55±\\pm0\.02Swin\-Tf77\.54±\\pm0\.0176\.24±\\pm0\.0378\.18±\\pm0\.0277\.38±\\pm0\.0477\.80±\\pm0\.0177\.94±\\pm0\.0477\.54±\\pm0\.03ViT\-B/1671\.91±\\pm0\.0163\.87±\\pm0\.0267\.02±\\pm0\.0368\.92±\\pm0\.0269\.13±\\pm0\.0365\.75±\\pm0\.0365\.00±\\pm0\.02RECConvNeXt81\.89±\\pm0\.0174\.59±\\pm0\.0276\.08±\\pm0\.0177\.98±\\pm0\.0278\.45±\\pm0\.0376\.65±\\pm0\.0375\.91±\\pm0\.02Swin\-Tf82\.05±\\pm0\.0177\.16±\\pm0\.0278\.85±\\pm0\.0379\.20±\\pm0\.0179\.63±\\pm0\.0179\.19±\\pm0\.0278\.75±\\pm0\.03ViT\-B/1676\.75±\\pm0\.065\.58±\\pm0\.0168\.26±\\pm0\.0271\.11±\\pm0\.0371\.46±\\pm0\.0467\.15±\\pm0\.0366\.03±\\pm0\.01ViT\-B/16kk\-NNConvNeXt76\.89±\\pm0\.0472\.90±\\pm0\.0274\.62±\\pm0\.0275\.27±\\pm0\.0475\.81±\\pm0\.0774\.18±\\pm0\.0473\.70±\\pm0\.01Swin\-Tf76\.79±\\pm0\.0775\.46±\\pm0\.0277\.51±\\pm0\.0176\.74±\\pm0\.0677\.05±\\pm0\.0477\.04±\\pm0\.0676\.61±\\pm0\.02ViT\-B/1669\.33±\\pm0\.0362\.49±\\pm0\.0265\.64±\\pm0\.0167\.69±\\pm0\.0468\.10±\\pm0\.0364\.28±\\pm0\.0363\.78±\\pm0\.02RECConvNeXt80\.01±\\pm0\.0273\.16±\\pm0\.0275\.03±\\pm0\.0275\.90±\\pm0\.0277\.07±\\pm0\.0274\.85±\\pm0\.0374\.85±\\pm0\.01Swin\-Tf80\.15±\\pm0\.0276\.11±\\pm0\.0178\.15±\\pm0\.0277\.58±\\pm0\.0378\.44±\\pm0\.0277\.54±\\pm0\.0577\.44±\\pm0\.03ViT\-B/1672\.55±\\pm0\.0263\.39±\\pm0\.0066\.34±\\pm0\.0168\.87±\\pm0\.0269\.45±\\pm0\.0464\.94±\\pm0\.0364\.16±\\pm0\.02

### 5\.4\.Qualitative and Visual Analysis

In addition to the quantitative evaluation focused on the effectiveness of downstream tasks, the experimental analysis also considered qualitative aspects\. Figure[2](https://arxiv.org/html/2608.29004#S5.F2)presents a visual analysis comparing the retrieval results obtained using the original features, the interpretable techniques, and the proposed approach, which combines manifold learning and interpretable representations\. The reported examples refer to ViT/B16 features on theFlowersdataset, considering GRaCE in isolation and GRaCE\+RDPAC for the proposed approach\. The blue border indicates the query image, green borders denote relevant images, and red borders indicate non\-relevant ones\. Significant effectiveness gains can be observed\.

![Refer to caption](https://arxiv.org/html/2608.29004v1/visualization_retrieval.png)Figure 2\.Qualitative retrieval results\.Figure[3](https://arxiv.org/html/2608.29004#S5.F3)presents a visualization of the interpretable representation\. Each row illustrates the representation obtained for a dataset instance, organized according to dataset classes \(species\)\. The columns represent the dimensions associated with prototypes\. At the bottom of the figure, selected prototypes are illustrated\. The color scale represents low or high values assigned to each dimension and, therefore, the similarity to the corresponding prototype\. The association between dimensions and prototypes enables a clear, human\-guided interpretation of the representations\. In addition, strong evidence of disentanglement can be observed\. The matrix is predominantly inactive \(blue\), indicating quantitative sparsity and the isolation of semantic concepts associated with specific dimensions\.

