A random version of principal component analysis in data clustering. (April 2018) - Palese, Luigi Leonardo
Graphical abstract: Highlights: Dimensionality reduction techniques are extremely important in science today. PCA is widely used, but it requires the knowledge of the covariance matrix. Algorithms based on random projection are increasingly used. An new random projection algorithm is proposed, very similar to PCA. It is easy to implement, conceptually simple and numerically robust. Abstract: Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance/correlation matrix of the analyzed data. However, to properly work with high-dimensional data sets, PCA poses severe mathematical constraints on the minimum number of different replicates, or samples, that must be included in the analysis. Generally, improper sampling is due to a small number of data respect to the number of the degrees of freedom that characterize the ensemble. In the field of life sciences it is often important to have an algorithm that can accept poorly dimensioned data sets, including degenerated ones. Here a new random projection algorithm is proposed, in which a random symmetric matrix surrogates the covariance/correlation matrix of PCA, while maintaining the data clustering capacity. We demonstrate that what is important for clustering efficiency of PCA is not the exact form of the covariance/correlation matrix, but simply its symmetry.