Answering logical queries on knowledge graphs (KG) poses a significant challenge for machine reasoning. The primary obstacle in this task stems from the inherent incompleteness of KGs. Existing research has predominantly focused on addressing the issue of missing edges in KGs, thereby neglecting another aspect of incompleteness: the emergence of new entities. Furthermore, most of the existing methods tend to reason over each logical operator separately, rather than comprehensively analyzing the query as a whole during the reasoning process. In this paper, we propose a query-aware prompt-fused framework named Pro-QE, which could incorporate existing query embedding methods and address the embedding of emerging entities through contextual information aggregation. Additionally, a query prompt, which is generated by encoding the symbolic query, is introduced to gather information relevant to the query from a holistic perspective. To evaluate the efficacy of our model in the inductive setting, we introduce two new challenging benchmarks. Experimental results demonstrate that our model successfully handles the issue of unseen entities in logical queries. Furthermore, the ablation study confirms the efficacy of the aggregator and prompt components.

Knowledge graphs (KGs) have become vitally important in modern recommender systems, effectively improving performance and interpretability. Fundamentally, recommender systems aim to identify user interests based on historical interactions and recommend suitable items. However, existing works overlook two key challenges: (1) an interest corresponds to a potentially large set of related items, and (2) the lack of explicit, fine-grained exploitation of KG information and interest connectivity. This leads to an inability to reflect distinctions between entities and interests when modeling them in a single way. Additionally, the granularity of concepts in the knowledge graphs used for recommendations tends to be coarse, failing to match the fine-grained nature of user interests. This homogenization limits the precise exploitation of knowledge graph data and interest connectivity. To address these limitations, we introduce a novel embedding-based model called InBox. Specifically, various knowledge graph entities and relations are embedded as points or boxes, while user interests are modeled as boxes encompassing interaction history. Representing interests as boxes enables containing collections of item points related to that interest. We further propose that an interest comprises diverse basic concepts, and box intersection naturally supports concept combination. Across three training steps, InBox significantly outperforms state-of-the-art methods like HAKG and KGIN on recommendation tasks. Further analysis provides meaningful insights into the variable value of different KG data for recommendations.

Knowledge graph (KG) completion aims to find out missing triples in a KG. Some tasks, such as link prediction and instance completion, have been proposed for KG completion. They are triple-level tasks with some elements in a missing triple given to predict the missing element of the triple. However, knowing some elements of the missing triple in advance is not always a realistic setting. In this paper, we propose a novel graph-level automatic KG completion task calledTriple Set Prediction (TSP)which assumes none of the elements in the missing triples is given. TSP is to predict a set of missing triples given a set of known triples. To properly and accurately evaluate this new task, we propose 4 evaluation metrics including 3 classification metrics and 1 ranking metric, considering both the partial-open-world and the closed-world assumptions. Furthermore, to tackle the huge candidate triples for prediction, we propose a novel and efficient subgraph-based method GPHT that can predict the triple set fast. To fairly compare the TSP results, we also propose two types of methods RuleTensor-TSP and KGE-TSP applying the existing rule- and embedding-based methods for TSP as baselines. During experiments, we evaluate the proposed methods on two datasets extracted from Wikidata following the relation-similarity partial-open-world assumption proposed by us, and also create a complete family data set to evaluate TSP results following the closed-world assumption. Results prove that the methods can successfully generate a set of missing triples and achieve reasonable scores on the new task, and GPHTperforms better than the baselines with significantly shorter prediction time.

Knowledge graphs (KGs) have become valuable knowledge resources in various applications, and knowledge graph embedding (KGE) methods have garnered increasing attention in recent years. However, conventional KGE methods still face challenges when it comes to handling unseen entities or relations during model testing. To address this issue, much effort has been devoted to various fields of KGs. In this paper, we use a set of general terminologies to unify these methods and refer to them collectively as Knowledge Extrapolation. We comprehensively summarize these methods, classified by our proposed taxonomy, and describe their interrelationships. Additionally, we introduce benchmarks and provide comparisons of these methods based on aspects that are not captured by the taxonomy. Finally, we suggest potential directions for future research.

Band selection (BS) is an effective approach to alleviate the spectral redundancy of a hyperspectral image (HSI). The emerging deep-learning-based BS methods have become a hot topic due to their ability to model nonlinear relationships between spectral bands. However, existing deep-learning-based BS methods fail to accurately extract the representativeness of each band as a result of the limitation of interpretation networks. Moreover, existing deep-learning methods cannot fully utilize the interband correlation and the spatial information of HSIs for BS. To solve these issues, in this letter, we propose a novel Transformer reconstruction network for unsupervised BS, termed BSFormer. Specifically, the Transformer reconstruction network, which contributes to leveraging the spectral–spatial information of the HSI, consists of a Transformer-based band attention (TBA) module and a convolutional autoencoder (CAE)-based reconstruction module. On this basis, we design a novel band evaluation criterion composed of representative metric and redundancy metric, which are interpreted with the help of the multihead self-attention layer in the TBA module. The designed criterion can fully use the band representativeness and interband correlation for BS. Experimental results on three well-known hyperspectral datasets verify that the proposed BSFormer can yield better classification performance than the competitors.

