Figure 31 - available via license: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Content may be subject to copyright.
Geodesic estimation using the heat method applied to G ⋆ yields results close to the true geodesics (top). Other kernels yield suboptimal results for most choices of k (bottom); in particular, notice how the tip of the tail is usually inferred to be closer than it should (due to its being directly connected to the body in the underlying graph, cf. Fig. 24). Yellow points are closer to the source (marked with an arrow in the ground truth plot).
Source publication
Invoking the manifold assumption in machine learning requires knowledge of the manifold's geometry and dimension, and theory dictates how many samples are required. However, in applications data are limited, sampling may not be uniform, and manifold properties are unknown and (possibly) non-pure; this implies that neighborhoods must adapt to the lo...
Context in source publication
Context 1
... Fig. 31, we compare the results using weighted graphs from various kernels on the stingray dataset; interestingly, heat geodesics computed from G ⋆ hold reasonably well even when facing a continuous change in dimensionality. : Geodesic estimation using the heat method applied to G ⋆ yields results close to the true geodesics (top). Other ...
Similar publications
Manifold learning, which has emerged in recent years, plays an increasingly important role in machine learning. However, because inevitable noises and outliers destroy the manifold structure of data, the dimensionality reduction effect of manifold learning will be reduced. Therefore, this paper proposes a denoising algorithm for high-dimensional da...
