TY - JOUR
T1 - Reliability of optimal linear projection of growing scale-free networks
AU - Erola, Pau
AU - Borge-Holthoefer, Javier
AU - Gomez, Sergio
AU - Arenas, Alex
PY - 2012/1/1
Y1 - 2012/1/1
N2 - 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.
AB - 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.
KW - evolving graph
KW - stability
KW - Truncated singular value decomposition
UR - http://www.scopus.com/inward/record.url?scp=84864801095&partnerID=8YFLogxK
U2 - 10.1142/S0218127412501593
DO - 10.1142/S0218127412501593
M3 - Article (Academic Journal)
AN - SCOPUS:84864801095
SN - 0218-1274
VL - 22
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
IS - 7
M1 - 1250159
ER -