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Convergence Properties of Score-Based Models using Graduated Optimisation for Linear Inverse Problems
In this work, we show that score-based generative models (SGMs) can be used in a graduated optimisation framework to solve inverse problems.
Spatially Coherent Clustering Based on Orthogonal Nonnegative Matrix Factorization
Classical approaches in cluster analysis are typically based on a feature space analysis.
Invariance and Inverse Stability under ReLU
We flip the usual approach to study invariance and robustness of neural networks by considering the non-uniqueness and instability of the inverse mapping.
A Survey on Surrogate Approaches to Non-negative Matrix Factorization
Motivated by applications in hyperspectral imaging we investigate methods for approximating a high-dimensional non-negative matrix $\mathbf{\mathit{Y}}$ by a product of two lower-dimensional, non-negative matrices $\mathbf{\mathit{K}}$ and $\mathbf{\mathit{X}}.$ This so-called non-negative matrix factorization is based on defining suitable Tikhonov functionals, which combine a discrepancy measure for $\mathbf{\mathit{Y}}\approx\mathbf{\mathit{KX}}$ with penalty terms for enforcing additional properties of $\mathbf{\mathit{K}}$ and $\mathbf{\mathit{X}}$.
Analysis of Invariance and Robustness via Invertibility of ReLU-Networks
Studying the invertibility of deep neural networks (DNNs) provides a principled approach to better understand the behavior of these powerful models.