![Refer to caption](https://arxiv.org/html/2608.29004v1/heatmap_grace_rdpac.png)Figure 3\.Heatmap visualization of the interpretable representation created by the GRaCE\+RDPAC combination of the proposed approach\. Each row corresponds to a dataset instance, and columns represent dimensions associated with prototypes\. The color scale indicates the similarity between each instance and the corresponding prototype\.
### 5\.5\.Limitations

While the proposed framework demonstrates consistent gains, some limitations should be acknowledged\. First, the approach exhibits limited scalability in dynamic scenarios: incorporating new samples requires recomputing ranked lists, a cost that grows linearly with dataset size\. Second, the neighborhood parameterskkandLLare adjusted per dataset and lack an automatic selection strategy, requiring practitioner tuning\. Third, certain backbone–manifold combinations yield degraded performance, suggesting sensitivity to the geometric structure of specific feature spaces that warrants further investigation\.

## 6\.Conclusions

This paper introduced a novel framework for context\-aware interpretable representations, effectively combining rank\-based manifold learning with prototype\-driven embedding generation\. Our core contribution lies in bridging the geometric and interpretability gaps, transforming high\-dimensional, opaque feature spaces into sparse, self\-explaining structures that remain faithful to the intrinsic data topology\. Experimental results across diverse benchmarks validate that the proposed approach either preserves or improves effectiveness in image retrieval and semi\-supervised classification via Graph Convolutional Networks \(GCNs\)\. Beyond quantitative gains, the qualitative\-visual analysis confirms that the identified prototypes provide intuitive, human\-centric explanations\.

Future research will investigate the limitations while evaluating the integration of self\-supervised contrastive learning strategies upon the interpretable representations, aiming to further distill discriminative features while maintaining the structural transparency of the embeddings\.

###### Acknowledgements\.

The authors are grateful to the National Council for Scientific and Technological Development — CNPq \(grant \#313193/2023\-1\), the São Paulo Research Foundation — FAPESP \(grant \#2024/04890\-5 and \#2025/07171\-2\), and Petrobras \(grant \#2023/00095\-3\) for their financial support\.

## References

- Almeidaet al\.\(2025\)T\. C\. C\. Almeida, G\. Rosseto Letício, L\. P\. Valem, A\. Freitas, and D\. C\. Guimarães PedronetteEffective graph and rank\-based contextual embeddings for textual and multimedia data\.In2025 International Joint Conference on Neural Networks \(IJCNN\),Vol\.,pp\. 1–8\.External Links:[Document](https://dx.doi.org/10.1109/IJCNN64981.2025.11229362)Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p3.1),[§2\.1](https://arxiv.org/html/2608.29004#S2.SS1.p3.1),[§3\.2](https://arxiv.org/html/2608.29004#S3.SS2.SSSx2.p1.1),[§4\.2](https://arxiv.org/html/2608.29004#S4.SS2.SSSx1.p1.1),[§4\.3](https://arxiv.org/html/2608.29004#S4.SS3.SSSx2.p1.1),[§5\.2](https://arxiv.org/html/2608.29004#S5.SS2.p1.1),[Table 5](https://arxiv.org/html/2608.29004#S5.T5.6.1.6.1)\.
- Alves de Fernandoet al\.\(2020\)F\. Alves de Fernando, D\. C\. G\. Pedronette, G\. José de Sousa, L\. P\. Valem, and I\. R\. GuilhermeRaDE: a rank\-based graph embedding approach\.InProceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications \(VISIGRAPP 2020\) \- Volume 5: VISAPP,pp\. 142–152\.External Links:[Document](https://dx.doi.org/10.5220/0008985901420152)Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p3.1),[§2\.1](https://arxiv.org/html/2608.29004#S2.SS1.p3.1),[§3\.2](https://arxiv.org/html/2608.29004#S3.SS2.SSSx2.p1.1),[§4\.3](https://arxiv.org/html/2608.29004#S4.SS3.SSSx2.p1.1),[§5\.2](https://arxiv.org/html/2608.29004#S5.SS2.p1.1),[Table 5](https://arxiv.org/html/2608.29004#S5.T5.6.1.5.1)\.
