  In graph motivated learning, label propagation largely depends on data
affinity represented as edges between connected data points. The affinity
assignment implicitly assumes even distribution of data on the manifold. This
assumption may not hold and may lead to inaccurate metric assignment due to
drift towards high-density regions. The drift affected heat kernel based
affinity with a globally fixed Parzen window either discards genuine neighbors
or forces distant data points to become a member of the neighborhood. This
yields a biased affinity matrix. In this paper, the bias due to uneven data
sampling on the Riemannian manifold is catered to by a variable Parzen window
determined as a function of neighborhood size, ambient dimension, flatness
range, etc. Additionally, affinity adjustment is used which offsets the effect
of uneven sampling responsible for the bias. An affinity metric which takes
into consideration the irregular sampling effect to yield accurate label
propagation is proposed. Extensive experiments on synthetic and real-world data
sets confirm that the proposed method increases the classification accuracy
significantly and outperforms existing Parzen window estimators in graph
Laplacian manifold regularization methods.
