TY - JOUR
T1 - An Entropy Weighted Nonnegative Matrix Factorization Algorithm for Feature Representation
AU - Wei, Jiao
AU - Tong, Can
AU - Wu, Bingxue
AU - He, Qiang
AU - Qi, Shouliang
AU - Yao, Yudong
AU - Teng, Yueyang
N1 - Publisher Copyright:
© 2012 IEEE.
PY - 2023/9/1
Y1 - 2023/9/1
N2 - Nonnegative matrix factorization (NMF) has been widely used to learn low-dimensional representations of data. However, NMF pays the same attention to all attributes of a data point, which inevitably leads to inaccurate representations. For example, in a human-face dataset, if an image contains a hat on a head, the hat should be removed or the importance of its corresponding attributes should be decreased during matrix factorization. This article proposes a new type of NMF called entropy weighted NMF (EWNMF), which uses an optimizable weight for each attribute of each data point to emphasize their importance. This process is achieved by adding an entropy regularizer to the cost function and then using the Lagrange multiplier method to solve the problem. Experimental results with several datasets demonstrate the feasibility and effectiveness of the proposed method. The code developed in this study is available at https://github.com/Poisson-EM/Entropy-weighted-NMF.
AB - Nonnegative matrix factorization (NMF) has been widely used to learn low-dimensional representations of data. However, NMF pays the same attention to all attributes of a data point, which inevitably leads to inaccurate representations. For example, in a human-face dataset, if an image contains a hat on a head, the hat should be removed or the importance of its corresponding attributes should be decreased during matrix factorization. This article proposes a new type of NMF called entropy weighted NMF (EWNMF), which uses an optimizable weight for each attribute of each data point to emphasize their importance. This process is achieved by adding an entropy regularizer to the cost function and then using the Lagrange multiplier method to solve the problem. Experimental results with several datasets demonstrate the feasibility and effectiveness of the proposed method. The code developed in this study is available at https://github.com/Poisson-EM/Entropy-weighted-NMF.
KW - Clustering
KW - entropy regularizer
KW - low-dimensional representation
KW - nonnegative matrix factorization (NMF)
UR - http://www.scopus.com/inward/record.url?scp=85133788480&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85133788480&partnerID=8YFLogxK
U2 - 10.1109/TNNLS.2022.3184286
DO - 10.1109/TNNLS.2022.3184286
M3 - Article
C2 - 35767485
AN - SCOPUS:85133788480
SN - 2162-237X
VL - 34
SP - 5381
EP - 5391
JO - IEEE Transactions on Neural Networks and Learning Systems
JF - IEEE Transactions on Neural Networks and Learning Systems
IS - 9
ER -