  In this article, we study curvature-like feature value of data sets in
Euclidean spaces. First, we formulate such curvature functions with desirable
properties under the manifold hypothesis. Then we make a test property for the
validity of the curvature function by the law of large numbers, and check it
for the function we construct by numerical experiments. These experiments also
suggest the conjecture that the mean of the curvature of sample manifolds
coincides with the curvature of the mean manifold. Our construction is based on
the dimension estimation by the principal component analysis and the Gaussian
curvature of hypersurfaces. Our function depends on provisional parameters
$\varepsilon, \delta$, and we suggest dealing with the resulting functions as a
function of these parameters to get some robustness. As an application, we
propose a method to decompose data sets into some parts reflecting local
structure. For this, we embed the data sets into higher dimensional Euclidean
space using curvature values and cluster them in the embedding space. We also
give some computational experiments that support the effectiveness of our
methods.
