Topological comparison of some dimension reduction methods using persistent homology on EEG data

06/02/2023
by   Eddy Kwessi, et al.
0

In this paper, we explore how to use topological tools to compare dimension reduction methods. We first make a brief overview of some of the methods often used dimension reduction such as Isometric Feature Mapping, Laplacian Eigenmaps, Fast Independent Component Analysis, Kernel Ridge Regression, t-distributed Stochastic Neighbor Embedding. We then give a brief overview of some topological notions used in topological data analysis, such as, barcodes, persistent homology, and Wasserstein distance. Theoretically, these methods applied on a data set can be interpreted differently. From EEG data embedded into a manifold of high dimension, we apply these methods and we compare them across persistent homologies of dimension 0, 1, and 2, that is, across connected components, tunnels and holes, shells around voids or cavities. We find that from three dimension clouds of points, it is not clear how distinct from each other the methods are, but Wasserstein and Bottleneck distances, topological tests of hypothesis, and various methods show that the methods qualitatively and significantly differ across homologies.

READ FULL TEXT

page 12

page 13

page 15

research
09/04/2017

Persistent homology for low-complexity models

We show that recent results on randomized dimension reduction schemes th...
research
09/12/2022

On topological data analysis for structural dynamics: an introduction to persistent homology

Topological methods can provide a way of proposing new metrics and metho...
research
10/21/2021

Autonomous Dimension Reduction by Flattening Deformation of Data Manifold under an Intrinsic Deforming Field

A new dimension reduction (DR) method for data sets is proposed by auton...
research
05/31/2022

AVIDA: Alternating method for Visualizing and Integrating Data

High-dimensional multimodal data arises in many scientific fields. The i...
research
06/03/2020

Generalized Penalty for Circular Coordinate Representation

Topological Data Analysis (TDA) provides novel approaches that allow us ...
research
12/16/2020

Event History and Topological Data Analysis

Persistent homology is used to track the appearance and disappearance of...
research
11/08/2019

Persistent Homology as Stopping-Criterion for Natural Neighbor Interpolation

In this study the method of natural neighbours is used to interpolate da...

Please sign up or login with your details

Forgot password? Click here to reset