Fangfang Li

Fangfang Li, Quanxue Gao, Cheng Deng et al.

The K-means one-step dimensionality reduction clustering method has made some progress in addressing the curse of dimensionality in clustering tasks. However, it combines the K-means clustering and dimensionality reduction processes for optimization, leading to limitations in the clustering effect due to the introduced hyperparameters and the initialization of clustering centers. Moreover, maintaining class balance during clustering remains challenging. To overcome these issues, we propose a unified framework that integrates manifold learning with K-means, resulting in the self-supervised graph embedding framework. Specifically, we establish a connection between K-means and the manifold structure, allowing us to perform K-means without explicitly defining centroids. Additionally, we use this centroid-free K-means to generate labels in low-dimensional space and subsequently utilize the label information to determine the similarity between samples. This approach ensures consistency between the manifold structure and the labels. Our model effectively achieves one-step clustering without the need for redundant balancing hyperparameters. Notably, we have discovered that maximizing the $\ell_{2,1}$-norm naturally maintains class balance during clustering, a result that we have theoretically proven. Finally, experiments on multiple datasets demonstrate that the clustering results of Our-LPP and Our-MFA exhibit excellent and reliable performance.

Shikun Mei, Fangfang Li, Quanxue Gao et al.

Anchor-based methods are a pivotal approach in handling clustering of large-scale data. However, these methods typically entail two distinct stages: selecting anchor points and constructing an anchor graph. This bifurcation, along with the initialization of anchor points, significantly influences the overall performance of the algorithm. To mitigate these issues, we introduce a novel method termed Anchor-free Clustering based on Anchor Graph Factorization (AFCAGF). AFCAGF innovates in learning the anchor graph, requiring only the computation of pairwise distances between samples. This process, achievable through straightforward optimization, circumvents the necessity for explicit selection of anchor points. More concretely, our approach enhances the Fuzzy k-means clustering algorithm (FKM), introducing a new manifold learning technique that obviates the need for initializing cluster centers. Additionally, we evolve the concept of the membership matrix between cluster centers and samples in FKM into an anchor graph encompassing multiple anchor points and samples. Employing Non-negative Matrix Factorization (NMF) on this anchor graph allows for the direct derivation of cluster labels, thereby eliminating the requirement for further post-processing steps. To solve the method proposed, we implement an alternating optimization algorithm that ensures convergence. Empirical evaluations on various real-world datasets underscore the superior efficacy of our algorithm compared to traditional approaches.

Fangfang Li, Guandong Xu, Longbing Cao

Recommender systems research has experienced different stages such as from user preference understanding to content analysis. Typical recommendation algorithms were built on the following bases: (1) assuming users and items are IID, namely independent and identically distributed, and (2) focusing on specific aspects such as user preferences or contents. In reality, complex recommendation tasks involve and request (1) personalized outcomes to tailor heterogeneous subjective preferences; and (2) explicit and implicit objective coupling relationships between users, items, and ratings to be considered as intrinsic forces driving preferences. This inevitably involves the non-IID complexity and the need of combining subjective preference with objective couplings hidden in recommendation applications. In this paper, we propose a novel generic coupled matrix factorization (CMF) model by incorporating non-IID coupling relations between users and items. Such couplings integrate the intra-coupled interactions within an attribute and inter-coupled interactions among different attributes. Experimental results on two open data sets demonstrate that the user/item couplings can be effectively applied in RS and CMF outperforms the benchmark methods.