Spectral clustering requires the time-consuming decomposition of the Laplacian matrix of the similarity graph, thus limiting its applicability to large datasets. To improve the efficiency of spectral clustering, a top-down approach was recently proposed, which first divides the data into several micro-clusters (granular-balls), then splits these micro-clusters when they are not ``compact'', and finally uses these micro-clusters as nodes to construct a similarity graph for more efficient spectral clustering. However, this top-down approach is challenging to adapt to unevenly distributed or structurally complex data. This is because constructing micro-clusters as a rough ball struggles to capture the shape and structure of data in a local range, and the simplistic splitting rule that solely targets ``compactness'' is susceptible to noise and variations in data density and leads to micro-clusters with varying shapes, making it challenging to accurately measure the similarity between them. To resolve these issues and improve spectral clustering, this paper first proposes to start from local structures to obtain micro-clusters, such that the complex structural information inside local neighborhoods is well captured by them. Moreover, by noting that Euclidean distance is more suitable for convex sets, this paper further proposes a data splitting rule that couples local density and data manifold structures, so that the similarities of the obtained micro-clusters can be easily characterized. A novel similarity measure between micro-clusters is then proposed for the final spectral clustering. A series of experiments based on synthetic and real-world datasets demonstrate that the proposed method has better adaptability to structurally complex data than granular-ball based methods.

Density-based mode-seeking methods generate a density-ascending dependency from low-density points towards higher-density neighbors. Current mode-seeking methods identify modes by breaking some dependency connections, but relying heavily on local data characteristics, requiring case-by-case threshold settings or human intervention to be effective for different datasets. To address this issue, we introduce a novel concept called typicality, by exploring the locally defined dependency from a global perspective, to quantify how confident a point would be a mode. We devise an algorithm that effectively and efficiently identifies modes with the help of the global-view typicality. To implement and validate our idea, we design a clustering method called TANGO, which not only leverages typicality to detect modes, but also utilizes graph-cut with an improved path-based similarity to aggregate data into the final clusters. Moreover, this paper also provides some theoretical analysis on the proposed algorithm. Experimental results on several synthetic and extensive real-world datasets demonstrate the effectiveness and superiority of TANGO. The code is available at https://github.com/SWJTU-ML/TANGO_code.

Traditional logic-based belief revision research focuses on designing rules to constrain the behavior of revision operators. Frameworks have been proposed to characterize iterated revision rules, but they are often too loose, leading to multiple revision operators that all satisfy the rules under the same belief condition. In many practical applications, such as safety critical ones, it is important to specify a definite revision operator to enable agents to iteratively revise their beliefs in a deterministic way. In this paper, we propose a novel framework for iterated belief revision by characterizing belief information through preference relations. Semantically, both beliefs and new evidence are represented as belief algebras, which provide a rich and expressive foundation for belief revision. Building on traditional revision rules, we introduce additional postulates for revision with belief algebra, including an upper-bound constraint on the outcomes of revision. We prove that the revision result is uniquely determined given the current belief state and new evidence. Furthermore, to make the framework more useful in practice, we develop a particular algorithm for performing the proposed revision process. We argue that this approach may offer a more predictable and principled method for belief revision, making it suitable for real-world applications.

MOTIVATION: The rapid development of single-cell RNA sequencing (scRNA-seq) has significantly advanced biomedical research. Clustering analysis, crucial for scRNA-seq data, faces challenges including data sparsity, high dimensionality, and variable gene expressions. Better low-dimensional embeddings for these complex data should maintain intrinsic information while making similar data close and dissimilar data distant. However, existing methods utilizing neural networks typically focus on minimizing reconstruction loss and maintaining similarity in embeddings of directly related cells, but fail to consider dissimilarity, thus lacking separability and limiting the performance of clustering. RESULTS: We propose a novel clustering algorithm, called scHNTL (scRNA-seq data clustering augmented by high-order neighbors and triplet loss). It first constructs an auxiliary similarity graph and uses a Graph Attentional Autoencoder to learn initial embeddings of cells. Then it identifies similar and dissimilar cells by exploring high-order structures of the similarity graph and exploits a triplet loss of contrastive learning, to improve the embeddings in preserving structural information by separating dissimilar pairs. Finally, this improvement for embedding and the target of clustering are fused in a self-optimizing clustering framework to obtain the clusters. Experimental evaluations on 16 real-world datasets demonstrate the superiority of scHNTL in clustering over the state-of-the-arts single-cell clustering algorithms. AVAILABILITY AND IMPLEMENTATION: Python implementation of scHNTL is available at Figshare (https://doi.org/10.6084/m9.figshare.27001090) and Github (https://github.com/SWJTU-ML/scHNTL-code).

