Nearest neighbors and correlation dimension for dimensionality estimation. Application to factor analysis of real biological time series data

Determining the number of components in dimensionality reduction techniques is still one of the open problems of research on data analysis. These methods are often used in knowledge extraction of multivariate great dimensional data, but very often the number of components is assumed to be known. One of the classical methods to estimate this dimensionality is based on the Principal Components Analysis (PCA) eigenvalues [1, 2]. However, this method supposes that the model is linear and the signals are Gaussian. To be able to consider non-linear and non-Gaussian cases, we propose in this paper “measure based methods” as nearest neighbors dimension and correlation dimension. The comparaison between the three methods is evaluated both with simulated data and with real biological data, which are gene expression time series. The main goal of this study is to estimate the minimum number of factors.