KEYWORDS: Detection and tracking algorithms, Principal component analysis, Error analysis, 3D image processing, Bismuth, Vector spaces, Data modeling, Object recognition, Data hiding, Associative arrays
Riemannian Manifold Learning (RML) is a global algorithm proposed recently, so it can't preserve the local geometry
property of neighboring data well. An algorithm of multi-structure based on RML is proposed in order to solve the
problem. In the algorithm, all points were projected by PCA firstly so as to the extracted character is irrelevant, then
constructed a neighbor graph. The most important step was that all data points were classified to two parts, for the
k - NN of a base point, it adopted a weight which can preserve local property of the base point and neighboring nods to
get the low-dimensional embedding coordinates. As for the other points, it still used the RML algorithm. Thus the new
algorithm can both preserve the metrics at all scales and keep the geometrical property of local neighbor to the
maximum. Experimental results on synthetic data and MNIST data set demonstrate that the new algorithm can reflect the
intrinsic property better than the other manifold learning algorithms.
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