- Anandet al\.\(2025\)A\. Anand, S\. Saha, and V\. VenkteshExplainable information retrieval\.InAdvances in Information Retrieval: 47th European Conference on Information Retrieval, ECIR 2025,Berlin, Heidelberg,pp\. 254–261\.External Links:ISBN 978\-3\-031\-88719\-2Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p2.1)\.
- Angelovet al\.\(2025\)P\. Angelov, D\. Kangin, and Z\. ZhangIDEAL: interpretable\-by\-design algorithms for learning from foundation feature spaces\.Neurocomputing626,pp\. 129464\.External Links:[Document](https://dx.doi.org/10.1016/j.neucom.2025.129464)Cited by:[§2\.3](https://arxiv.org/html/2608.29004#S2.SS3.p3.1)\.
- Bengioet al\.\(2013\)Y\. Bengio, A\. Courville, and P\. VincentRepresentation learning: a review and new perspectives\.IEEE Transactions on Pattern Analysis and Machine Intelligence35\(8\),pp\. 1798–1828\.External Links:[Document](https://dx.doi.org/10.1109/TPAMI.2013.50)Cited by:[§2\.2](https://arxiv.org/html/2608.29004#S2.SS2.p1.1)\.
- Chenet al\.\(2019\)C\. Chen, O\. Li, D\. Tao, A\. Barnett, C\. Rudin, and J\. K\. SuThis looks like that: deep learning for interpretable image recognition\.InAdvances in Neural Information Processing Systems,Vol\.32,pp\.\.External Links:[Link](https://proceedings.neurips.cc/paper_files/paper/2019/file/adf7ee2dcf142b0e11888e72b43fcb75-Paper.pdf)Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p3.1),[§2\.3](https://arxiv.org/html/2608.29004#S2.SS3.p2.1)\.
- Chenet al\.\(2020\)F\. Chen, Y\. Wang, B\. Wang, and C\.\-C\. J\. KuoGraph representation learning: a survey\.APSIPA Transactions on Signal and Information Processing9\(1\)\.External Links:[Link](http://dx.doi.org/10.1017/ATSIP.2020.13),[Document](https://dx.doi.org/10.1017/atsip.2020.13)Cited by:[§2\.1](https://arxiv.org/html/2608.29004#S2.SS1.p1.1)\.
- Dosovitskiyet al\.\(2021\)A\. Dosovitskiy, L\. Beyer, A\. Kolesnikov, D\. Weissenborn, X\. Zhai, T\. Unterthiner, M\. Dehghani, M\. Minderer, G\. Heigold, S\. Gelly, J\. Uszkoreit, and N\. HoulsbyAn image is worth 16x16 words: transformers for image recognition at scale\.InInternational Conference on Learning Representations,Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p1.1),[§4\.1](https://arxiv.org/html/2608.29004#S4.SS1.p2.1)\.
- Ermolovet al\.\(2022\)A\. Ermolov, L\. Mirvakhabova, V\. Khrulkov, N\. Sebe, and I\. OseledetsHyperbolic vision transformers: combining improvements in metric learning\.In2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition \(CVPR\),Vol\.,pp\. 7399–7409\.External Links:[Document](https://dx.doi.org/10.1109/CVPR52688.2022.00726)Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p2.1)\.
- Fernandoet al\.\(2022\)F\. A\. d\. Fernando, D\. C\. G\. Pedronette, G\. J\. d\. Sousa, L\. P\. Valem, and I\. R\. GuilhermeRaDE\+: A semantic rank\-based graph embedding algorithm\.International Journal of Information Management Data Insights2\(1\),pp\. 100078\.External Links:[Document](https://dx.doi.org/10.1016/j.jjimei.2022.100078)Cited by:[§2\.1](https://arxiv.org/html/2608.29004#S2.SS1.p3.1),[§3\.2](https://arxiv.org/html/2608.29004#S3.SS2.SSSx2.p1.1),[§4\.3](https://arxiv.org/html/2608.29004#S4.SS3.SSSx2.p1.1)\.
