2011/01/11 by PAU EROLA, Pau Erola, JAVIER BORGE-HOLTHOEFER +5
Environmental Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Curse of dimensionality #Data set #Ecosystem dynamics and resilience #Matrix (chemical analysis) #Principal component analysis #Projection (relational algebra) #Reliability (semiconductor) #Set (abstract data type) #Singular value #Singular value decomposition #Statistical and numerical algorithms #physics.comp-ph #physics.data-an
paper · pdf · doi:10.1142/s0218127412501593
published as International Journal of Bifurcation and Chaos 22 (2012) 1250159
arxiv created 2011/01/11 · openalex publication_date 2012/07/01 · arxiv updated 2015/03/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Singular Value Decomposition (SVD) is a technique based on linear projection theory, which has been frequently used for data analysis. It constitutes an optimal (in the sense of least squares) decomposition of a matrix in the most relevant directions of the data variance. Usually, this information is used to reduce the dimensionality of the data set in a few principal projection directions, this is called Truncated Singular Value Decomposition (TSVD). In situations where the data is continuously changing, the projection might become obsolete. Since the change rate of data can be fast, it is an interesting question whether the TSVD projection of the initial data is reliable. In the case of complex networks, this scenario is particularly important when considering network growth. Here we study the reliability of the TSVD projection of growing scale-free networks, monitoring its evolution at global and local scales.