Cluster analysis in high dimensional data is a difficult but desirable task. Many existing methods fail to cluster high dimensional data due to what is known as the curse of dimensionality. Therefore, sophisticated clustering methods are in wide development. Along these lines, spectral modularity maximization emerged from the theory of random matrices and graph modularity. The method is based on a filtering of the spectral decomposition of similarity matrices. Despite the recent success of this method, we uncover a fundamental challenge of spectral modularity: the spectral modularity breaks down as the number of groups in a data set grows. To mitigate this challenge, we propose two solutions: one solution based on a regularization and one solution based on a normalization. We perform a thorough empirical analysis of the clustering performance of the solutions and find that, not only do our methods resolve the breakdown of spectral modularity, but they also outperform existing clustering methods in
a variety of settings.

In this study, we investigate the usage of generative adversarial networks for modelling a collection of sounds. The proposed method incites an interpretation of musical sound synthesis based on audio collections rather than synthesizer component controls. This promises the generation of arbitrarily complex sounds without the restrictions of traditional synthesizer components. Furthermore,
the method promises to introduce non-linear interpolations within abritrarily varied collections of sounds. These two elements motivate a new approach in creating musical instruments. Here, we introduce a proof of principle method with qualifications and quantifactions of the results. First, we cover the imagelike audio signal representation and neural network architectures that compose a trainable system capable of producing audio signals. Despite some artifacts, the trained system is able to produce structural similarities in the spectral information compared to the training data set. Furthermore, we introduce a metric to quantitatively compare signal characteristics between two sets of signals. The difference between characteritics appears to decline throughout the training of the system.