Graph-structured data is ubiquitous in today's connected world, driving extensive research in graph analysis. Graph Neural Networks (GNNs) have shown great success in this field, leading to growing interest in developing fair GNNs for critical applications. However, most existing fair GNNs focus on statistical fairness notions, which may be insufficient when dealing with statistical anomalies. Hence, motivated by the causal theory, there has been growing attention to mitigating root causes of unfairness utilizing graph counterfactuals. Unfortunately, existing methods for generating graph counterfactuals invariably require the sensitive attribute. Nevertheless, in many real-world applications, it is usually infeasible to obtain sensitive attributes due to privacy or legal issues, which challenge existing methods. In this paper, we propose a framework named Fairwos (improving Fairness withQut sensitive attributes). In particular, we first propose a mechanism to generate pseudo-sensitive attributes to remedy the problem of missing sensitive attributes, and then design a strategy for finding graph counterfactuals from the real dataset. To train fair GNNs, we propose a method to ensure that the embeddings from the original data are consistent with those from the graph counterfactuals, and dynamically adjust the weight of each pseudo-sensitive attribute to balance its contribution to fairness and utility. Furthermore, we theoretically demonstrate that minimizing the relation between these pseudo-sensitive attributes and the prediction can enable the fairness of GNNs. Experimental results on six real-world datasets show that our approach outperforms state-of-the-art methods in balancing utility and fairness.

Spatial co-location pattern mining is an important task in spatial data mining. However, traditional mining frameworks often produce too many prevalent patterns of which only a small proportion may be truly interesting to end users. To satisfy user preferences, this work proposes an interactive probabilistic post-mining method to discover user-preferred co-location patterns from the early-round of mined results by iteratively involving user's feedback and probabilistically refining preferred patterns. We first introduce a framework of interactively post-mining preferred co-location patterns, which enables a user to effectively discover the co-location patterns tailored to his/her specific preference. A probabilistic model is further introduced to measure the user feedback-based subjective preferences on resultant co-location patterns. This measure is used to not only select sample co-location patterns in the iterative user feedback process but also rank the results. The experimental results on real and synthetic data sets demonstrate the effectiveness of our approach.

Spatial co-location pattern mining is an interesting and important task in spatial data mining which discovers the subsets of spatial features frequently observed together in nearby geographic space. However, the traditional framework of mining prevalent co-location patterns produces numerous redundant co-location patterns, which makes it hard for users to understand or apply. In this paper we study the problem of reducing redundancy in a collection of prevalent co-location patterns. We first introduce the concept of semantic distance between two co-location patterns, and then define redundant co-locations by introducing the concept of δ-covered, where δ (0≤δ≤1) is a coverage measure. We develop two algorithms RRclosed and RRnull to perform the redundancy reduction for prevalent co-location patterns. Our performance studies on the synthetic and real-world data sets demonstrate that our method effectively reduces the size of the original collection of closed co-location patterns by about 50%. Furthermore, the RRnull method runs much faster than the related closed co-location pattern mining algorithm.

Spatial co-location pattern mining is an interesting and important task in spatial data mining which discovers the subsets of spatial features frequently observed together in nearby geographic space. However, the traditional framework of mining prevalent colocation patterns produces numerous redundant co-location patterns, which makes it hard for users to understand or apply. To address this issue, in this paper, we study the problem of reducing redundancy in a collection of prevalent co-location patterns by utilizing the spatial distribution information of co-location instances. We first introduce the concept of semantic distance between a co-location pattern and its super-patterns, and then define redundant co-locations by introducing the concept of d-covered, where δ (0 ≤ δ ≤ 1) is a coverage measure. We develop two algorithms RRclosed and RRnull to perform the redundancy reduction for prevalent co-location patterns. The former adopts the post-mining framework that is commonly used by existing redundancy reduction techniques, while the latter employs the mine-and-reduce framework that pushes redundancy reduction into the co-location mining process. Our performance studies on the synthetic and real-world data sets demonstrate that our method effectively reduces the size of the original collection of closed co-location patterns by about 50 percent. Furthermore, the RRnull method runs much faster than the related closed co-location pattern mining algorithm.