Source-linked AI summary
Network Embedding: on Compression and Learning
Esra Akbas, Mehmet Aktas
TL;DR
Large real-world graphs can hinder direct application of existing network embedding methods. NECL merges vertices with similar neighborhoods into super-nodes and embeds the compressed graph; experiments report improved efficiency without decreased classification effectiveness.
Problem
Huge real-world graphs may obstruct direct application of existing network embedding methods, motivating compression that retains global structure and local vertex relationships.
Source: §1 · p. 1Method
NECL merges vertices with similar neighborhoods into super-nodes, embeds the compressed graph with methods such as DeepWalk and Node2vec, and uses super-node representations for the original vertices.
Source: §1 · pp. 2–3Results
NECL embeddings show better efficiency with less walking and training time and similar or better accuracy on multi-class and multi-label classification tasks across several real-world networks.
Source: §1 · p. 3, §5 · p. 11Takeaways & Limitations
Experiments support using compressed graphs with DeepWalk and Node2vec on real-world classification tasks without decreasing effectiveness.
Source: §1 · pp. 2–3, §5 · p. 11The optimization assumes conditional independence of neighborhood vertices given the source representation, ignoring vertex ordering in the random walk.
Source: §2.1 · p. 3
Abstract
from arXiv · showhide
Recently, network embedding that encodes structural information of graphs into a vector space has become popular for network analysis. Although recent methods show promising performance for various applications, the huge sizes of graphs may hinder a direct application of existing network embedding method to them. This paper presents NECL, a novel efficient Network Embedding method with two goals. 1) Is there an ideal Compression of a network? 2) Will the compression of a network significantly boost the representation Learning of the network? For the first problem, we propose a neighborhood similarity based graph compression method that compresses the input graph to get a smaller graph without losing any/much information about the global structure of the graph and the local proximity of the vertices in the graph. For the second problem, we use the compressed graph for network embedding instead of the original large graph to bring down the embedding cost. NECL is a general meta-strategy to improve the efficiency of all of the state-of-the-art graph embedding algorithms based on random walks, including DeepWalk and Node2vec, without losing their effectiveness. Extensive experiments on large real-world networks validate the efficiency of NECL method that yields an average improvement of 23 - 57% embedding time, including walking and learning time without decreasing classification accuracy as evaluated on single and multi-label classification tasks on real-world graphs such as DBLP, BlogCatalog, Cora and Wiki.
1. INTRODUCTION
Large real-world graphs can hinder direct use of network embedding methods. NECL compresses graphs by merging vertices with similar neighborhoods, then embeds the compressed graph to reduce cost while aiming to preserve structural information and effectiveness.
1. INTRODUCTION
- Network embedding maps graph data into a low-dimensional vector space to capture vertex characteristics or roles based on connections.Applications include node classification and link prediction.Source: §1 · p. 1
- Large graph sizes can obstruct direct application of existing embedding methods, while graph compression aims to retain global structure and local vertex relationships.The paper frames compression and improved representation learning as two questions.Source: §1 · pp. 1–2
- Vertices with similar neighborhoods can produce similar random-walk paths and representations, so processing them separately can repeat walking and learning.NECL instead learns representations for merged super-nodes.Source: §1 · pp. 1–2
- NECL merges vertices with similar neighborhood sets into super-nodes, aiming to preserve global graph structure and local proximity.The compressed graph is then used for embedding, with super-node representations assigned to the original vertices they represent.Source: §1 · pp. 2–3
- NECL(DW) and NECL(N2V) show better efficiency with less walking and training time, and similar or better accuracy on multi-class and multi-label classification tasks.The comparison covers several real-world networks.Source: §1 · p. 3
2. NETWORK EMBEDDING USING SIMILARITY BASED COMPRESSION
NECL compresses graphs by merging vertices with similar neighborhoods, then applies random-walk embedding to the smaller graph. Its compression is designed to retain graph structure and proximity while reducing redundant walking and learning.
