TY - JOUR
T1 - Row-Sparse Principal Component Analysis via Coordinate Descent Method
AU - Nie, Feiping
AU - Chen, Qiang
AU - Yu, Weizhong
AU - Li, Xuelong
N1 - Publisher Copyright:
© 1989-2012 IEEE.
PY - 2024/7/1
Y1 - 2024/7/1
N2 - In this paper, we propose a novel algorithm to solve the row-sparse principal component analysis problem without relying on any data structure assumption. Sparse principal component analysis was proposed to improve the interpretability of principal component analysis by restricting the number of non-zero elements in each loading vector, but the varying sparsity patterns among different leading vectors may result in trouble on some occasions, such as feature selection. Then row-sparse principal component analysis was proposed, which demands the same sparse pattern among different loading vectors. However, the optimization of row-sparse principal component analysis problems is NP-hard. Although some algorithms were proposed to solve this problem, but they are only applicable to the specific data structure. In this paper, we transform the original row-sparse principal component analysis problem into a new equivalent problem that can be solved by coordinate descent method without relying on any data structure assumption. Then by carefully eliminating redundant structures to avoid repeating computation, we propose a more efficient coordinate descent method to solve this problem. Furthermore, no parameter needs to be tuned in our algorithm. Finally, extensive experiments are conducted on the real world data sets to demonstrate the superiority of our algorithm.
AB - In this paper, we propose a novel algorithm to solve the row-sparse principal component analysis problem without relying on any data structure assumption. Sparse principal component analysis was proposed to improve the interpretability of principal component analysis by restricting the number of non-zero elements in each loading vector, but the varying sparsity patterns among different leading vectors may result in trouble on some occasions, such as feature selection. Then row-sparse principal component analysis was proposed, which demands the same sparse pattern among different loading vectors. However, the optimization of row-sparse principal component analysis problems is NP-hard. Although some algorithms were proposed to solve this problem, but they are only applicable to the specific data structure. In this paper, we transform the original row-sparse principal component analysis problem into a new equivalent problem that can be solved by coordinate descent method without relying on any data structure assumption. Then by carefully eliminating redundant structures to avoid repeating computation, we propose a more efficient coordinate descent method to solve this problem. Furthermore, no parameter needs to be tuned in our algorithm. Finally, extensive experiments are conducted on the real world data sets to demonstrate the superiority of our algorithm.
KW - coordinate descent
KW - feature selection
KW - principal component analysis
KW - Row-sparse
UR - http://www.scopus.com/inward/record.url?scp=85182931337&partnerID=8YFLogxK
U2 - 10.1109/TKDE.2024.3351851
DO - 10.1109/TKDE.2024.3351851
M3 - 文章
AN - SCOPUS:85182931337
SN - 1041-4347
VL - 36
SP - 3460
EP - 3471
JO - IEEE Transactions on Knowledge and Data Engineering
JF - IEEE Transactions on Knowledge and Data Engineering
IS - 7
ER -