Acoustic scene recordings are represented by different types of handcrafted or Neural Network-derived features. These features, typically of thousands of dimensions, are classified in state of the art approaches using kernel machines, such as the Support Vector Machines (SVM). However, the complexity of training these methods increases with the dimensionality of these input features and the size of the dataset. A solution is to map the input features to a randomized lower-dimensional feature space. The resulting random features can approximate non-linear kernels with faster linear kernel computation. In this work, we computed a set of 6,553 input features and used them to compute random features to approximate three types of kernels, Gaussian, Laplacian and Cauchy. We compared their performance using an SVM in the context of the DCASE Task 1 - Acoustic Scene Classification. Experiments show that both, input and random features outperformed the DCASE baseline by an absolute 4%. Moreover, the random features reduced the dimensionality of the input by more than three times with minimal loss of performance and by more than six times and still outperformed the baseline. Hence, random features could be employed by state of the art approaches to compute low-storage features and perform faster kernel computations.