People often use qualitative relations to describe locations or directional information, especially in written communication, such as ‘the restaurant is located at the southeast corner of the square’. However, when a large number of spatial entities are involved, qualitative relations alone are not intuitive enough for people to understand a spatial configuration. In fact, many applications, e.g. pertaining to sharing travel experiences, use sketch maps, i.e. maps focusing on the main features of an area whilst abstracting exact scale measurements, to help demonstrate abstract qualitative relations with more intuitive geometric points. Current approaches for generating point sketch maps from qualitative spatial relations require a high level of expertise, face inherent difficulties with efficiently processing large-scale data in bulk, and are vulnerable to inaccurate or conflicting information contained in qualitative data. To address these limitations, by incorporating machine learning techniques, we propose to translate the problem into an optimization problem of data reconstruction, enabling a novel end-to-end approach for generating point sketch maps from qualitative directional relations in bulk. Experiments on real-world datasets show that the proposed approach has very high accuracy and is robust even with a large portion of inaccurate or incomplete information.

Co-clustering methods make use of the correlation between samples and attributes to explore the co-occurrence structure in data. These methods have played a significant role in gene expression analysis, image segmentation, and document clustering. In bipartite graph partition-based co-clustering methods, the relationship between samples and attributes is described by constructing a diagonal symmetric bipartite graph matrix, which is clustered by the philosophy of spectral clustering. However, this not only has high time complexity but also the same number of row and column clusters. In fact, the number of categories of rows and columns often changes in the real world. To address these problems, this paper proposes a novel fast flexible bipartite graph model for the co-clustering method (FBGPC) that directly uses the original matrix to construct the bipartite graph. Then, it uses the inflation operation to partition the bipartite graph in order to learn the co-occurrence structure of the original data matrix based on the inherent relationship between bipartite graph partitioning and co-clustering. Finally, hierarchical clustering is used to obtain the clustering results according to the set relationship of the co-occurrence structure. Extensive empirical results show the effectiveness of our proposed model and verify the faster performance, generality, and flexibility of our model.

In this paper, we present an online (incremental) algorithm for checking the satisfiability of qualitative spatio-temporal data, with direct implications to other fundamental knowledge representation and reasoning problems for such data, like the problems of deductive closure and redundancy removal. In particular, qualitative data come in the form of human-like, symbolic, descriptions such as "region x contains or overlaps region y", which are abundant in the Web of Data. Our approach is also able to maintain, to some extent, any sparse graph structure that may be inherent in the data, i.e., it acts parsimoniously and only tries to infer new information when needed for soundness and completeness. To this end, we complement our practical algorithm with certain theoretical results to assert its correctness and efficiency. A subsequent evaluation with publicly available large-scale real-world and random datasets against the state of the art, shows the interest and promise of our method.

We introduce and study a notion of robustness in Qualitative Constraint Networks (QCNs), which are typically used to represent and reason about abstract spatial and temporal information. In particular, given a QCN, we are interested in obtaining a robust qualitative solution, or, a robust scenario of it, which is a satisfiable scenario that has a higher perturbation tolerance than any other, or, in other words, a satisfiable scenario that has more chances than any other to remain valid after it is altered. This challenging problem requires to consider the entire set of satisfiable scenarios of a QCN, whose size is usually exponential in the number of constraints of that QCN; however, we present a first algorithm that is able to compute a robust scenario of a QCN using linear space in the number of constraints. Preliminary results with a dataset from the job-shop scheduling domain, and a standard one, show the interest of our approach and highlight the fact that not all solutions are created equal.

