Publication result detail

Finding the optimal number of low dimension with locally linear embedding algorithm

YANG, T.; FU, D.; MENG, J; PAN, J; BURGET, R.

Original Title

Finding the optimal number of low dimension with locally linear embedding algorithm

English Title

Finding the optimal number of low dimension with locally linear embedding algorithm

Type

WoS Article

Original Abstract

1) The problem this paper is going to solve is how to determine the optimal number of dimension when using dimensionality reduction methods, and in this paper, we mainly use local linear embedding (LLE) method as example. 2) The solution proposed is on the condition of the parameter k in LLE is set in advance. Firstly, we select the parameter k, and compute the distance matrix of each feature in the source data and in the data after dimensionality reduction. Then, we use the Log-Euclidean metric to compute the divergence of the distance matrix between the features in the original data and in the low-dimensional data. Finally, the optimal low dimension is determined by the minimum Log-Euclidean metric. 3) The performances are verified by a public dataset and a handwritten digit dataset experiments and the results show that the dimension found by the method is better than other dimension number when classifying the dataset.

English abstract

1) The problem this paper is going to solve is how to determine the optimal number of dimension when using dimensionality reduction methods, and in this paper, we mainly use local linear embedding (LLE) method as example. 2) The solution proposed is on the condition of the parameter k in LLE is set in advance. Firstly, we select the parameter k, and compute the distance matrix of each feature in the source data and in the data after dimensionality reduction. Then, we use the Log-Euclidean metric to compute the divergence of the distance matrix between the features in the original data and in the low-dimensional data. Finally, the optimal low dimension is determined by the minimum Log-Euclidean metric. 3) The performances are verified by a public dataset and a handwritten digit dataset experiments and the results show that the dimension found by the method is better than other dimension number when classifying the dataset.

Keywords

Manifold learning; LLE; Log-Euclidean metric; distance matrix

Key words in English

Manifold learning; LLE; Log-Euclidean metric; distance matrix

Authors

YANG, T.; FU, D.; MENG, J; PAN, J; BURGET, R.

RIV year

2022

Released

19.01.2021

Publisher

IOS PRESS

Location

AMSTERDAM

ISBN

1472-7978

Periodical

Journal of Computational Methods in Sciences and Engineering

Volume

20

Number

4

State

United Kingdom of Great Britain and Northern Ireland

Pages from

1163

Pages to

1173

Pages count

11

URL

https://www.researchgate.net/publication/340639579_Finding_the_optimal_number_of_low_dimension_with_locally_linear_embedding_algorithm

BibTex

@article{BUT175739,
  author="YANG, T. and FU, D. and MENG, J and PAN, J and BURGET, R.",
  title="Finding the optimal number of low dimension with locally linear embedding algorithm",
  journal="Journal of Computational Methods in Sciences and Engineering",
  year="2021",
  volume="20",
  number="4",
  pages="1163--1173",
  doi="10.3233/JCM-204198",
  issn="1472-7978",
  url="https://www.researchgate.net/publication/340639579_Finding_the_optimal_number_of_low_dimension_with_locally_linear_embedding_algorithm"
}