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Important but rare and subtle processes driving galaxy morphology andstar-formation may be missed by traditional spiral, elliptical, irregular orS\'ersic bulge/disk classifications. To overcome this limitation, we use aprincipal component analysis of non-parametric morphological indicators(concentration, asymmetry, Gini coefficient, $M_{20}$, multi-mode, intensityand deviation) measured at rest-frame $B$-band (corresponding to HST/WFC3 F125Wat 1.4 $< z <$ 2) to trace the natural distribution of massive ($>10^{10}M_{\odot}$) galaxy morphologies. Principal component analysis (PCA) quantifiesthe correlations between these morphological indicators and determines therelative importance of each. The first three principal components (PCs) capture$\sim$75 per cent of the variance inherent to our sample. We interpret thefirst principal component (PC) as bulge strength, the second PC as dominated byconcentration and the third PC as dominated by asymmetry. Both PC1 and PC2correlate with the visual appearance of a central bulge and predict galaxyquiescence. PC1 is a better predictor of quenching than stellar mass, as asgood as other structural indicators (S\'ersic-n or compactness). We divide thePCA results into groups using an agglomerative hierarchical clustering method.Unlike S\'ersic, this classification scheme separates compact galaxies fromlarger, smooth proto-elliptical systems, and star-forming disk-dominated clumpygalaxies from star-forming bulge-dominated asymmetric galaxies. Distinguishingbetween these galaxy structural types in a quantitative manner is an importantstep towards understanding the connections between morphology, galaxy assemblyand star-formation.

Beyond Spheroids and Discs: Classifications of CANDELS Galaxy Structure at 1.4 < z < 2 via Principal Component Analysis