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. 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 δ-covered, where $\delta \,(0\leq \delta \leq 1)$ 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.

Co-location pattern mining plays an important role in spatial data mining. With the rapid growth of spatial datasets, the usefulness of co-location patterns is strongly limited by the huge amount of discovered patterns. Although several methods have been proposed to reduce the number of discovered patterns, these statistical algorithms are unable to guarantee that the extracted co-location patterns are user preferred. Therefore, it is crucial to help the decision maker discover his/her preferred co-location patterns via efficient interactive procedures. This article proposes a new interactive approach that enables the user to discover his/her preferred co-location patterns. First, we present a novel and flexible interactive framework to assist the user in discovering his/her preferred co-location patterns. Second, we propose using ontologies to measure the similarity of two co-location patterns. Furthermore, we design a pruning scheme by introducing a pattern filtering model for expressing the user’s preference, to reduce the number of the final output. By applying our proposed approach over voluminous sets of co-location patterns, we show that the number of filtered co-location patterns is reduced to several dozen or less and, on average, 80% of the selected co-location patterns are user preferred.

Co-location pattern mining refers to discovering neighboring relationships of spatial features distributed in geographic space. With the rapid growth of spatial datasets, the usefulness of co-location patterns is strongly limited by the large number of discovered patterns containing multiple redundancies. To address this problem, in this article, we propose a novel approach for discovering the super participation index-closed (SPI-closed) co-location patterns which are a newly proposed lossless condensed representation of co-location patterns by considering distributions of the spatial instances. In the proposed approach, first, a linear-time method is designed to generate complete and correct neighboring cliques using extended neighboring relationships. Based on these cliques, a hash structure is then constructed to store the distributions of the co-location patterns in a condensed way. Finally, using this hash structure, the SPI-closed co-location patterns (SCPs) are efficiently discovered even if the prevalence threshold is changed, while similar approaches have to restart their mining processes. To confirm the efficiency of the proposed method, we compared its performance with similar approaches in the literature on multiple real and synthetic spatial datasets. The experiments confirm that our new approach is more efficient, effective, and flexible than similar approaches.

The coordination of multi-agent is one of the critical problems in Multi-agent Reinforcement Learning (MARL). The traditional methods of MARL focus on finding a stochastically acceptable solution called Nash Equilibrium (NE) for all agents from the Markov Game in which multiple equilibria exist. However, learning a fair equilibrium is crucial for the sustainability and stability of collaboration in the long-term coordination game, especially when the leadership competition exists. In this article, we propose the bi-level reinforcement learning method N-Bi-AC, whose solution is a Pareto improvement for traditional NE, to choose a fair Equilibrium. There are two parts in our method, the first is that we propose the Negotiator to determine the leader in stage game, and the other is to update the Q-value of agents in the game by using a bi-level actor-critic learning method based on the Joint Mixed Strategy Equilibrium Q-learning algorithm (JMSE Q-learning). The convergence proof is given, and the learning algorithm is compared with the state-of-the-art algorithms. We found that the proposed N-Bi-AC method successfully converged to a fair NE, which guarantees the fairness of agents in different matrix game environments.