Towards Explaining the Spectrogram of Graph Spectral Clustering in Text Document Domain

In previous research, the authors found that the spectrogram of eigenvalues of combinatorial Laplacian of the document similarity matrix is relevant for tasks like graph spectral classification, clustering etc.. This paper investigates the hypothesis that this property can be attributed to the specific “style” of writing, that is to the distribution of words in the documents belonging to a given category of documents. The investigation is performed via generating artificial documents from a predefined parameterized word distribution. The document similarity matrices are computed and the spectrum of the corresponding combinatorial Laplacian is interrogated. The parameters are varied to determine their impact. We present the impact of these parameters on the shape of the spectrogram.