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Subjective classification of galaxies can mislead us in the quest of the origin regarding formation and evolution of galaxies since this is necessarily limited to a few features. The human mind is not able to apprehend the complex correlations in a manyfold parameter space, and multivariate analyses are the best tools to understand the differences among various kinds of objects. In this series of papers, an objective classification of 362,923 galaxies from the Value Added Galaxy Catalogue (VAGC) is carried out with the help of two methods of multivariate analysis. First, Independent Component Analysis (ICA) is used to determine a set of derived independent components that are linear combinations of 47 observed features (viz. ionized lines, Lick indices, photometric and morphological properties, star formation rates etc.) of the galaxies. Subsequently, a K-means cluster analysis is applied on the nine independent components to obtain ten distinct and homogeneous groups. In this first paper, we describe the methods and the main results. It appears that the nine Independent Components represent a complete physical description of galaxies (velocity dispersion, ionisation, metallicity, surface brightness and structure). We find that our ten groups can be essentially placed into traditional and empirical classes (from colour-magnitude and emission-line diagnostic diagrams, early- vs late-types) despite the classical corresponding features (colour, line ratios and morphology) being not significantly correlated with the nine Independent Components. More detailed physical interpretation of the groups will be performed in subsequent papers., Comment: The first version of this paper was entitled "Multivariate Study of the Star Formation Rate in Galaxies: Bimodality Revisited" and submitted in June 2017. This accepted version is slightly shortened and more focused on the statistical analysis

An objective classification of the globular clusters of NGC 5128 has been carried out by using a model-based approach of cluster analysis. The set of observable parameters includes structural parameters, spectroscopically determined Lick indices and radial velocities from the literature. The optimum set of parameters for this type of analysis is selected through a modified technique of Principal Component Analysis, which differs from the classical one in the sense that it takes into consideration the effects of outliers present in the data. Then a mixture model based approach has been used to classify the globular clusters into groups. The efficiency of the techniques used is tested through the comparison of the misclassification probabilities with those obtained using the K-means clustering technique. On the basis of the above classification scheme three coherent groups of globular clusters have been found. We propose that the clusters of one group originated in the original cluster formation event that coincided with the formation of the elliptical galaxy, and that the clusters of the two other groups are of external origin, from tidally stripped dwarf galaxies on random orbits around NGC 5128 for one group, and from an accreted spiral galaxy for the other., Comment: 54 pages, accepted for publication in ApJ