We present a study aimed at understanding the physical phenomena underlying the formation and evolution of galaxies following an alternative analysis of spectroscopic data. Spectra encode the history of star formation and the chemical enrichment of galaxies. The standard approach, based on comparisons with population synthesis models, reveals the presence of substantial degeneracies among the parameters, most notably between age and metallicity. These degeneracies are due to the high correlatedness of the data, along with uncertainties in the parameters that describe the models. The main objective of this project is to use multivariate techniques, such as principal component analysis (PCA), to decipher the star formation histories of galaxies by considering the observational data as the main source of information instead of comparing data and synthesis models. In PCA, information is directly related to the variance of the spectral elements and defines the so-called principal components as eigenvectors produced by the decorrelation of the covariance matrix. We apply PCA to a homogenous sample of galaxy spectra from the Sloan Digital Sky Survey (SDSS) in the velocity dispersion range 100-150km/s, including all three types of galaxies concerning nebular emission – namely star-forming, AGN, and quiescent – according to the standard BPT classification, to assess the properties of the spectra in a model-independent way. Population synthesis is only used a posteriori to give physical meaning to the trends found from PCA. This approach probes different spectral intervals and allows us to assess the variance contributed by nebular emission (from the ionized gas component), the continuum from the stellar photospheres, as well as the stellar absorption lines. Our preliminary results find that galaxy spectra are overall highly compressible, with one component locking a large fraction of total variance, especially in star-forming and AGN galaxies, a result that is independent of the contribution from emission lines. Moreover, the highest fraction of this variance is contributed by the continuum. However, we note that the higher-order principal components cannot be simply ascribed to noise and also encode, in a cumulative sense, a large amount of information. By projecting the observational data onto the lower dimensional parameter space spanned by the principal components, we identify subclasses within each set of galaxies that are explored regarding their evolutionary phase, a result that enables us to understand the transition from star formation to quiescence and the role of AGN.