Semi-supervised Embedding in Attributed Networks with Outliers

1 Introduction

• PLAN embedding must jointly incorporate graph structure, attributes, and partial labels while supporting unseen vertices and accounting for outliers.Earlier work addressed these challenges only in part: inductive solutions were recent, and prior embedding work did not explicitly account for outliers.Source: §1 · p. 1
• SEANO uses vertex attributes and neighborhood information as dual inputs, with label and context predictions as supervised and unsupervised outputs.The shared embedding layers integrate structure, attributes, and labels.Source: §1 · p. 1
• SEANO significantly outperforms state-of-the-art methods in semi-supervised classification under both transductive and inductive settings.Its learned embeddings can also be generated for vertices unseen during training.Source: §1 · p. 1
• SEANO uses a subset of its parameters as outlier scores, reports advantages over baseline outlier detectors, and demonstrates the method in flood mapping.The flood-mapping case study uses satellite images.Source: §1 · pp. 1–2

Network Embedding

• Most attributed-network embedding methods are transductive; Planetoid and GraphSAGE support inductive learning, but each has limitations for semi-supervised embedding.Planetoid is specialized for semi-supervised classification, while GraphSAGE does not directly support semi-supervised learning.Source: §2 · p. 2
• Planetoid embeddings may not generalize to visualization or clustering, whereas GraphSAGE supports unsupervised or fully supervised settings.These limitations distinguish the two cited inductive methods from the semi-supervised setting addressed by SEANO.Source: §2 · p. 2

Outlier Detection

• Network-outlier methods considered topology and vertex attributes, but embedding-based methods did not address attributed networks.Earlier approaches also examined subgraph frequency, community structure, and vertex attributes.Source: §2 · p. 2

3.2 The Proposed Model

• SEANO fuses vertex attributes with neighborhood attributes at the embedding layer, then predicts labels and network context from the shared representation.A PLAN is an undirected graph with vertex attributes and labels, most of which are unknown.Source: §3 · pp. 2–3

Semi-supervised Embedding Learning

• The supervised component learns from labeled vertices, while context prediction on labeled and unlabeled vertices captures topological structure.For labeled vertices, contexts can include both same-label vertices and nearby vertices from random walks; unlabeled vertices use structure contexts.Source: §3 · pp. 3–4

Inductive Embedding Learning

• SEANO can infer embeddings for unseen vertices from their attributes and neighborhoods, using λ_i = 0.5 as its conservative setting for new vertices.The embedding calculation depends on the vertex and neighborhood attributes and λ_i.Source: §3 · pp. 3–4

3.2.2 Loss Functions

• The unsupervised component predicts context from vertex and neighborhood attributes, and negative sampling replaces the full-vertex computation to reduce training cost.Context vertices are generated from random walks and, for labeled vertices, may also be sampled from vertices with the same label.Source: §3 · p. 4

3.2.3 Model Training

• Mini-batch stochastic gradient descent alternates updates to the supervised and unsupervised components, which share layers and jointly update their shared parameters.The learned aggregation weight is constrained to [0, 1] by setting λ_i = σ(ω_i).Source: §3 · p. 5

Redressing Outliers in Embedding Learning

• The learned aggregation weight λ_i controls the balance between vertex and neighborhood attributes and serves as an outlier score, with lower values indicating greater outlier likelihood.When vertex attributes are anomalous relative to their context, SEANO learns to rely more on neighborhood attributes.Source: §3 · pp. 3, 5, Table 3 · p. 5

4.1 Transductive Learning

• In transductive classification, SEANO combines vertex attributes, graph structure, and available labels, while simple concatenation of embeddings and attributes can underperform SVM.The experiments compare methods using different subsets of information and report that systematic fusion is needed for quality embeddings.Source: §4 · pp. 6–7
• SEANO consistently outperforms state-of-the-art methods in transductive vertex classification and shows the least performance drop on noisy datasets.The comparison includes the classification-accuracy results in Table 4; the experiments also evaluate noisy versions of the datasets.Source: §4 · pp. 5–7, Table 4 · p. 7

4.2 Inductive Embedding Learning

• SEANO significantly outperforms other methods in inductive classification, with accuracy gains of 19% on Cora and 8% on Citeseer over the second-best baseline.It performs almost equally well inductively as transductively, with only a slight accuracy decrease when test vertices are unobserved during training.Source: §4 · p. 7, Table 5 · p. 7

4.3 Outlier Detection using SEANO

• SEANO’s aggregation weights yield outlier detection performance above ALAD on Cora* and Pubmed*, but slightly below ALAD on Citeseer*.The evaluation injects 5% outliers and measures precision; Table 6 reports the comparison.Source: §4 · p. 8, Table 6 · p. 8

4.4 Case Study: Flood Mapping

• On Houston-large, SEANO comfortably outperforms the flood-mapping and image-segmentation baselines in water/land classification.Houston-large contains 3,926,150 pixel vertices and 15,692,353 edges, with 100 expert-labeled instances sampled for training.Source: §4 · p. 8, Table 7 · p. 9
• SEANO’s flood-mapping visualization delineates water areas including long, thin rivers, while many examined outliers correspond to reflective metal surfaces.Among the top 80 outliers, a majority were associated with shipping containers, ships, or large cylindrical tanks; these surfaces have higher HH and HV values than neighboring pixels.Source: Figure 2 · p. 8, §4 · p. 9

• SEANO learns robust embeddings that jointly preserve graph proximity, attribute affinity, and label information while accounting for outlier effects.Source: §5 · p. 9
• Experiments on real-world data and a flood-mapping case study demonstrate SEANO’s efficacy over the state of the art.Source: §5 · p. 9
• Future work will adapt SEANO to attributed hyper-networks and heterogeneous information networks.Source: §5 · p. 9