- Gautamet al\.\(2024\)S\. Gautam, A\. Boubekki, M\. M\. Höhne, and M\. KampffmeyerPrototypical self\-explainable models without re\-training\.Transactions on Machine Learning Research\.External Links:ISSN 2835\-8856Cited by:[§2\.3](https://arxiv.org/html/2608.29004#S2.SS3.p2.1),[§2\.3](https://arxiv.org/html/2608.29004#S2.SS3.p3.1)\.
- Grover and Leskovec \(2016\)A\. Grover and J\. LeskovecNode2vec: Scalable Feature Learning for Networks\.InProceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining,KDD ’16,pp\. 855–864\.External Links:[Document](https://dx.doi.org/10.1145/2939672.2939754)Cited by:[§2\.1](https://arxiv.org/html/2608.29004#S2.SS1.p1.1)\.
- Heet al\.\(2016\)K\. He, X\. Zhang, S\. Ren, and J\. SunDeep Residual Learning for Image Recognition\.In2016 IEEE Conference on Computer Vision and Pattern Recognition \(CVPR\),pp\. 770–778\.External Links:[Document](https://dx.doi.org/10.1109/CVPR.2016.90)Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p1.1)\.
- Higginset al\.\(2017\)I\. Higgins, L\. Matthey, A\. Pal, C\. Burgess, X\. Glorot, M\. Botvinick, S\. Mohamed, and A\. LerchnerBeta\-VAE: learning basic visual concepts with a constrained variational framework\.InInternational Conference on Learning Representations,External Links:[Link](https://openreview.net/forum?id=Sy2fzU9gl)Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p3.1),[§2\.2](https://arxiv.org/html/2608.29004#S2.SS2.p1.1)\.
- Houet al\.\(2022\)Z\. Hou, X\. Liu, Y\. Cen, Y\. Dong, H\. Yang, C\. Wang, and J\. TangGraphMAE: self\-supervised masked graph autoencoders\.InProceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining,KDD ’22,New York, NY, USA,pp\. 594–604\.External Links:ISBN 9781450393850,[Link](https://doi.org/10.1145/3534678.3539321),[Document](https://dx.doi.org/10.1145/3534678.3539321)Cited by:[§2\.1](https://arxiv.org/html/2608.29004#S2.SS1.p2.1)\.
- Huanget al\.\(2019\)X\. Huang, L\. Wu, and Y\. YeA Review on Dimensionality Reduction Techniques\.International Journal of Pattern Recognition and Artificial Intelligence33\(10\),pp\. 1950017\.External Links:[Document](https://dx.doi.org/10.1142/S0218001419500174)Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p2.1),[§3\.2](https://arxiv.org/html/2608.29004#S3.SS2.SSSx1.p1.1)\.
- Kipf and Welling \(2017\)T\. N\. Kipf and M\. WellingSemi\-supervised classification with graph convolutional networks\.InInternational Conference on Learning Representations,External Links:[Link](https://openreview.net/forum?id=SJU4ayYgl)Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p3.1),[§2\.1](https://arxiv.org/html/2608.29004#S2.SS1.p2.1),[§5\.3](https://arxiv.org/html/2608.29004#S5.SS3.p1.1)\.
- Kohet al\.\(2020\)P\. W\. Koh, T\. Nguyen, Y\. S\. Tang, S\. Mussmann, E\. Pierson, B\. Kim, and P\. LiangConcept bottleneck models\.InProceedings of the 37th International Conference on Machine Learning,Proceedings of Machine Learning Research, Vol\.119,pp\. 5338–5348\.Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p3.1),[§2\.3](https://arxiv.org/html/2608.29004#S2.SS3.p1.1)\.
- Levada \(2022\)A\. L\. M\. LevadaA curvature based isometric feature mapping\.In2022 26th International Conference on Pattern Recognition \(ICPR\),Vol\.,pp\. 557–563\.External Links:[Document](https://dx.doi.org/10.1109/ICPR56361.2022.9956591)Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p2.1),[§1](https://arxiv.org/html/2608.29004#S1.p3.1),[§2\.3](https://arxiv.org/html/2608.29004#S2.SS3.p3.1)\.
