Nonnegative matrix factorization (NMF) has been successfully applied in several data mining tasks. Recently, there is an increasing interest the acceleration of NMF, due to its high cost on large matrices. On other hand, privacy issue NMF over federated worthy attention, since prevalently image and text analysis which may involve leveraging (e.g, medical record) across parties (e.g., hospitals)...

In this paper, we study the problem of nonnegative graph embedding, originally investigated in [14] for reaping the benefits from both nonnegative data factorization and the specific purpose characterized by the intrinsic and penalty graphs [13]. Our contributions are two-fold. On the one hand, we present a multiplicative iterative procedure for nonnegative graph embedding, which significantly ...

Nonnegative matrix factorization (NMF) has become a prominent signal processing and data analysis technique. To address streaming data, online methods for NMF have been introduced recently, mainly restricted to the linear model. In this paper, we propose a framework for online nonlinear NMF, where the factorization is conducted in a kernel-induced feature space. By exploring recent advances in ...

Hyperspectral unmixing is a crucial preprocessing step for material classification and recognition. In the last decade, nonnegative matrix factorization (NMF) and its extensions have been intensively studied to unmix hyperspectral imagery and recover the material end-members. As an important constraint for NMF, sparsity has been modeled making use of the L1 regularizer. Nonetheless, recent stud...

Real data are usually complex and contain various components. For example, face images have expressions and genders. Each component mainly reflects one aspect of data and provides information others do not have. Therefore, exploring the semantic information of multiple components as well as the diversity among them is of great benefit to understand data comprehensively and in-depth. However, th...

Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n × m matrix M into a product of a nonnegative n × d matrix W and a nonnegative d × m matrix H. Restricted NMF requires in addition that the column spaces of M and W coincide. Finding the minimal inner dimension d is known to be NP-hard, both for NMF and restricted NMF. We show that restricted NMF is closel...

Matrix factorization techniques have been frequently applied in information processing tasks. Among them, Non-negative Matrix Factorization (NMF) have received considerable attentions due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts-based in human brain. On the other hand, from geometric perspective the data is usually sampl...

The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization. A multi-objective optimization problem finds conical combinations of templates that approximate a given data matrix. The templates are chosen so that as far...