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Data visualization through non linear dimensionality reduction using feature based Ricci flow embedding
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Data visualization through non linear dimensionality reduction using feature based Ricci flow embedding
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Journal Article
Data visualization through non linear dimensionality reduction using feature based Ricci flow embedding
2022
Overview
Data visualization in high-dimensional space is a significant problem in machine learning. In many data sets, the data apparently lie on a high dimensional ambient space due to redundant features, while the intrinsic dimension is very low. This work proposes an analytical approach to use Feature Based Ricci Flow Embedding (FBRFE) as a nonlinear dimensionality reduction technique. For visualization purposes, we have considered nonlinear data with an intrinsic dimension of 2
D
but lie on an ambient space 3
D
and reduced the dimensionality accordingly. FBRFE uses conformal mapping that preserves the angle between the points in the higher dimensional manifold. At first, a surface triangulation mesh is formed using all the data points, and then circle packing is done in order to compute the respective angles between the data points. Then, conformal mapping is performed through the surface Ricci flow algorithm. After that, the 3
D
surface triangulation mesh is flattened into 2
D
using a seed face flattening algorithm to reduce the dimensionality of the data. Comparison results show that FBRFE visualizes the data in a lower dimension with a much better mean correlation up to 120.17
%
and less overlapping than the existing conventional algorithms.
Publisher
Springer US,Springer Nature B.V
