Community Detection in Networks with Node Attributes (1401.7267v1)

Abstract: Community detection algorithms are fundamental tools that allow us to uncover organizational principles in networks. When detecting communities, there are two possible sources of information one can use: the network structure, and the features and attributes of nodes. Even though communities form around nodes that have common edges and common attributes, typically, algorithms have only focused on one of these two data modalities: community detection algorithms traditionally focus only on the network structure, while clustering algorithms mostly consider only node attributes. In this paper, we develop Communities from Edge Structure and Node Attributes (CESNA), an accurate and scalable algorithm for detecting overlapping communities in networks with node attributes. CESNA statistically models the interaction between the network structure and the node attributes, which leads to more accurate community detection as well as improved robustness in the presence of noise in the network structure. CESNA has a linear runtime in the network size and is able to process networks an order of magnitude larger than comparable approaches. Last, CESNA also helps with the interpretation of detected communities by finding relevant node attributes for each community.

• The paper presents CESNA, which combines network edges and node attributes to boost community detection accuracy by 47% compared to traditional methods.
• It employs a block-coordinate ascent method for linear scalability, making it effective for networks with millions of nodes.
• CESNA assigns overlapping hard memberships using logistic regression weights, offering clear, interpretable associations between communities and node attributes.

Community Detection in Networks with Node Attributes

Community detection plays a pivotal role in the analysis of complex networks, allowing us to uncover the inherent organization and modular structures within these systems. Standard methods often detect communities based on either network structure or node attributes independently; however, each of these data modalities can provide complementary information that can enhance the detection process, particularly in noisy or incomplete networks. The paper "Community Detection in Networks with Node Attributes" by Jaewon Yang, Julian McAuley, and Jure Leskovec introduces an advanced method called CESNA (Communities from Edge Structure and Node Attributes), which integrates both these modalities using a statistical approach.

Key Contributions

CESNA distinguishes itself from existing methods in several aspects:

1. Integration of Network Structure and Node Attributes: CESNA simultaneously models the network edges and node attributes. This dual consideration enhances community detection accuracy, making the method robust even when one data source, particularly the network structure, is noisy or incomplete.
2. Scalability: The algorithm can handle networks with millions of nodes efficiently. CESNA leverages a block-coordinate ascent method, making its runtime linear with the size of the network, outperforming comparative state-of-the-art methods by an order of magnitude in terms of scalability.
3. Overlapping Hard-Membership Communities: Unlike soft-membership models that assume nodes belong to communities with certain probabilities, CESNA assigns nodes to overlapping communities with hard memberships. This is critical for accurately modelling networks where nodes commonly belong to multiple communities.
4. Interpretability: By associating logistic regression weights to community-specific attributes, CESNA provides meaningful interpretation of the detected communities. This makes it easier to understand and characterise why a particular community exists based on shared node attributes.

Theoretical Implications

The proposed method builds on the affiliation network model and logistic regression to capture the relationship between community membership, network edges, and node attributes. CESNA’s generative model assumes communities "generate" both the network and the node attributes, allowing for a dynamic interplay between the two data sources.

The derivation of the edge probability function,

$P_{uv} = 1 - \exp(- \sum_c F_{uc}\cdot F_{vc}),$

is rooted in probabilistic modeling, enabling CESNA to account for the contribution of multiple communities toward edge formation. The logistic model further segregates attributes into those which are strong indicators of community structures and those which are not, via the term,

$$Q_{uk} = \frac{1}{1 + \exp( - \sum_{c} W_{kc} \cdot F_{uc})}.$$

This approach ensures that relevant attributes are weighted appropriately, improving the robustness and accuracy of community detection.

Empirical Results

Experiments conducted across multiple datasets—ranging from social networks like Facebook and Twitter to content-sharing platforms such as Flickr—demonstrate CESNA's superior performance over existing community detection algorithms. Specifically, CESNA exhibits significant improvements in detecting communities, achieving a 47% increase in accuracy compared to traditional methods.

Scalability and Robustness

One of CESNA’s major strengths is its computational efficiency. The runtime of CESNA scales linearly with the network size, making it feasible for application in large-scale real-world networks that contain millions of nodes and edges. Furthermore, CESNA gracefully handles incomplete network structures—its performance degrades minimally as more edges are removed, leveraging the available node attributes to maintain detection quality.

Practical Implications and Future Directions

CESNA's ability to incorporate and make use of node attributes has practical implications for various domains:

1. Social Networks: By understanding the attributes associated with communities (e.g., educational background, interests), social media platforms can make better recommendations for friend suggestions, group memberships, and targeted advertisements.
2. Biological Networks: In protein-protein interaction networks, CESNA could identify functional modules by incorporating protein attributes, potentially unveiling new biological insights that are not apparent from the interaction data alone.
3. E-commerce: Platforms can identify clusters of users with similar purchasing patterns and preferences more accurately, enhancing personalized marketing and product recommendations.

Future developments could extend CESNA's applicability by integrating more complex attribute types (numerical, ordinal) and considering temporal dynamics in networks. Introducing mechanisms to cluster attributes alongside nodes can further enhance the interpretability of detected communities. Additionally, combining CESNA with data from information diffusion processes or other metadata might yield even richer insights into community structures.

In summary, CESNA stands out not only in its methodological advancements but also in its practical applicability to large-scale network analysis, paving the way for more nuanced and interpretable community detection in diverse domains.