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Unsupervised representation learning techniques are commonly employed to analyze high-dimensional or unstructured data. In some cases, users may have prior knowledge of the topology of the data, such as a known cluster structure or the fact that it follows a tree- or graph-based structure. However, generic methods for ensuring this inherent structure is evident in low-dimensional representations are lacking and it is unknown how imposing topological constraints affects downstream learning tasks. To fill this gap, we propose topological regularization - a generic approach based on algebraic topology to incorporate topological prior knowledge into low-dimensional representations. We introduce a class of topological loss functions and demonstrate that optimizing an embedding loss together with one of these loss functions as a regularizer results in embeddings that consider not only local proximities but also the desired topological structure. We provide a self-contained introduction to essential concepts in algebraic topology and offer intuitive guidance for designing topological loss functions suitable for a variety of data shapes, such as clusters, cycles, or bifurcations. We empirically assess the efficiency, robustness, and versatility of the proposed method when combined with linear and non-linear dimensionality reduction techniques, as well as graph embedding methods.

Recommender systems often face congestion, characterized by an uneven distribution in the frequency of item recommendations. The presence of congestion in recommendations is especially problematic in domains where users or items have limited availability. For example, recommending one vacancy to many job seekers results in frustration of job seekers and job market inefficiency. We propose a novel in-processing approach to job recommendation called ReCon, accounting for the congestion problem. Our approach is to use an optimal transport component to ensure a more equal spread of vacancies over job seekers, combined with a job recommendation model in a multi-objective optimization problem. Moreover, we propose a scalable solution so that ReCon is applicable to large-scale datasets. We evaluated our approach on several real-world job market datasets. The evaluation results show that ReCon has good performance on both congestion-related (e.g., Congestion, Coverage, and Gini Index) and desirability (e.g., NDCG, Recall, and Hit Rate) measures. In most cases, ReCon is Pareto optimal for some selections of hyper-parameters in comparison to the baselines.

Dynamic Link Prediction (DLP) addresses the prediction of future links in evolving networks. However, accurately portraying the performance of DLP algorithms poses challenges that might impede progress in the field. Importantly, common evaluation pipelines usually calculate ranking or binary classification metrics, where the scores of observed interactions (positives) are compared with those of randomly generated ones (negatives). However, a single metric is not sufficient to fully capture the differences between DLP algorithms, and is prone to overly optimistic performance evaluation. Instead, an in-depth evaluation should reflect performance variations across different nodes, edges, and time segments. In this work, we contribute tools to perform such a comprehensive evaluation. (1) We propose Birth–Death diagrams, a simple but powerful visualization technique that illustrates the effect of time-based train–test splitting on the difficulty of DLP on a given dataset. (2) We describe an exhaustive taxonomy of negative sampling methods that can be used at evaluation time. (3) We carry out an empirical study of the effect of the different negative sampling strategies. Our comparison between heuristics and state-of-the-art memory-based methods on various real-world datasets confirms a strong effect of using different negative sampling strategies on the test area under the curve (AUC). Moreover, we conduct a visual exploration of the prediction, with additional insights on which different types of errors are prominent over time.