- Liu and Yang \(2013\)G\. Liu and J\. YangContent\-based image retrieval using color difference histogram\.Pattern Recognition46\(1\),pp\. 188–198\(en\)\.External Links:[Document](https://dx.doi.org/10.1016/j.patcog.2012.06.001)Cited by:[§4\.1](https://arxiv.org/html/2608.29004#S4.SS1.p1.1)\.
- Liuet al\.\(2021\)Z\. Liu, Y\. Lin, Y\. Cao, H\. Hu, Y\. Wei, Z\. Zhang, S\. Lin, and B\. GuoSwin Transformer: Hierarchical Vision Transformer using Shifted Windows\.In2021 IEEE/CVF International Conference on Computer Vision \(ICCV\),pp\. 9992–10002\.External Links:[Document](https://dx.doi.org/10.1109/ICCV48922.2021.00986)Cited by:[§4\.1](https://arxiv.org/html/2608.29004#S4.SS1.p2.1)\.
- Liuet al\.\(2022\)Z\. Liu, H\. Mao, C\. Wu, C\. Feichtenhofer, T\. Darrell, and S\. XieA ConvNet for the 2020s\.In2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition \(CVPR\),Vol\.,pp\. 11966–11976\.External Links:[Document](https://dx.doi.org/10.1109/CVPR52688.2022.01167)Cited by:[§4\.1](https://arxiv.org/html/2608.29004#S4.SS1.p2.1)\.
- Locatelloet al\.\(2019\)F\. Locatello, S\. Bauer, M\. Lučić, G\. Rätsch, S\. Gelly, B\. Schölkopf, and O\. F\. BachemChallenging common assumptions in the unsupervised learning of disentangled representations\.InInternational Conference on Machine Learning,Note:Best Paper AwardExternal Links:[Link](http://proceedings.mlr.press/v97/locatello19a.html)Cited by:[§2\.2](https://arxiv.org/html/2608.29004#S2.SS2.p2.1)\.
- Maet al\.\(2019\)J\. Ma, P\. Cui, K\. Kuang, X\. Wang, and W\. ZhuDisentangled graph convolutional networks\.InProceedings of the 36th International Conference on Machine Learning,Proceedings of Machine Learning Research, Vol\.97,pp\. 4212–4221\.External Links:[Link](https://proceedings.mlr.press/v97/ma19a.html)Cited by:[§2\.2](https://arxiv.org/html/2608.29004#S2.SS2.p1.1)\.
- Marconatoet al\.\(2023\)E\. Marconato, A\. Passerini, and S\. TesoInterpretability is in the mind of the beholder: a causal framework for human\-interpretable representation learning\.Entropy25\(12\)\.External Links:[Link](https://www.mdpi.com/1099-4300/25/12/1574),ISSN 1099\-4300,[Document](https://dx.doi.org/10.3390/e25121574)Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p2.1)\.
- McInneset al\.\(2018\)L\. McInnes, J\. Healy, N\. Saul, and L\. GroßbergerUMAP: uniform manifold approximation and projection\.Journal of Open Source Software3\(29\),pp\. 861\.External Links:[Document](https://dx.doi.org/10.21105/joss.00861)Cited by:[§3\.2](https://arxiv.org/html/2608.29004#S3.SS2.SSSx1.p2.1.1)\.
- Nilsback and Zisserman \(2006\)M\.\-E\. Nilsback and A\. ZissermanA Visual Vocabulary for Flower Classification\.In2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition \(CVPR\),Vol\.2,pp\. 1447–1454\.External Links:[Link](http://ieeexplore.ieee.org/document/1640927/),[Document](https://dx.doi.org/10.1109/CVPR.2006.42)Cited by:[§4\.1](https://arxiv.org/html/2608.29004#S4.SS1.p1.1)\.
- Oikarinenet al\.\(2023\)T\. Oikarinen, S\. Das, L\. M\. Nguyen, and T\. WengLabel\-free concept bottleneck models\.InThe Eleventh International Conference on Learning Representations,Cited by:[§2\.3](https://arxiv.org/html/2608.29004#S2.SS3.p1.1)\.