To effectively and efficiently deal with large-scale spatial data is critical for applications in the age of information technology. Compact representation of spatial knowledge is one of the emerging research techniques that contribute to this capability. In this article, we consider the problem of compactly representing qualitative directional relations between extended objects, modelled in the Cardinal Direction Calculus (CDC) of Goyal and Egenhofer. For a large dataset of regions, this approach first constructs a simplified geometry for each region, which preserves CDC relations between regions, and then represents each simplified geometry compactly, so that the storage size is small while retrieving CDC relations from the representation is still reasonably fast. More specifically, the method called necessary cut is used to construct simple geometries , and the two methods, viz. the polygon representation and the rectangle representation , are devised to compactly represent the constructed geometries in cubic time w.r.t. the size of the corresponding simple geometry. Theoretical analyses demonstrate that the two representations, especially the rectangle representation, are promising to have small storage size. Moreover, our empirical evaluations on real-world datasets show that, for each dataset the new approach can produce a rectangle representation that has dominant performance against the state of the art techniques in reducing the storage size of the relations, while the average efficiency of retrieving CDC relations based on the rectangle representation is about the same as the fastest method in the literature.

Redundancy checking is an important task in AI subfields such as knowledge representation and constraint solving. This paper considers redundant topological constraints, defined in the region connection calculus RCC8. We say a constraint in a set C of RCC8 constraints is redundant if it is entailed by the rest of C. A prime subnetwork of C is a subset of C which contains no redundant constraints and has the same solution set as C. It is natural to ask how to compute such a prime subnetwork, and when it is unique. While this problem is in general intractable, we show that, if S is a subalgebra of RCC8 in which weak composition distributes over nonempty intersections, then C has a unique prime subnetwork, which can be obtained in cubic time by removing all redundant constraints simultaneously from C. As a by-product, we show that any path-consistent network over such a distributive subalgebra is minimal.

The Simple Temporal Problem (STP) has been widely used in various applications to schedule tasks. For dynamical systems, scheduling needs to be efficient and flexible to handle uncertainty and perturbation. To this end, modern approaches usually encode the temporal information as an STP instance. This representation contains redundant information, which can not only take a significant amount of storage space, but also make scheduling inefficient due to the non-concise representation. In this paper, we investigate the problem of simplifying an STP instance by removing redundant information. We show that such a simplification can result in a unique minimal representation without loss of temporal information, and present an efficient algorithm to achieve this task. Evaluation on a large benchmark dataset of STP exhibits a significant reduction in redundant information for the involved instances.

This paper develops a new mechanism to efficiently compute and compactly store qualitative spatial relations between spatial objects, focusing on topological and directional relations for large datasets of region objects. The central idea is to use minimum bounding rectangles (MBRs) to approximately represent region objects with arbitrary shape and complexity and only store spatial relations that cannot be unambiguously inferred from the relations of corresponding MBRs. We demonstrate, both in theory and practice, that our approach requires considerably less construction time and storage space, and can answer queries more efficiently than the state-of-the-art methods.

In this article we show that the Voronoi-based nine-intersection (V9I) model proposed by Chen et al. (2001, A Voronoi-based 9-intersection model for spatial relations. International Journal of Geographical Information Science, 15 (3), 201–220) is more expressive than what has been believed before. Given any two spatial entities A and B, the V9I relation between A and B is represented as a 3 × 3 Boolean matrix. For each pair of types of spatial entities that is, points, lines, and regions, we first show that most Boolean matrices do not represent a V9I relation by using topological constraints and the definition of Voronoi regions. Then, we provide illustrations for all the remaining matrices. This guarantees that our method is sound and complete. In particular, we show that there are 18 V9I relations between two areas with connected interior, while there are only nine four-intersection relations. Our investigations also show that, unlike many other spatial relation models, V9I relations are context or shape sensitive. That is, the existence of other entities or the shape of the entities may affect the validity of certain relations.