A novel method to determine the number of latent dimensions with SVD

Determining the number of latent dimensions is a ubiquitous problem in machine learning. In this study, we introduce a novel method that relies on SVD to discover the number of latent dimensions. The general principle behind the method is to compare the curve of singular values of the SVD decomposition of a data set with the randomized data set curve. The inferred number of latent dimensions corresponds to the crossing point of the two curves. To evaluate our methodology, we compare it with competing methods such as Kaisers eigenvalue-greater-than-one rule (K1), Parallel Analysis (PA), Velicers MAP test (Minimum Average Partial). We also compare our method with the Silhouette Width (SW) technique which is used in different clustering methods to determine the optimal number of clusters. The result on synthetic data shows that the Parallel Analysis and our method have similar results and more accurate than the other methods, and that our methods is slightly better result than the Parallel Analysis method for the sparse data sets.