- Parkhiet al\.\(2012\)O\. M\. Parkhi, A\. Vedaldi, A\. Zisserman, and C\. V\. JawaharCats and dogs\.In2012 IEEE Conference on Computer Vision and Pattern Recognition,Vol\.,pp\. 3498–3505\.External Links:[Document](https://dx.doi.org/10.1109/CVPR.2012.6248092)Cited by:[§4\.1](https://arxiv.org/html/2608.29004#S4.SS1.p1.1)\.
- Pedronetteet al\.\(2021a\)D\. C\. G\. Pedronette, L\. V\. Pascotti, and L\. J\. LateckiEfficient rank\-based diffusion process with assured convergence\.Journal of Imaging7\(3\)\.External Links:[Link](https://www.mdpi.com/2313-433X/7/3/49),ISSN 2313\-433X,[Document](https://dx.doi.org/10.3390/jimaging7030049)Cited by:[§3\.2](https://arxiv.org/html/2608.29004#S3.SS2.SSSx1.p3.1.1),[§4\.3](https://arxiv.org/html/2608.29004#S4.SS3.SSSx1.p1.1)\.
- Pedronette and Torres \(2015\)D\. C\. G\. Pedronette and R\. d\. S\. TorresUnsupervised Effectiveness Estimation for Image Retrieval Using Reciprocal Rank Information\.In2015 28th SIBGRAPI Conference on Graphics, Patterns and Images \(SIBGRAPI\),pp\. 321–328\.External Links:[Document](https://dx.doi.org/10.1109/SIBGRAPI.2015.28)Cited by:[§3\.2](https://arxiv.org/html/2608.29004#S3.SS2.SSSx2.p3.1),[§4\.3](https://arxiv.org/html/2608.29004#S4.SS3.SSSx2.p1.1.1)\.
- Pedronetteet al\.\(2019\)D\. C\. G\. Pedronette, L\. P\. Valem, J\. Almeida, and R\. da S\. TorresMultimedia retrieval through unsupervised hypergraph\-based manifold ranking\.IEEE Transactions on Image Processing28\(12\),pp\. 5824–5838\.External Links:[Document](https://dx.doi.org/10.1109/TIP.2019.2920526)Cited by:[§3\.2](https://arxiv.org/html/2608.29004#S3.SS2.SSSx1.p4.1.1),[§4\.3](https://arxiv.org/html/2608.29004#S4.SS3.SSSx1.p1.1)\.
- Pedronetteet al\.\(2021b\)D\. C\. G\. Pedronette, L\. P\. Valem, and R\. da S\. TorresA bfs\-tree of ranking references for unsupervised manifold learning\.Pattern Recognition111,pp\. 107666\.External Links:ISSN 0031\-3203,[Document](https://dx.doi.org/https%3A//doi.org/10.1016/j.patcog.2020.107666),[Link](https://www.sciencedirect.com/science/article/pii/S0031320320304696)Cited by:[§3\.2](https://arxiv.org/html/2608.29004#S3.SS2.SSSx1.p5.1.1),[§4\.3](https://arxiv.org/html/2608.29004#S4.SS3.SSSx1.p1.1)\.
- Pereira\-Ferreroet al\.\(2024\)V\.H\. Pereira\-Ferrero, T\.G\. Lewis, L\.P\. Valem, L\.G\.P\. Ferrero, D\.C\.G\. Pedronette, and L\.J\. LateckiUnsupervised affinity learning based on manifold analysis for image retrieval: a survey\.Computer Science Review53,pp\. 100657\.External Links:ISSN 1574\-0137,[Document](https://dx.doi.org/https%3A//doi.org/10.1016/j.cosrev.2024.100657)Cited by:[§3\.2](https://arxiv.org/html/2608.29004#S3.SS2.SSSx1.p1.1)\.
- Perozziet al\.\(2014\)B\. Perozzi, R\. Al\-Rfou, and S\. SkienaDeepWalk: online learning of social representations\.InProceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining,KDD ’14,pp\. 701–710\.External Links:[Document](https://dx.doi.org/10.1145/2623330.2623732)Cited by:[§2\.1](https://arxiv.org/html/2608.29004#S2.SS1.p1.1),[§5\.2](https://arxiv.org/html/2608.29004#S5.SS2.p1.1),[Table 5](https://arxiv.org/html/2608.29004#S5.T5.6.1.3.1)\.
