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It is well-known that recently proposed Linear Parameter-Varying (LPV) subspace identification techniques suffer from a curse of dimensionality leading to an ill-posed parameter estimation problem. In this paper we will focus on regularization methods to solve the parameter estimation problem. Tikhonov and TSVD regularization are conventional general-purpose regularization methods. These general-purpose regularization methods give preference to a solution with a small 2-norm. In principle many other types of additional information about the desired solution can be incorporated in order to stabilize the ill-posed problem. The main contribution of this paper is that we propose a novel regularization strategy for LPV subspace methods: the nuclear norm regularization method. By applying state-of-the-art convex optimization techniques, the method stabilizes the parameter estimation problem by including information on the desired solution that is specific to the (LPV) subspace identification scheme. We will conclude the paper with a summarizing comparison between the different regularization techniques.