Bayesian Nonnegative Matrix Factorization With Dirichlet Process Mixtures

Variational Bayesian Gaussian mixture model for off‐grid DOA estimation

“…Assuming that the signal noise received by the array is consistent at the same moment, thus we can assume {τ m,k } M m=1 = τ k at the same time. τ k follows Gamma prior [21] as…”

“…Assuming that the signal noise received by the array is consistent at the same moment, thus we can assume $$\lbrace \tau _{m,k}\rbrace _{m=1}^{M} = \tau _k$$ at the same time. $$\tau _k$$ follows Gamma prior [21] as $$$$\begin{equation} p(\mathbf {\tau }_k) = \mathcal {G} (\tau _k;a,b) \triangleq f_{\tau _k}. \end{equation}$$$$Let $$ \mathbf {z}_t = [ z_t^{1}, \ldots, z_t^{K}]$$ is the assignment vector that $$z_t^{k} = 1$$ means the vector $$\mathbf {E}_{ t}$$ is assigned to the k ‐th cluster noise.…”

Graph Convolutional Networks based Non-Negative Matrix Factorization aware Community detection

“…In addition, community discovery is essentially a node clustering problem, so NMF is also suitable for community discovery. At present, there are many community discovery methods based on NMF, mainly by extending the basic NMF model to solve the community discovery problem of various complex networks, for example, community discovery method SNMF based on symmetric NMF [16,27], community-based on joint NMF The discovery method S2-jNMF [28], the semi-supervised NMF-based community method SPOCD [29], SMpC [30] and the deep NMF-based community method DANMF [31], etc. Although these methods have achieved specific performance improvements to varying degrees, since NMF is essentially a linear model, these methods are still linear and do not have nonlinear expression capabilities.…”