- Piaggesiet al\.\(2024\)S\. Piaggesi, M\. Khosla, A\. Panisson, and A\. AnandDINE: Dimensional Interpretability of Node Embeddings\.IEEE Transactions on Knowledge and Data Engineering36\(12\),pp\. 7986–7997\.External Links:[Document](https://dx.doi.org/10.1109/TKDE.2024.3425460)Cited by:[§2\.1](https://arxiv.org/html/2608.29004#S2.SS1.p3.1),[§5\.2](https://arxiv.org/html/2608.29004#S5.SS2.p1.1),[Table 5](https://arxiv.org/html/2608.29004#S5.T5.6.1.4.1)\.
- Piaggesiet al\.\(2025\)S\. Piaggesi, A\. Panisson, and M\. KhoslaDisentangled and self\-explainable node representation learning\.Transactions on Machine Learning Research\.Note:External Links:ISSN 2835\-8856,[Link](https://openreview.net/forum?id=s51TQ8Eg1e)Cited by:[§2\.2](https://arxiv.org/html/2608.29004#S2.SS2.p1.1)\.
- Rudin \(2019\)C\. RudinStop explaining black box machine learning models for high stakes decisions and use interpretable models instead\.Nature Machine Intelligence1\(5\),pp\. 206–215\(en\)\.Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p2.1)\.
- Salehi and Davulcu \(2020\)A\. Salehi and H\. DavulcuGraph Attention Auto\-Encoders\.In2020 IEEE 32nd International Conference on Tools with Artificial Intelligence \(ICTAI\),Vol\.,Los Alamitos, CA, USA,pp\. 989–996\.External Links:ISSN,[Document](https://dx.doi.org/10.1109/ICTAI50040.2020.00154),[Link](https://doi.ieeecomputersociety.org/10.1109/ICTAI50040.2020.00154)Cited by:[§2\.1](https://arxiv.org/html/2608.29004#S2.SS1.p2.1)\.
- Tanget al\.\(2015\)J\. Tang, M\. Qu, M\. Wang, M\. Zhang, J\. Yan, and Q\. MeiLINE: Large\-scale Information Network Embedding\.InProceedings of the 24th International Conference on World Wide Web,pp\. 1067–1077\.External Links:[Document](https://dx.doi.org/10.1145/2736277.2741093)Cited by:[§2\.1](https://arxiv.org/html/2608.29004#S2.SS1.p1.1)\.
- Valemet al\.\(2022\)L\. P\. Valem, V\. Atsushi Sato Kawai, V\. H\. Pereira\-Ferrero, and D\. Carlos Guimarães PedronetteA novel rank correlation measure for manifold learning on image retrieval and person re\-id\.In2022 IEEE International Conference on Image Processing \(ICIP\),Vol\.,pp\. 1371–1375\.External Links:[Document](https://dx.doi.org/10.1109/ICIP46576.2022.9898060)Cited by:[§3\.2](https://arxiv.org/html/2608.29004#S3.SS2.SSSx2.p1.1),[§4\.3](https://arxiv.org/html/2608.29004#S4.SS3.SSSx2.p1.1.2)\.
- Valemet al\.\(2023\)L\. P\. Valem, D\. C\. G\. Pedronette, and L\. J\. LateckiGraph Convolutional Networks based on manifold learning for semi\-supervised image classification\.Computer Vision and Image Understanding227,pp\. 103618\.External Links:[Document](https://dx.doi.org/10.1016/j.cviu.2022.103618)Cited by:[§4\.2](https://arxiv.org/html/2608.29004#S4.SS2.SSSx2.p1.1)\.
- Valem and Pedronette \(2017\)L\. P\. Valem and D\. C\. G\. PedronetteAn unsupervised distance learning framework for multimedia retrieval\.InProceedings of the 2017 ACM on International Conference on Multimedia Retrieval,ICMR ’17,New York, NY, USA,pp\. 107–111\.External Links:ISBN 978\-1\-4503\-4701\-3,[Link](http://doi.acm.org/10.1145/3078971.3079017),[Document](https://dx.doi.org/10.1145/3078971.3079017)Cited by:[§4\.3](https://arxiv.org/html/2608.29004#S4.SS3.SSSx1.p1.1)\.
