Reviews: Efficient Optimization for Linear Dynamical Systems with Applications to Clustering and Sparse Coding

Summary: the paper proposes a clustering method for linear dynamical systems, based on minimizing the kernalized norm between extended observability spaces. Since the objective function contains terms involving discrete Lypanunov equations (DLEs), the paper derives how to pass the derivatives through, yielding a gradient descent algorithm. Experiments are presented on 2 datasets, for LDS clustering and sparse codebook learning. Originality: 1) novelty: the paper is moderately novel, but fairly straightforward. The difference with other related works [3,9,10,11,12] in terms of objective functions, assumptions/constraints, canonical forms should be discussed more.