  We present a galaxy classification system for 238 (E1-Sdm) CALIFA (Calar Alto
Legacy Integral Field Area) galaxies based on the shapes and amplitudes of
their circular velocity curves (CVCs). We infer the CVCs from the de-projected
surface brightness of the galaxies, after scaling by a constant mass-to-light
ratio based on stellar dynamics - solving axisymmetric Jeans equations via
fitting the second velocity moment $V_{\mathrm{rms}}=\sqrt{V^2+\sigma^2}$ of
the stellar kinematics. We use principal component analysis (PCA) applied to
the CVC shapes to find characteristic features and use a $k$-means classifier
to separate circular curves into classes. This objective classification method
identifies four different classes, which we name slow-rising (SR), flat (FL),
round-peaked (RP) and sharp-peaked (SP) circular curves.
  SR are typical for low-mass, late-type (Sb-Sdm), young, faint, metal-poor and
disc-dominated galaxies. SP are typical for high-mass, early-type (E1-E7), old,
bright, metal-rich and bulge-dominated galaxies. FL and RP appear presented by
galaxies with intermediate mass, age, luminosity, metallicity, bulge-to-disk
ratio and morphologies (E4-S0a, Sa-Sbc). The discrepancy mass factor,
$f_d=1-M_{*}/M_{dyn}$, have the largest value for SR and SP classes ($\sim$ 74
per cent and $\sim$ 71 per cent, respectively) in contrast to the FL and RP
classes (with $\sim$ 59 per cent and $\sim$ 61 per cent, respectively).
Circular curve classification presents an alternative to typical morphological
classification and appears more tightly linked to galaxy evolution.