- Vaswaniet al\.\(2017\)A\. Vaswani, N\. Shazeer, N\. Parmar, J\. Uszkoreit, L\. Jones, A\. N\. Gomez, Ł\. Kaiser, and I\. PolosukhinAttention is all you need\.InAdvances in Neural Information Processing Systems,Vol\.30,pp\.\.Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p1.1)\.
- Veličkovićet al\.\(2019\)P\. Veličković, W\. Fedus, W\. L\. Hamilton, P\. Liò, Y\. Bengio, and R\. D\. HjelmDeep graph infomax\.InInternational Conference on Learning Representations,External Links:[Link](https://openreview.net/forum?id=rklz9iAcKQ)Cited by:[§2\.1](https://arxiv.org/html/2608.29004#S2.SS1.p2.1)\.
- Wahet al\.\(2011\)C\. Wah, S\. Branson, P\. Welinder, P\. Perona, and S\. BelongieThe caltech\-ucsd birds\-200\-2011 dataset\.Technical reportCalifornia Institute of Technology\.External Links:Cited by:[§4\.1](https://arxiv.org/html/2608.29004#S4.SS1.p1.1)\.
- Wanget al\.\(2021\)J\. Wang, H\. Liu, X\. Wang, and L\. JingInterpretable image recognition by constructing transparent embedding space\.In2021 IEEE/CVF International Conference on Computer Vision \(ICCV\),Vol\.,pp\. 875–884\.External Links:[Document](https://dx.doi.org/10.1109/ICCV48922.2021.00093)Cited by:[§2\.3](https://arxiv.org/html/2608.29004#S2.SS3.p2.1)\.
- Wanget al\.\(2024\)X\. Wang, H\. Chen, S\. Tang, Z\. Wu, and W\. ZhuDisentangled representation learning\.IEEE Transactions on Pattern Analysis and Machine Intelligence46\(12\),pp\. 9677–9696\.External Links:[Document](https://dx.doi.org/10.1109/TPAMI.2024.3420937)Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p3.1)\.
- Wuet al\.\(2019\)F\. Wu, A\. Souza, T\. Zhang, C\. Fifty, T\. Yu, and K\. WeinbergerSimplifying Graph Convolutional Networks\.InProceedings of the 36th International Conference on Machine Learning,Proceedings of Machine Learning Research, Vol\.97,pp\. 6861–6871\.External Links:[Link](https://proceedings.mlr.press/v97/wu19e.html)Cited by:[§4\.3](https://arxiv.org/html/2608.29004#S4.SS3.SSSx3.p1.1)\.
- Yanget al\.\(2023\)Y\. Yang, A\. Panagopoulou, S\. Zhou, D\. Jin, C\. Callison\-Burch, and M\. YatskarLanguage in a bottle: language model guided concept bottlenecks for interpretable image classification\.In2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition \(CVPR\),Vol\.,pp\. 19187–19197\.External Links:[Document](https://dx.doi.org/10.1109/CVPR52729.2023.01839)Cited by:[§2\.3](https://arxiv.org/html/2608.29004#S2.SS3.p1.1)\.
- Zhaoet al\.\(2021\)W\. Zhao, Y\. Rao, Z\. Wang, J\. Lu, and J\. ZhouTowards interpretable deep metric learning with structural matching\.In2021 IEEE/CVF International Conference on Computer Vision \(ICCV\),Vol\.,pp\. 9867–9876\.External Links:[Document](https://dx.doi.org/10.1109/ICCV48922.2021.00974)Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p2.1)\.
- Zhenget al\.\(2018\)L\. Zheng, Y\. Yang, and Q\. TianSIFT meets cnn: a decade survey of instance retrieval\.IEEE Transactions on Pattern Analysis and Machine Intelligence40\(5\),pp\. 1224–1244\.External Links:[Document](https://dx.doi.org/10.1109/TPAMI.2017.2709749)Cited by:[§1](https://arxiv.org/html/2608.29004#S1.p1.1)\.