Data visualization through non linear dimensionality reduction using feature based Ricci flow embedding

Adarsh Prasad Behera

doi:10.1007/s11042-021-11479-7

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Data visualization through non linear dimensionality reduction using feature based Ricci flow embedding

2022-01-03

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Adarsh Prasad Behera *

Jagriti Singh

Shekhar Verma

Manish Kumar

DOI：10.1007/s11042-021-11479-7

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Abstract

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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 2D but lie on an ambient space 3D 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 3D surface triangulation mesh is flattened into 2D 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.

Keywords:

Data visualization

Ambient space

Intrinsic dimension

Dimensionality reduction

Manifold

Ricci flow

Conformal mapping

Mean correlation