Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
A Generalized Framework for Network Component Analysis
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Document clustering using nonnegative matrix factorization
Information Processing and Management: an International Journal
Projected Gradient Methods for Nonnegative Matrix Factorization
Neural Computation
Structural Properties of Gene Regulatory Networks: Definitions and Connections
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Matrices and Matroids for Systems Analysis
Matrices and Matroids for Systems Analysis
| Hi-index | 0.00 |
In many signal processing and data mining applications, we need to approximate a given matrix Yof "sensor measurements" over several experiments by a low-rank product Y≈ A·X, where Xcontains source signals for each experiment, Acontains source-sensor mixing coefficients, and bothAand Xare unknown. We assume that the only a-priori information available is that Amust have zeros at certain positions; this constrains the source-sensor network connectivity pattern.In general, different AXfactorizations approximate a given Yequally well, so a fundamental question is how the connectivity restricts the solution space. We present a combinatorial characterization of uniqueness up to diagonal scaling, called structural identifiabilityof the model, using the concept of structural rank from combinatorial matrix theory.Next, we define an optimization problem that arises in the need for efficient experimental design: to minimize the number of sensors while maintaining structural identifiability. We prove its NP-hardness and present a mixed integer linear programming framework with two cutting-plane approaches. Finally, we experimentally compare these approaches on simulated instances of various sizes.