Data correlation, number of significant principal components and shape of molecules. The K correlation index

Data correlation is an old great problem in multivariate analysis. In this paper a new correlation index, called K, is proposed to evaluate the correlation content into the data. Their mathematical properties are simple and their behavior is tested on some theoretical cases and compared with other correlation indices on 31 real data sets. From the proposed K correlation index, two functions are derived with the aim to estimate the significant number of principal components to retain in Principal Component Analysis. An extensive comparison with several other methods is also performed on real data sets. The obtained results show that the two functions give a number of significant principal components which can be interpreted as the maximum theoretical number and the safest number, respectively