Here, we have employed principal component analysis (PCA) and linear discriminant analysis (LDA) to analyze the Mie-calculated UV-Vis spectra of gold nanospheres (GNS). Eigen spectra of PCA perform the Fano-type resonances. PCA vector spectra determine the 3D vector fields which reveal the homoclinic orbit strange attractor. Quantum confinement effects are observed by the 3D representation of LDA. Standing wave patterns resulting from oscillations of ion-acoustic phonon and electron waves are illustrated through the eigen spectra of LDA. Such capabilities of GNPs have brought high attention to the high energy density physics applications. Furthermore, accurate prediction of gold nanoparticle (GNP) sizes using machine learning could provide rapid analysis without the need for expensive analysis. Two hybrid algorithms consist of unsupervised PCA and two different supervised ANN have been used to estimate the diameters of GNPs. PCA-based artificial neural networks(ANN) were found to estimate the diameters with a high accuracy.