A new method for SSMF improves upon existing algorithms.
problem Identify identifiable solutions in simplex-structured matrix factorization.
method Dual simplex volume maximization approach.
result The proposed method outperforms state-of-the-art SSMF algorithms.
Proposes a new matrix factorization model for interval-valued matrices.
problem Matrix factorization for matrices with entries in a given interval.
method Bounded simplex-structured matrix factorization (BSSMF) with fast algorithm for missing data.
result BSSMF provides a unique decomposition under certain conditions.
New algorithms for SSMF with weaker identifiability conditions than SSC.
problem Identifying unique decompositions in simplex-structured matrix factorization.
method Extracting facets containing the largest number of points to ensure identifiability.
result Our algorithms recover unique decompositions under weaker conditions than SSC.
Consider a structured matrix factorization model where one factor is restricted to have its columns lying in the unit simplex. This simplex-structured matrix factorization (SSMF) model and the associated factorization techniques have spurred much interest in research topics over different areas, such as hyperspectral u…
Paper checks SSC for matrix factorizations using Gurobi.
problem Checking the SSC for various matrix factorizations.
method Formulated as a non-convex quadratic optimization problem over a bounded set, solved with Gurobi.
result SSC can be checked in reasonable time for realistic scenarios.
In the probabilistic topic models, the quantity of interest---a low-rank matrix consisting of topic vectors---is hidden in the text corpus matrix, masked by noise, and the Singular Value Decomposition (SVD) is a potentially useful tool for learning such a low-rank matrix. However, the connection between this low-rank m…
We consider the problem of estimating community memberships of nodes in a network, where every node is associated with a vector determining its degree of membership in each community. Existing provably consistent algorithms often require strong assumptions about the population, are computationally expensive, and only p…
The paper proposes a new model to analyze directed networks and accurately estimate community memberships.
problem Modeling and estimating community memberships in directed networks with heterogeneous degrees.
method Directed Degree Corrected Mixed Membership (DiDCMM) model and DiMSC algorithm.
result The proposed DiMSC algorithm is asymptotically consistent and provides error bounds for community membership vectors.
DiMMSB models directed mixed membership networks, identifying distinct community structures.
problem Modeling directed mixed membership networks with distinct community structures.
method Directed Mixed Membership Stochastic Blockmodel (DiMMSB) with DiSP algorithm.
result DiSP algorithm is asymptotically consistent and outperforms competitors.
New method identifies latent components in PNL mixtures without strong assumptions.
problem Identifying latent components in PNL mixtures under unknown nonlinear functions.
method Carefully designed UML criterion to identify a null space associated with the mixing system.
result Identification/removal of unknown nonlinearity under minimal conditions.
New method identifies latent components in nonlinear mixtures without stringent assumptions.
problem Unraveling latent components in nonlinearly mixed data.
method Constrained autoencoder-based algorithm for identifiability under relaxed assumptions.
result Comprehensive sample complexity results and new identifiability conditions.