Rule mining is an effective approach for reasoning over knowledge graph (KG). Existing works mainly concentrate on mining rules. However, there might be several rules that could be applied for reasoning for one relation, and how to select appropriate rules for completion of different triples has not been discussed. In this paper, we propose to take the context information into consideration, which helps select suitable rules for the inference tasks. Based on this idea, we propose a transformer-based rule mining approach, Ruleformer. It consists of two blocks: 1) an encoder extracting the context information from subgraph of head entities with modified attention mechanism, and 2) a decoder which aggregates the subgraph information from the encoder output and generates the probability of relations for each step of reasoning. The basic idea behind Ruleformer is regarding rule mining process as a sequence to sequence task. To make the subgraph a sequence input to the encoder and retain the graph structure, we devise a relational attention mechanism in Transformer. The experiment results show the necessity of considering these information in rule mining task and the effectiveness of our model.

Answering complex queries over knowledge graphs (KG) is an important yet challenging task because of the KG incompleteness issue and cascading errors during reasoning. Recent query embedding (QE) approaches embed the entities and relations in a KG and the first-order logic (FOL) queries into a low dimensional space, making the query can be answered by dense similarity searching. However, previous works mainly concentrate on the target answers, ignoring intermediate entities' usefulness, which is essential for relieving the cascading error problem in logical query answering. In addition, these methods are usually designed with their own geometric or distributional embeddings to handle logical operators like union, intersection, and negation, with the sacrifice of the accuracy of the basic operator -- projection, and they could not absorb other embedding methods to their models. In this work, we propose a Neural and Symbolic Entangled framework (ENeSy) for complex query answering, which enables the neural and symbolic reasoning to enhance each other to alleviate the cascading error and KG incompleteness. The projection operator in ENeSy could be any embedding method with the capability of link prediction, and the other FOL operators are handled without parameters. With both neural and symbolic reasoning results contained, ENeSy answers queries in ensembles. We evaluate ENeSy on complex query answering benchmarks, and ENeSy achieves the state-of-the-art, especially in the setting of training model only with the link prediction task.

NeuralKG is an open-source Python-based library for diverse representation learning of knowledge graphs. It implements three kinds of Knowledge Graph Embedding (KGE) methods, including conventional KGEs, GNN-based KGEs, and Rule-based KGEs. With a unified framework, NeuralKG successfully reproduces link prediction results of these methods on benchmarks, freeing users from the laborious task of reimplementing them, especially for some methods originally written in non-python programming languages. Besides, NeuralKG is highly configurable and extensible. It provides various decoupled modules that can be mixed and adapted to each other. Thus with NeuralKG, developers and researchers can quickly implement their own designed models and obtain the optimal training methods to achieve the best performance efficiently. We built a website http://neuralkg.zjukg.org to organize an open and shared KG representation learning community. The library, experimental methodologies, and model reimplement results of NeuralKG are all publicly released at https://github.com/zjukg/NeuralKG.

In this paper, we propose a method for visual tracking based on local sparse representation. Image patches from the object and the background are split into image blocks to construct local representations. Within the subclass discriminant framework, a discriminative subspace is learned to distinguish the object image blocks from the background image blocks while preserving their multimodal structure. A dictionary is constructed using the centers of the object subclasses. With this dictionary, sparse coding is implemented on the projected vectors corresponding to the image blocks, and the sparse coefficients are concatenated to obtain a local sparse code as the feature that represents the image patch. Considering the subclass discriminant constraint and the sparsity constraint imposed on the sparse coding, the subspace learning and sparse representation problems are converted into a joint optimization problem with respect to a transformation matrix and sparse coefficients. To enhance the tracking accuracy, two dictionaries are devised, one to incorporate the original observations of the target and the other to incorporate the latest observations, thereby providing two templates to characterize the appearance of the target. Histogram intersection over the local sparse codes provides an evaluation of the confidence. Finally, the candidate with the maximal confidence is selected as the object image patch. Compared with several state-of-the-art algorithms, our method demonstrates a superior performance when applied to challenging sequences.

The Hough transform is a popular technique used in the field of image processing and computer vision. With a Hough transform technique, not only the normal angle and distance of a line but also the line-segment's length and midpoint (centroid) can be extracted by analysing the voting distribution around a peak in the Hough space. In this paper, a method based on minimum-entropy analysis is proposed to extract the set of parameters of a line segment. In each column around a peak in Hough space, the voting values specify probabilistic distributions. The corresponding entropies and statistical means are computed. The line-segment's normal angle and length are simultaneously computed by fitting a quadratic polynomial curve to the voting entropies. The line-segment's midpoint and normal distance are computed by fitting and interpolating a linear curve to the voting means. The proposed method is tested on simulated images for detection accuracy by providing comparative results. Experimental results on real-world images verify the method as well. The proposed method for line-segment detection is both accurate and robust in the presence of quantization error, background noise, or pixel disturbances.