With the successful application of granular computing in anomaly detection, a variety of tools including fuzzy information entropy can achieve superior detection results. However, fuzzy information entropy calculates fuzzy similarity through a global strategy, ignoring the local information in the data. To address this deficiency, this paper constructs a fuzzy$k$NN entropy theory and applies it to identify anomalies. Firstly, fuzzy$k$-similarity and fuzzy$k$NN are defined, and$k$NN entropy theory and the related information-theoretic metrics are proposed. Then, the relevant definitions and propositions of fuzzy$k$NN entropy, fuzzy$k$-joint entropy, fuzzy$k$-conditional information entropy, as well as fuzzy$k$-mutual information are elaborated. Based on the proposed theory, an anomaly detection model is constructed. At first, the fuzzy$k$-similarity relation matrix is constructed based on the fuzzy$k$-similarity in the proposed theory, and the relative fuzzy$k$NN entropy is calculated. Based on the relative fuzzy$k$NN entropy, the fuzzy$k$-relation anomaly degree is defined to characterize the anomaly intensity of fuzzy$k$NN information granules. Then, the anomaly factor based on fuzzy$k$NN entropy is built to represent the anomaly degree of data objects. Finally, the corresponding Fuzzy$k$NN Entropy-based Anomaly Detection algorithm (F$k$EAD) is designed. Comparative experiments are conducted with 11 state-of-the-art anomaly detection methods on thirty public datasets. The results reveal that the proposed method achieves better performance.

In information systems lacking decision-making information, effectively leveraging fuzzy rough sets for outlier detection in complex data is challenging, especially in capturing inherent uncertainty and multi-granularity characteristics to construct discriminative outlier scores. However, existing fuzzy rough sets-based outlier detection methods often suffer from three key limitations: (1) Local data distributions are often ignored when calculating fuzzy relation matrices, resulting in inaccurate fuzzy similarity representations; (2) Use of all objects in fuzzy upper and lower approximations can weaken noise resistance and increase computational complexity; (3) Single-granularity data processing reduces efficiency and may fail to capture the multi-granularity nature of data, thereby limiting the adaptability of these methods in complex data environments. To address these issues, we propose to fusesNatural neighbor fuzzy approximations withGranular-ball representation forOutlierDetection (NGOD), which integrates the multi-granularity granular-ball representation and fuzzy rough sets to improve the effectiveness and robustness of unsupervised outlier detection. Specifically, we first define a local distribution-aware fuzzy relation, enabling more discriminative similarity calculations between samples. To improve the effectiveness and robustness of fuzzy upper and lower approximations, we propose a multi-granularity natural neighbor fuzzy approximation model, which effectively utilizes the inherent uncertainty and local abnormal information of data in approximations. Moreover, by introducing natural neighbors, NGOD can adaptively capture local abnormal information in the data without setting neighborhoods manually. Finally, the outlier factors of each sample are calculated in NGOD to measure their outlier degrees. Extensive experiments on diverse datasets demonstrate that NGOD outperforms state-of-the-art methods, validating its superior performance and adaptability. The NGOD code and associated datasets are publicly available athttps://github.com/Mxeron/NGOD.

Deep multi-view clustering leverages deep neural networks to achieve promising performance, but almost all existing methods implicitly assume that all views are aligned correctly. This assumption is unrealistic in many real-world scenarios, where noise, occlusion, or sensor differences can inevitably cause misaligned data. Based on this observation, we reveal and study a practical but understudied problem in multi-view clustering (MVC), i.e., noisy correspondence (NC). Considering this problem, we argue that the main challenge is to prevent the model from overfiting NC. To this end, we propose a novel Robust Multi-view Clustering with Noisy Correspondence (RMCNC) method, which alleviates the influence of the misaligned pairs from multi-view data. To be specific, we first compute a united probability with all positive pairs to learn cross-view alignment consistency, thereby alleviating the adverse impact of the individual false positives. To further mitigate the overfitting problem, we propose a noise-tolerance multi-view contrastive loss that avoids overemphasizing noisy data. Moreover, RMCNC is a unified framework, which can deal with both partially view-aligned and NC problems in multi-view clustering. To the best of our knowledge, it could be the first study on NC in multi-view clustering. The experimental results on eight benchmark datasets indicate our RMCNC achieves competitive performance and robustness.

Cross-modal retrieval takes one type of data as the query to retrieve relevant data of another type. Most of existing cross-modal retrieval approaches were proposed to learn a common subspace in a joint manner, where the data from all modalities have to be involved during the whole training process. For these approaches, the optimal parameters of different modality-specific transformations are dependent on each other and the whole model has to be retrained when handling samples from new modalities. In this paper, we present a novel cross-modal retrieval method, called Scalable Deep Multimodal Learning (SDML). It proposes to predefine a common subspace, in which the between-class variation is maximized while the within-class variation is minimized. Then, it trains m modality-specific networks for m modalities (one network for each modality) to transform the multimodal data into the predefined common subspace to achieve multimodal learning. Unlike many of the existing methods, our method can train different modality-specific networks independently and thus be scalable to the number of modalities. To the best of our knowledge, the proposed SDML could be one of the first works to independently project data of an unfixed number of modalities into a predefined common subspace. Comprehensive experimental results on four widely-used benchmark datasets demonstrate that the proposed method is effective and efficient in multimodal learning and outperforms the state-of-the-art methods in cross-modal retrieval.