  The discovering of low-dimensional manifolds in high-dimensional data is one
of the main goals in manifold learning. We propose a new approach to identify
the effective dimension (intrinsic dimension) of low-dimensional manifolds. The
scale space viewpoint is the key to our approach enabling us to meet the
challenge of noisy data. Our approach finds the effective dimensionality of the
data over all scale without any prior knowledge. It has better performance
compared with other methods especially in the presence of relatively large
noise and is computationally efficient.
