-
- Saito Naoki
- カリフォルニア大学デイヴィス校数学科
Bibliographic Information
- Other Title
-
- グラフ・ネットワーク上での応用調和解析
- グラフ ・ ネットワーク ジョウ デ ノ オウヨウ チョウワ カイセキ
Search this article
Description
In recent years, the advent of new sensor technologies and social network infrastructure has provided huge opportunities and challenges for analyzing data recorded on such networks. For analyzing data recorded on regular lattices, computational harmonic analysis tools such as the Fourier and wavelet transforms have well-developed theories and proven track records of success. It is therefore quite important to extend such tools from the classical setting of regular lattices to the more general setting of graphs and networks. In this article, we first review basics of Laplacian matrices of a graph whose eigenpairs are often interpreted as the frequencies and the Fourier basis vectors on a given graph. We point out, however, that such an interpretation is misleading unless the underlying graph is unweighted path or cycle. We then discuss our recent effort of constructing multiscale basis dictionaries on a graph including the Hierarchical Graph Laplacian Eigenbasis Dictionary and the Generalized Haar-Walsh Wavelet Packet Dictionary, which are viewed as the generalization of the classical hierarchical block DCTs and the Haar-Walsh wavelet packets for the graph setting.
Journal
-
- Bulletin of the Japan Society for Industrial and Applied Mathematics
-
Bulletin of the Japan Society for Industrial and Applied Mathematics 25 (3), 102-111, 2015
The Japan Society for Industrial and Applied Mathematics
- Tweet
Details 詳細情報について
-
- CRID
- 1390282680741798144
-
- NII Article ID
- 110009989106
-
- NII Book ID
- AN10288886
-
- ISSN
- 09172270
- 24321982
-
- NDL BIB ID
- 026791568
-
- Text Lang
- ja
-
- Data Source
-
- JaLC
- NDL
- CiNii Articles
-
- Abstract License Flag
- Disallowed