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Fuzzy $c$ -means (FCM) clustering is a promising method to handle uncertainties in data clustering. However, the traditional FCM and most of its variants cannot address incomplete inputs. To this aim, a novel fuzzy clustering framework is put forward to perform highly accurate clustering on incomplete data. It adopts twofold ideas: 1) Utilizing a nonnegative latent factor model to prefill the missing data in the inputs by rigidly extracting involved entities’ latent features, where the principle of a minibatch gradient descent algorithm is incorporated into a single latent factor-dependent, nonnegative and multiplicative update algorithm to accelerate the convergence rate; and 2) integrating the distribution of inputs and the weights of local features into the objective function through sparse self-representation and weighting allocation to focus on crucial features. In this way, a NLF analysis-incorporated and feature-weighted fuzzy double $c$ -means clustering (NF $^2$ D) method is achieved, where the data distribution and instance correlation are simultaneously considered with care. Experiments on 12 real-world datasets including both data and images with different missing rates show that the proposed NF $^2$ D method has a significant superiority over state-of-the-art fuzzy clustering methods. [ABSTRACT FROM AUTHOR]

Undirected, sparse and large-scaled networks existing ubiquitously in practical engineering are vitally important since they usually contain rich information in various patterns. Matrix factorization (MF) technique is an efficient method to extract the useful latent factors (LFs) from the LF model, which directly gives rise to the so-called MF model. However, most MF models cannot maintain some frequently encountered constraints such as nonnegativity of LFs and the symmetry of the target network. In addition, in spite of its potential capability of obtaining the effectiveness of both the computation and the storage, the currently developed double factorization (DF)-based model still suffers from the problem of the low prediction accuracy due to the limited amount of LFs. To address the above problems, a novel MF model is proposed in terms of the triple-factorization (TF) technique, thereby leading to TF-based symmetric and nonnegative latent factor (SNLF) models. Compared with the traditional DF-based SNLF model, the proposed TF-based SNLF model is equipped with: 1) constraints on symmetry and nonnegativity; 2) desirable performance with high accuracy; 3) the convergence of the algorithm; and 4) fairly low storage and computational complexity. Furthermore, in order to reduce overfitting so as to further improve the model performance, regularization is precisely considered into the proposed TF-based SNLF model. Experiments on real datasets show that the proposed TF-based SNLF model has a whelming ability of improving the estimation accuracy for the missing data as well as guaranteeing the symmetry of the target network and the nonnegativity of LFs at a little expense of the computation and storage burden. Moreover, it is easy to be implemented for the data analysis. [ABSTRACT FROM AUTHOR]