This paper deals with the identification of linear hybrid systems switching between multiple linear subsystems. We propose a new approach based on the geometric properties of hybrid systems in parameter space. More precisely, the data are mapped in that space such that each submodel is represented by a hypersphere. Then, we show how these hyperspheres can be easily separated by Principal Component Analysis (PCA) and derive a condition under which this separation is optimal for systems with two modes. Finally, classical (robust) regression is applied to estimate the system parameters from the classified data set. A simple procedure is also proposed to extend the method to the identification of switched systems with multiple modes. Experiments show that the final algorithm can accurately estimate both the parameters and the number of modes while being simple to apply and far more robust to noise than other methods.