Visual and Network Embeddings

• Visual and network embeddings are techniques for transforming complex visual and graph data into compact, low-dimensional vectors that preserve structural properties.
• They employ deep neural networks and random walk strategies to enable efficient clustering, similarity search, and classification.
• Recent advances integrate multi-modal and relational views, enhancing interpretability and performance in diverse machine learning workflows.

Visual and network embeddings comprise a diverse suite of methodologies for representing complex visual and graph-structured data as points in continuous, typically low-dimensional vector spaces. These embeddings serve as the foundation for a variety of machine learning and data analysis workflows, enabling tasks such as clustering, classification, similarity search, and, crucially, scalable visualization. Approaches address both single-modality data (e.g., images, individual networks) and multi-modal or multi-view settings (e.g., networks with heterogeneous edge types or coupled visual and kinematic observations), emphasizing both the preservation of structural information and the interpretability of learned representations.

1. Canonical Approaches to Visual Embedding

Image embedding architectures generally leverage deep convolutional neural networks to map high-dimensional image input $I$ to compact feature vectors $\beta(I)\in\mathbb{R}^C$. For similarity-based applications, the cosine similarity function

$$S(a, b) = \frac{\beta(a)\cdot\beta(b)}{\|\beta(a)\|\|\beta(b)\|}$$

is widely adopted to quantify instance-level proximity in the embedding space. The visualization of feature attributions underlying these similarities is addressed by spatially decomposing $S(a, b)$ into per-pixel or per-region contribution maps. Specifically, for average pooling, contribution at grid $(i, j)$ is

$$C^a(i, j; a, b) = \frac{\alpha(a)_{i, j}\cdot\beta(b)}{K^2\,\|\beta(a)\|\|\beta(b)\|},$$

where $\alpha(a)_{i, j}$ are local activations preceding pooling. Channel-wise aggregation and upsampling yield interpretable heatmaps, facilitating domain-inspection of discriminative features and attention (Stylianou et al., 2019).

Deep generative frameworks introduce an explicit bidirectional mapping between latent embedding vectors $z_i\in\mathbb{R}^d$ and high-dimensional visual instances $x_i$. Non-parametric architectures, such as the Deep Generative Neural Embedding (GNE), utilize a direct embedding lookup $z_i=E[i]$, trained jointly with a generative decoder $g_\theta$ to reconstruct the observation, optimized under

$$\mathcal{L}(E, \theta) = \sum_{i=1}^N \|g_\theta(E[i]) - x_i\|_2^2 + \lambda\sum_{i=1}^N \|E[i]\|_2^2,$$

enabling both flexible embedding editing and human-in-the-loop visualization. Unlike variational autoencoders, these models do not enforce a global latent prior, permitting arbitrary manipulation of individual data-point embeddings without entangling the representation manifold (Yerebakan et al., 2023).

2. Foundational Network Embedding Methods

Network embedding is defined by the mapping of graph nodes to $\mathbb{R}^d$, preserving selected topological properties. Random walk-based approaches, notably DeepWalk, node2vec, and struc2vec, dominate the field.

• DeepWalk: Samples uniform random walks, casting nodes as words and walks as sentences to optimize a Skip-Gram objective,

$$\max_\theta \prod_{(u, c)\in D} p(c|u; \theta),\quad p(c|u) = \frac{\exp(\mathbf{v}_c^\top \mathbf{v}_u)}{\sum_{w\in V}\exp(\mathbf{v}_w^\top \mathbf{v}_u)},$$

where $D$ contains observed center-context pairs (Shmueli, 2019).

• node2vec: Generalizes DeepWalk by introducing $(p, q)$ parameters that interpolate between breadth- and depth-first search strategies in random walk generation, controlling neighborhood exploration.
• LINE: Distinguishes between first-order (direct adjacency) and second-order (neighborhood similarity) proximity, optimizing logistic loss or softmax objectives over sampled edges.
• struc2vec: Embeds structural equivalence by constructing a multi-layer context graph encoding degree-sequence similarity, with biased random walks sampling structurally similar contexts rather than purely local neighborhoods.
• metapath2vec: Addresses heterogeneous networks by guiding walks via user-specified metapaths, ensuring context windows are type-aware.

All these methods rely on negative sampling and stochastic gradient updates, naturally supporting incremental embedding as graphs evolve. Dimensionality reduction techniques (PCA, t-SNE, UMAP) are subsequently used for visualization, with dense community or role structures observable directly in the projections (Shmueli, 2019, Li et al., 2018).