2.1 Preliminaries
- Random-walk embedding learns vertex representations from co-occurrence within sampled paths, capturing higher-order proximity through methods such as DeepWalk’s Skip-gram training.The framework represents vertices in a low-dimensional space and optimizes the likelihood of sampled neighborhoods.Source: §2.1 · p. 3
2.2.1 Motivation
- Vertices with identical neighbors have matching transition probabilities and walks, so one learned super-node representation can represent both while preserving first- and second-order proximity.The example assigns the super-edge weight according to the number of original edges it represents, preserving transition probabilities after merging.Source: §2.2.1 · p. 4
2.2 Neighborhood Similarity based Graph Compression
- NECL merges vertices with similar neighborhoods into super-nodes, producing a smaller graph intended to preserve local and global structure.The resulting compressed graph also provides the basis for embedding instead of the original graph.Source: §2.2.2 · p. 4
2.2.2 Graph Compressing
- Neighborhood similarity is based on common neighbors, normalized by vertex degrees, and vertices above a threshold are merged.The stated similarity ranges from 0 for no shared neighbors to 1 for identical neighbor sets.Source: §2.2.2 · p. 5
- The algorithm checks only two-step neighbor pairs because nonzero neighborhood similarity requires shared neighbors; a lower threshold merges more vertices but may reduce accuracy.The threshold therefore trades compression efficiency against embedding effectiveness.Source: §2.2.2 · p. 5
9 end
NECL embeds the weighted compressed graph and maps each super-node representation back to its original vertices.
9 end
- During compression, edges incident to a merged super-node accumulate the weights of the original edges.The algorithm adds an edge when needed and updates its weight with the corresponding original edge weight.Source: §9 · p. 5
- If vertices are merged successively, the algorithm checks whether a vertex already belongs to a super-node before performing the next merge.This allows a super-node to contain more than two original vertices.Source: §9 · p. 5
2.2.3 Network embedding on compressed graph
- NECL applies a random-walk embedding algorithm to the weighted compressed graph, then assigns each original vertex its super-node’s representation through the mapping.Weighted random walks account for the compressed graph’s edge weights.Source: §2.2.3 · p. 5
3. EXPERIMENTS
The experiments evaluate NECL’s efficiency and effectiveness on real-world network classification tasks.
3. EXPERIMENTS
- The experiments assess efficiency and effectiveness on multi-class and multi-label classification tasks in real-world networks.The passage says the study reports dataset and embedding-method overviews, performance, and efficiency improvements.Source: §3 · p. 5
- The experimental section presents an overview of the datasets and embedding methods used for evaluation.Source: §3 · p. 5
- The supplied experimental passage states that algorithm performance and efficiency improvements are discussed but gives no numerical results.Source: §3 · p. 5
7 end
NECL compresses graphs using neighborhood similarity, then embeds the smaller graphs. Across single-label and multi-label classification, it achieves similar accuracy in less time, while compression thresholds and dataset structure affect the results.
