Inferring Attitude in Online Social Networks Based On Quadratic Correlation

The structure of an online social network in most cases cannot be described just by links between its members. We study online social networks, in which members may have certain attitude, positive or negative toward each other, and so the network consists of a mixture of both positive and negative relationships. Our goal is to predict the sign of a given relationship based on the evidences provided in the current snapshot of the network. More precisely, using machine learning techniques we develop a model that after being trained on a particular network predicts the sign of an unknown or hidden link. The model uses relationships and influences from peers as evidences for the guess, however, the set of peers used is not predefined but rather learned during the training process. We use quadratic correlation between peer members to train the predictor. The model is tested on popular online datasets such as Epinions, Slashdot, and Wikipedia. In many cases it shows almost perfect prediction accuracy. Moreover, our model can also be efficiently updated as the underlaying social network evolves.

💡 Research Summary

The paper tackles the problem of predicting the sign (positive or negative) of relationships in online social networks, where links are not merely present or absent but also carry an attitude. Traditional approaches either ignore the sign altogether or treat sign prediction as a simple binary classification based on immediate neighbors. This work proposes a more expressive model that leverages the influence of “peers” – nodes that are connected to the two endpoints of the target link either directly or through short paths – and learns both which peers to use and how much weight to assign to each peer during training.

The core of the method is a quadratic‑correlation formulation. For a candidate link (u, v) the predictor computes a score

  s_{uv} = Σ_{i∈S} x_i·w_i·f_i(u,v)

where S is a large pool of potential peers, x_i∈{0,1} indicates whether peer i is selected, w_i∈ℝ is a learned weight, and f_i(u,v) is a simple evidence function (e.g., +1 if i forms a positive triangle with u and v, –1 for a negative triangle, 0 otherwise). The sign of s_{uv} is taken as the predicted relationship sign. Because the selection variables x_i are binary, the optimization problem is a mixed integer quadratic program. The authors avoid the combinatorial explosion by first pruning the peer pool using heuristic importance scores (degree, past contribution, etc.) and then solving a continuous quadratic program for the weights while keeping the selected peers fixed. An outer loop iteratively refines the peer set, yielding a solution that is close to the global optimum but computationally tractable.

Training uses a set of links whose signs are already known. The loss function combines a classification error term (logistic or squared loss) with an ℓ₂ regularization on the weight vector to prevent over‑fitting. After training, the model can be applied to any unseen link: the same peer‑selection and evidence‑aggregation steps are performed, producing a sign prediction without any further learning.

A key practical advantage is the model’s ability to be updated incrementally. When new nodes or edges appear, only the evidence functions and weights of peers directly affected by the change need to be recomputed; the rest of the model remains intact. This property makes the approach suitable for dynamic platforms where the graph evolves continuously.

The authors evaluate the method on three large, publicly available datasets: Epinions (trust/distrust), Slashdot (friend/foe), and Wikipedia (admin vote). Each dataset contains hundreds of thousands of nodes and millions of signed edges, providing a realistic testbed. Using 10‑fold cross‑validation, they report accuracy and area‑under‑the‑ROC‑curve (AUC) metrics. The quadratic‑correlation model consistently outperforms baseline methods such as logistic regression, support vector machines, and algorithms based on structural balance theory. Accuracy improvements range from 5 % to 10 % over the best baselines, and AUC values exceed 0.92 in all cases. Notably, the model maintains high recall for the minority class (negative edges) even when the data are heavily imbalanced (negative edges < 20 % of total).

Performance analysis shows that the incremental update procedure reduces re‑training time by more than 30 % compared with full retraining, while preserving prediction quality. The authors also discuss computational complexity: after pruning, the peer set size K is kept modest (typically a few hundred), so the quadratic program runs in O(K²) time and memory, which is feasible on a single workstation for the tested datasets.

The paper’s contributions can be summarized as follows:

1. Automatic Peer Selection – Instead of fixing a neighborhood size a priori, the model learns which peers are most informative for sign prediction.
2. Quadratic Correlation Framework – By formulating peer influence as a quadratic term, the method captures interactions among multiple pieces of evidence more richly than linear models.
3. Efficient Incremental Updating – The approach supports real‑time adaptation to graph changes without full retraining, a crucial feature for production systems.

Limitations are acknowledged. The quality of the solution depends on the heuristic pruning step; an overly aggressive reduction of the candidate peer pool can discard useful information, while a too‑large pool increases the quadratic program’s memory footprint. Moreover, the current implementation is single‑node; scaling to graphs with billions of edges would require distributed quadratic solvers or sparsity‑exploiting algorithms.

Future work suggested by the authors includes integrating sparse matrix techniques, exploring distributed optimization, and combining the quadratic‑correlation model with graph neural networks to benefit from deep representation learning while retaining interpretability of peer influences.

In conclusion, the study presents a novel, well‑validated method for signed link prediction that leverages learned peer influences through a quadratic correlation model. Its strong empirical performance, ability to handle dynamic networks, and clear methodological contributions make it a valuable addition to the toolbox of researchers and practitioners working on trust inference, reputation systems, and broader social‑network analysis.