TY - JOUR
T1 - On the Comparisons of Decorrelation Approaches for Non-Gaussian Neutral Vector Variables
AU - Ma, Zhanyu
AU - Lu, Xiaoou
AU - Xie, Jiyang
AU - Yang, Zhen
AU - Xue, Jing-Hao
AU - Tan, Zheng-Hua
AU - Xiao, Bo
AU - Guo, Jun
PY - 2023/4
Y1 - 2023/4
N2 - As a typical non-Gaussian vector variable, a neutral vector variable contains nonnegative elements only, and its l1 -norm equals one. In addition, its neutral properties make it significantly different from the commonly studied vector variables (e.g., the Gaussian vector variables). Due to the aforementioned properties, the conventionally applied linear transformation approaches [e.g., principal component analysis (PCA) and independent component analysis (ICA)] are not suitable for neutral vector variables, as PCA cannot transform a neutral vector variable, which is highly negatively correlated, into a set of mutually independent scalar variables and ICA cannot preserve the bounded property after transformation. In recent work, we proposed an efficient nonlinear transformation approach, i.e., the parallel nonlinear transformation (PNT), for decorrelating neutral vector variables. In this article, we extensively compare PNT with PCA and ICA through both theoretical analysis and experimental evaluations. The results of our investigations demonstrate the superiority of PNT for decorrelating the neutral vector variables.
AB - As a typical non-Gaussian vector variable, a neutral vector variable contains nonnegative elements only, and its l1 -norm equals one. In addition, its neutral properties make it significantly different from the commonly studied vector variables (e.g., the Gaussian vector variables). Due to the aforementioned properties, the conventionally applied linear transformation approaches [e.g., principal component analysis (PCA) and independent component analysis (ICA)] are not suitable for neutral vector variables, as PCA cannot transform a neutral vector variable, which is highly negatively correlated, into a set of mutually independent scalar variables and ICA cannot preserve the bounded property after transformation. In recent work, we proposed an efficient nonlinear transformation approach, i.e., the parallel nonlinear transformation (PNT), for decorrelating neutral vector variables. In this article, we extensively compare PNT with PCA and ICA through both theoretical analysis and experimental evaluations. The results of our investigations demonstrate the superiority of PNT for decorrelating the neutral vector variables.
KW - Decorrelation
KW - neutral vector variable
KW - neutrality
KW - non-Gaussian
KW - nonlinear transformation
UR - http://www.scopus.com/inward/record.url?scp=85152165194&partnerID=8YFLogxK
U2 - 10.1109/TNNLS.2020.2978858
DO - 10.1109/TNNLS.2020.2978858
M3 - Journal article
SN - 2162-237X
VL - 34
SP - 1823
EP - 1837
JO - I E E E Transactions on Neural Networks and Learning Systems
JF - I E E E Transactions on Neural Networks and Learning Systems
IS - 4
ER -