3. Embedding and Visualization of Collections of Graphs

A key challenge arises when embedding not just nodes but entire graphs—as encountered in connectomics, molecular datasets, or evolving networks. Unsupervised neural architectures are employed to learn graph-level embeddings:

$$x = \mathrm{vec}(A^r) \in \mathbb{R}^N,\qquad z = f_\theta(\tilde{x}) = s(W\,\tilde{x} + b)\in\mathbb{R}^d,$$

where $A^r$ encodes $r$-step adjacency structure (typically $r=3$), $\tilde{x}$ is a corrupted version of $x$, and $z$ is the low-dimensional graph embedding. The loss is standard denoising reconstruction:

$$\mathcal{L}_{\text{DAE}}(\theta, \theta') = \frac{1}{m}\sum_{i=1}^m \|x^{(i)} - g_{\theta'}(f_\theta(\tilde{x}^{(i)}))\|_2^2.$$

Embedding vectors $z_i$ for each $G_i$ can be used directly for clustering (via spectral methods or $k$-means) or for supervised classification with SVMs. This yields significant runtime improvements and—empirically—higher accuracy compared to graph kernel or feature-based approaches (Gutiérrez-Gómez et al., 2019).

4. Multi-View, Multi-Modal, and Relational Embedding

Extensions to multi-relational and multi-modal data are non-trivial. In multi-view networks, such as those with several edge types, generative adversarial frameworks (e.g., MEGAN) align embeddings across views by optimizing over real and synthetic node-pair connectivity, captured by a minimax game between a generator $G$ (predicting multi-view edge distributions from embeddings) and a discriminator $D$ (distinguishing real from fake pairs):

$$\min_{G} \max_{D} V(G,D) = \sum_{i=1}^n \left[\mathbb{E}_{(v_i, v_j)\sim p_\text{data}}\log D(v_i, v_j) + \mathbb{E}_{(v_i, v_c)\sim p_g}\log(1 - D(v_i, v_c))\right].$$

Negative sampling strategies are tuned to ensure diversity and efficiency. MEGAN embeddings outperform single-view and alternative multi-view baselines on node classification, link prediction, and visualization tasks, with t-SNE projections exhibiting tighter and more separable clusters (Sun et al., 2019).

For multi-modal time series (e.g., video and kinematics in surgical robotics), relational graph neural architectures (MRG-Net) employ unimodal temporal encoders (ResNet-TCN for visual; LSTM-TCN fusion for kinematics), constructing a directed, multi-relation graph where nodes correspond to visual and kinematic embeddings. Message propagation occurs via stacked relational GCN layers, leveraging cross-modal and intra-modal relation types. Outputs are concatenated and passed to a softmax classifier, with performance gains attributed to explicit modeling of relational structure between data modalities (Long et al., 2020).

5. Visual Analytics for Embedding Assessment and Interpretation

Interpretability and algorithmic transparency remain critical. Visual analytics systems (EmbeddingVis) provide multi-level comparative inspection of embedding outputs by integrating:

1. Cluster-level views, juxtaposing 2D t-SNE projections and explicit node-metric brushing (degree, centrality, within-module degree, etc.).
2. Instance-level views, comparing ranking overlap between original graph metrics and embedding-space similarities for focal nodes, supported by NDCG evaluation.
3. Structural-level views, aggregating ego-network signatures and comparing embedding-space distance vectors for nodes in similar roles.

These coordinated interfaces enable both global assessment—e.g., whether embeddings preserve community structure or role similarity—and local analysis of neighbor retention. Through comparative studies, EmbeddingVis demonstrates that random-walk-based embeddings such as DeepWalk/node2vec preferentially preserve community-centric metrics, whereas structurally biased embeddings like struc2vec emphasize centralities and degree patterns. The system also exposes the hyperparameter sensitivity of embedding behavior (e.g., node2vec's $p$, $q$), helping practitioners optimize representations for downstream applications (Li et al., 2018).

6. Practical Considerations, Benchmarks, and Impact

Visual and network embeddings underpin advances in graph mining, retrieval, and visualization. Empirical benchmarks demonstrate that unsupervised neural network approaches for graph-level embedding dramatically outperform classical metrics and kernel methods in clustering NMI (up to $0.986$) and supervised accuracy (up to $87.2\% \pm 7.6\%$), often with significant computational savings (Gutiérrez-Gómez et al., 2019).

Multi-view and relational extensions, such as MEGAN and MRG-Net, further close the gap in heterogeneous and multi-modal domains, producing embeddings that generalize across views/modalities and are interpretable under visualization. Visualization techniques, particularly t-SNE and UMAP, remain key for both qualitative insight and diagnostic evaluation, but the integration of structural and metric correlations is essential for rigorous analysis.

A plausible implication is that explainable and interactive embedding frameworks, as promoted by visual analytics systems, will play an increasingly central role as network and visual data grow in both scale and complexity.

7. Future Directions and Open Challenges

Current research highlights persistent challenges in the interpretability of embeddings, the alignment across modalities and views, and the need to bridge user-defined structural metrics with learned representations. Methods such as NEExT aim to balance interpretability with efficiency by supporting user-defined feature construction, and provide fast embedding computation for large collections of graphs within an interpretable framework (Dehghan et al., 20 Mar 2025).

Progress in scalable, editable, and generative visual embeddings (as in GNE), along with improved relational modeling for data fusion (e.g., MRG-Net), suggests that future work will converge on principled, modular toolkits capable of both learning and explaining the representations underlying complex, heterogeneous datasets. Visualization and interactive analytics will likely remain indispensable for diagnosing embedding quality and supporting user-driven modeling.