3.1 Datasets
- The experiments use Cora and Wiki for single-label classification and DBLP and BlogCatalog for multi-label classification.Cora uses citation links and topic labels; BlogCatalog labels represent bloggers’ interests and published categories.Source: §3.1 · p. 6
3.2 Baseline methods
- DeepWalk and Node2vec serve as baselines, and the experiments compare each baseline with its NECL-compressed counterpart.Both baselines use random walks; Node2vec uses biased walks, while DeepWalk uses fixed-length walks.Source: §3.2 · p. 6
3.3 Classification
- Evaluation varies labeled-vertex ratios and λ, reports macro and micro F1 plus walking and embedding times, and averages results over 10 repetitions.Cora, Wiki, and DBLP use training ratios from 1% to 50%; BlogCatalog uses 10% to 80%.Source: §3.3 · pp. 6–7
3.3.1 Single-label Classification
- For Cora and Wiki, λ = 0.5 yields 33.4% and 37.65% efficiency improvements on Cora, and 46% and 50.7% on Wiki, versus DeepWalk and Node2vec, respectively.F1 scores show no significant change; λ < 0.5 makes the graphs too small and accuracy decreases dramatically.Source: §3.3.1 · p. 7
3.3.2 Multi-label Classification
- For DBLP, NECL reduces embedding time by 57.46% versus DeepWalk and 56.75% versus Node2vec, with macro and micro F1 scores very similar to the baselines.For λ ≥ 0.5, F1 scores are similar or slightly higher across training ratios; smaller λ values sharply reduce scores.Source: §3.3.2 · p. 7
- On BlogCatalog, NECL gains 28.2% and 23.4% in total running time versus DeepWalk and Node2vec, respectively, alongside slight F1 decreases.The reported macro and micro F1 decreases are 2.9% and 5.6% for DeepWalk, and 4.1% and 6.6% for Node2vec.Source: §3.3.2 · p. 7
3.3 Classification
- Across single-label and multi-label classification, NECL achieves similar accuracy in consistently less time using relatively smaller compressed graphs.The reported pattern holds across the evaluated tasks and datasets.Source: §3.3.2 · p. 7
3.4 Graph Compression
- Graph sizes decline as the similarity threshold λ changes; BlogCatalog’s size decreases more slowly until λ = 0.7 than those of Cora, Wiki, and DBLP.The authors suggest large neighbor sets in BlogCatalog may make higher similarity harder to attain.Source: §3.4 · p. 7
4. RELATED WORK
Earlier graph-embedding work includes dimensionality-reduction approaches and scalable methods using matrix factorization or neural networks, including random-walk methods. NECL adapts graph compression to random-walk embedding, unlike hierarchical coarsening approaches.
4. RELATED WORK
- Dimensionality-reduction embeddings include PCA and locally linear embeddings, while later scalable approaches use matrix factorization [25], neural networks [29] [32], and random walks [6] [11] [15] [17].Earlier methods could have at least quadratic time complexity in the number of vertices, limiting application to large-scale networks [30] [33].Source: Compressed · p. 10
Compressed
- HARP hierarchically coarsens related vertices and uses embeddings of coarsened graphs to initialize learning at the next level [10], whereas NECL uses non-hierarchical coarsening to capture local structure and improve random-walk methods’ efficiency.The supplied passage describes HARP’s coarsening as capturing global structure and providing a good initialization.Source: Compressed · p. 10
- Graph compression groups similar vertices into super-nodes to preserve selected graph properties, with approximations used to make graph problems simpler or provide initialization.Compressed or summary graphs are proposed as a way to retain key structures and patterns while making large graphs more amenable to existing methods.Source: Compressed · p. 10
- NECL extends graph compression to network representation learning and demonstrates the paradigm with DeepWalk and Node2vec.The supplied table captions specify single-label comparisons on Cora and Wiki and multi-label comparisons on DBLP and BlogCatalog, but provide no result values.Source: Table 2 · p. 8, Table 3 · p. 8, Compressed · p. 10
5. CONCLUSIONS
NECL combines related vertices into super-nodes that preserve neighborhood information, then uses the compressed graph to learn representations for original vertices. Experiments report efficiency gains without reduced effectiveness; proposed extensions include other learning methods and similarity measures.
5. CONCLUSIONS
- NECL combines related vertices into super-nodes that preserve neighborhood information, then uses the compressed graph to learn representations for vertices in the original graph.The method is combined with DeepWalk and Node2vec.Source: §5 · pp. 10–11
- Experiments on real-world graphs report improved efficiency without decreased effectiveness on multi-class and multi-label classification tasks.The conclusion names DeepWalk and Node2vec embeddings as more efficient, with less walking and training time and similar or better accuracy than the original methods.Source: §5 · p. 11
- Proposed future extensions include applying NECL to matrix-factorization and deep-neural-network methods and testing different compression similarity measures.Source: §5 · p. 11